DECISION STRATEGY TO MINIMIZE REPLENISHMENT COSTS IN A
DISTRIBUTION CENTER WITH FORWARD-RESERVE STORAGE
A thesis presented to
the faculty of the
Fritz J. and Dolores H. Russ
College of Engineering and Technology
of
Ohio University
In partial fulfillment
of the requirement for the degree
Master of Science
by
Bradley K. Hollingsworth
June 2003
This thesis entitled
DECISION STRATEGY TO MINIMIZE REPLENISHMENT COSTS IN A
DISTRIBUTION CENTER WITH FORWARD-RESERVE STORAGE
by
Bradley K. Hollingsworth
has been approved
for the Department of Industrial and Manufacturing Systems Engineering
and the Russ College of Engineering and Technology
Dale T. Masel
Assistant Professor
R. Dennis Irwin
Dean, Fritz J. and Dolores H. Russ
College of Engineering and Technology
Hollingsworth, Bradley K. M.S. June 2003. Industrial and Manufacturing Systems
Engineering
Decision Strategy to Minimize Replenishment Costs in a Distribution Center with
Forward Reserve Storage (82 pp.)
Director of Thesis: Dale T. Masel
Order picking costs typically account for 50% of the operating costs in
distribution center (DC) operations. Many DCs use a forward-reserve storage strategy to
minimize these costs. This research is focused on minimizing replenishment costs while
maintaining pick savings through a dock-to-forward (DTF) technique, which bypasses
reserve storage to reduce additional handling.
Four decision strategies for allocating SKUs to discretionary pick faces to utilize
the DTF technique were developed and tested under typical distribution center
conditions. Two additional strategies were tested: one strategy that used DTF only to
meet that day’s demand and one strategy that did not use the DTF technique.
The method used to allocate SKUs to the forward pick area has a clear impact on
the replenishment costs. The best-performing DTF strategy reduced replenishment trips
by as much as 9% over a random strategy and by 24% over a system with no DTF.
Approved: Dale T. Masel
Assistant Professor of Industrial and Manufacturing Systems Engineering
ACKNOWLEDGMENTS
Thank you to my fiancée, April Pedone, and to my parents, Rod and Linda
Hollingsworth, for their love and their continuous support of my endeavors. Thank you
to Dr. Masel for all of the guidance and support. Also, thank you to the Russ College of
Engineering and Technology for the Stocker Fellowship, which provided the funding for
this research.
5
TABLE OF CONTENTS
1 Introduction...................................................................................................................... 8
1.1
Background ......................................................................................................... 8
1.2
Dock-to-forward (DTF) .................................................................................... 10
1.3
Objective ........................................................................................................... 12
2 Literature Review...................................................................................................... 14
2.1
Overview of Warehouse Operations................................................................. 14
2.1.1
Storage Assignment Policies..................................................................... 15
2.1.2
Operating Strategy .................................................................................... 17
2.1.3
Routing...................................................................................................... 19
2.2
Cross Docking................................................................................................... 20
2.3
Forward-Reserve Problem ................................................................................ 21
2.4
Duration of Stay................................................................................................ 28
3 Methodology ............................................................................................................. 30
3.1
Situation ............................................................................................................ 30
3.1.1
Replenishment........................................................................................... 30
3.1.2
Assumptions.............................................................................................. 31
3.2
Objective Function............................................................................................ 34
3.3
Inventory versus Demand ................................................................................. 38
3.4
Decision Strategies............................................................................................ 40
3.4.1
Random ..................................................................................................... 40
3.4.2
Demand-Based.......................................................................................... 40
3.4.3
Inventory-to-demand Ratio....................................................................... 41
3.4.4
Future Inventory-to-demand Ratio ........................................................... 42
4
Results....................................................................................................................... 43
4.1
Implementation ................................................................................................. 43
4.1.1
Excel Worksheets...................................................................................... 43
4.1.2
Macro ........................................................................................................ 44
4.2
Trial Experiment ............................................................................................... 46
4.3
Experiment........................................................................................................ 47
4.3.1
Experiment Setup...................................................................................... 47
4.3.2
Experiment Results ................................................................................... 49
4.3.3
Experiment Analysis................................................................................. 50
4.4
Differences in Ratio-Based Decision Strategies ............................................... 54
4.5
Comparison with other DC Strategies .............................................................. 56
5 Conclusions............................................................................................................... 59
5.1
Review of Results ............................................................................................. 59
5.2
Application........................................................................................................ 60
5.3
Future Work ...................................................................................................... 61
Bibliography ..................................................................................................................... 63
Appendix A: Visual Basic Macro Code............................................................................ 65
Appendix B: DC Demand and Receiving Data ................................................................ 73
6
LIST OF TABLES
Table 4-1: Trial Average Number of DTF Trips .............................................................. 47
Table 4-2: Demand Distribution ....................................................................................... 48
Table 4-3: Demand Classes for Experiment ..................................................................... 48
Table 4-4: Observed Average Number of DTF Trips per day.......................................... 49
Table 4-5: Paired T-Test Results ...................................................................................... 52
Table 4-6: Paired T-Test p Values .................................................................................... 52
Table 4-7: Average Number of Total Trips per Day ........................................................ 54
Table 4-8: Baseline Comparison of the Average Total Number of Trips per day............ 57
7
LIST OF FIGURES
Figure 3-1: Relationships for Objective Function ............................................................ 38
Figure 4-1: Average Number of DTF Trips...................................................................... 50
Figure 4-2: Average DTF Trips Versus Discretionary Pick Faces ................................... 53
Figure 4-3: Total Trips versus Average Number of DTF Trips........................................ 54
8
1 INTRODUCTION
Professionals worldwide have recognized order picking as the most costly activity
in warehousing and distribution center operations. It is believed that more than 50% of
the operating costs of a typical distribution center (DC) are associated with order picking
[18].
These costs are a result of the labor activities required such as traveling from the
input/output (I/O) point to the appropriate pick face, locating the correct stock keeping
unit (SKU), picking the SKUs from the pick face, and transporting the SKUs to the next
destination for sorting or shipping.
Since the laborious activities of order picking are a function of time, they also
place constraints on the throughput of the DC. In order to reduce operating costs and
increase throughput capability, many DC’s utilize a forward-reserve storage strategy.
Operating expense is one of three variables that affect the bottom line according
to Goldratt and Cox [6]. The three measurements used in lean manufacturing to evaluate
a business are operating expense, inventory expense, and throughput of sales. These
three measurements of the system determine the bottom line, profit [6]. By reducing
operating expense without changing inventory expense or throughput of sales, the profit
of an operation increases. This shows a direct relationship between the operating costs in
DC operations with the profit of the business it supports.
1.1
Background
The forward-reserve storage strategy separates a DC into two areas: the forward
pick area and the reserve storage area [4]. The forward pick area typically consists of a
9
small quantity of each of the most popular SKUs (or all SKUs in many cases) in the
facility. By limiting the quantity of each SKU in this area, the space required for storage
in the area is reduced significantly. This space reduction in the forward pick area creates
less travel between picks which reduces the order picking costs in this area while at the
same time increasing throughput.
The bulk of the inventory is stored in a reserve storage area. The reserve storage
area offers dense storage (i.e. a large quantity of items per cubic foot) that is less
accessible for order picking. While order picking for the least popular items may occur
here in some cases, this area is mainly used for the replenishment of the forward pick
area.
There exists an inverse relationship between the storage capacity of the forward
pick area and the number of replenishments [4]. As the size of the forward pick area
increases, the picking costs increase and the replenishment costs decrease or vice-versa.
This creates the situation known as the forward-reserve problem (FRP), determining the
optimum size of the forward pick area in order to reduce the total operating costs [4].
Two decisions affect the size of the forward pick area: (1) the decision of which SKUs to
assign to this area and (2) the decision of the quantity of these SKUs to allocate to this
area [4].
There are five primary operations in a warehouse and DC operation: receiving and
put away, picking, sorting, packaging, and shipping [18]. Replenishment in itself is
simply an extra put away and picking operation. In the forward-reserve storage strategy,
SKUs are put away in reserve storage upon receipt and are later picked and put away in
10
the forward pick area. While replenishment is an essential part of this forward-reserve
storage strategy, it is clearly additional handling and an additional operating expense.
A simple example of a forward reserve storage policy is seen in a typical grocery
store. The forward pick area is the part of the store open to the customers and all order
picking is done in this area (typically customers do not walk into the stock room to find
an item). Stock personnel replenish the forward pick area from the stock room, which is
the reserve storage area. The pick faces are the spaces on the shelves and the capacity of
the forward area is the total shelf space. Since all items are picked from the forward pick
area (store shelves), the assignment decision of the FRP is unnecessary. However, the
allocation decision in the FRP is not trivial.
1.2
Dock-to-forward (DTF)
The “dock-to-forward” (DTF) technique is a strategy used in industry to reduce
the additional handling due to replenishment. In this strategy, the warehouse or DC
identifies relationships between scheduled receipts and empty pick faces. Replenishment
occurs directly from the receiving dock to the forward pick area for any SKU that is both
received and either in need of replenishment on the same day or assigned to a
discretionary pick face that day.
This DTF operation bypasses the reserve storage
eliminating, the additional put away and picking operations by reducing the total number
of replenishments from the reserve storage.
One of the major principles of cross docking is to have a known customer prior to
receipt of a shipment of a SKU and opportunistic cross docking is that strategy occurring
11
in a warehouse or DC [7]. By identifying the receipt of a SKU as well as the demand for
that SKU in a warehouse or DC, the DTF technique utilizes the principles of cross
docking. In this case, the receipt is known based on a receiving schedule and the
customer is the empty pick face in the forward pick area that needs to be replenished.
While the DTF technique does reduce the total number of replenishments, it does
not eliminate replenishment altogether. The DTF technique allows for replenishment of
the empty pick faces in the forward pick area via direct put away from the receiving
dock. Once the empty pick faces in the forward pick area are full, the remaining SKUs
on the receiving dock must be put away in reserve storage. The forward pick area is
home to only a portion of the total storage capacity of the warehouse or DC, thus put
aways into the reserve storage area cannot be eliminated.
The DTF technique is not practical for DC’s that utilize First In, First Out (FIFO)
rules for managing inventory. Since the DTF technique bypasses reserve storage, a load
of a SKU is allowed to be moved into the forward pick area before a load of the same
SKU waiting in reserve. The load that was moved directly from the dock to the forward
pick area would be picked before the load waiting in reserve violating the FIFO rules.
The keys to utilizing this strategy are to identify potential DTF situations and to
make good decisions that create more opportunities to utilize this technique.
Identification of potential situations requires the coordination of the receiving schedule
and the replenishment orders within the Warehouse Management System (WMS).
12
1.3
Objective
The objective of this research is to develop a method of identifying DTF
candidates and allocating the best candidates to the forward pick area in order to reduce
replenishment costs. This identification and allocation is based on the ratio of a SKU’s
forward pick inventory to its demand (assuming it is on the dock and empty pick faces
are available).
The inventory-to-demand ratio is the number of days of inventory in the forward
pick area for a particular SKU. The smaller the ratio, the sooner the inventory in the
forward pick area will be depleted for a SKU (i.e. the faster this inventory will turn over).
Assigning SKUs to empty pick faces for DTF based on the smallest ratio fills these pick
faces with SKUs that will turn over the fastest. Since these SKUs will turn over the
fastest, the pick faces will become empty quicker and thus be available for a new DTF
sooner. The more frequently the empty pick faces are available, the more frequently DTF
can be performed, and the more the total number of replenishments can be reduced.
When a SKU is on the receiving schedule and needs to be replenished it is sent
from the dock to the forward pick area. After being replenished, the decision of whether
or not to move additional loads of a SKU into the forward pick area from the receiving
dock depends on the number empty pick faces and the ratio of the SKU’s forward pick
inventory and its demand. Since the storage capacity of the forward pick area is only a
small portion of the total storage capacity, the decision of which SKUs are good
candidates for additional DTF is not trivial.
13
The evaluation of this identification and allocation decision strategy is based on a
comparison of the replenishment costs between four decision strategies using the same
receiving schedule and demand. These four decision strategies use the DTF technique to
perform any possible replenishment and then assign DTF trips for discretionary pick
faces. These four decision strategies will also be compared, in terms of replenishment
costs, with two other strategies that represent other typical DC operations.
14
2
2.1
LITERATURE REVIEW
Overview of Warehouse Operations
The main operations that occur within a warehouse or DC include receiving, put
away, order picking, packaging, sorting, unitizing, and shipping [3]. The receiving
operation is simply unloading supplier shipments in the facility, which may include
organizing these SKUs and verifying the receipt. The put away operation is transporting
the SKUs to their storage location and placing them in that location.
Order picking is the retrieval of SKUs to fill a customer order, the prime function
of the facility [18]. Since order picking is considered to be the single largest operating
cost in distribution, many facilities are designed entirely around this operation [3]. For
example, an automated storage and retrieval system (AS/RS) may provide efficient order
picking of small parts [9]. On the other hand, pallet flow racks provide efficient order
picking of pallets with a high demand [3]. Since both the AS/RS and the pallet flow
racks require expensive and permanent structures, it is imperative that the facility designs
accommodate them in order to minimize the order picking costs.
The travel time required to retrieve SKUs is generally a large portion of the order
picking expenses, thus much effort is placed on reducing the amount of travel. The many
operating strategies for order picking include single order picking, batch picking, and
wave picking. Some storage systems, such as a carousel, bring the part to the picker
while others require pickers to travel to the part for retrieval [3]. In a facility with a
forward-reserve storage policy, order picking will also include replenishing the forward
pick area from the reserve storage [18].
15
The amount of travel required in order picking is affected by decisions such as the
storage assignment policy, the operating strategy, and the routing of the picker. The
storage assignment policy determines the location of the SKUs and thus the distance
traveled to and from the I/O point [5]. The operating strategy determines the number of
orders and the types of items that the picker retrieves. Routing determines the path of the
order picker as well as the sequence of items to retrieve and also affects the travel
distance.
Packaging is an operation that may occur after picking in order to make the SKUs
easier to handle. The packaging operation is especially important for SKUs of small size
since it allows many to be handled at one time. The warehouse or DC sorts SKUs by
customer once picking and packaging (if applicable) are complete. Unitizing is an
operation that may occur after sorting, which involves putting SKUs into containers for
shipping. Shipping is the transportation of an order to the customer [3].
2.1.1
Storage Assignment Policies
Goetschalckx and Ratliff [5] define a storage assignment policy as “a set of rules
which determines where the unit loads of the different products will be located in a
warehouse,” and state that two major policies exist, dedicated and shared.
Sadiq,
Landers, and Taylor [15] define dedicated storage assignment as a policy in which each
location is assigned to a specific SKU. Goetschalckx and Ratliff [5] discuss the second
major storage assignment policy, shared storage.
16
Sadiq, et al. [15] identify two methods of location assignment in dedicated
storage: class-based and turnover-based assignment. In class-based assignment, SKUs
are assigned a group (class) based on their Cube Per Order (CPO) index. An example of
turnover-based assignment is Heskett’s [10] use of the CPO index, which is a ratio of
storage space to demand for a SKU. Heskett assigns SKUs with the largest CPO index to
the nearest location to the I/O point and so forth. By positioning the majority of the picks
close to the I/O point, Heskett minimizes the travel required for order picking. Heskett’s
CPO index is proven to minimize this travel for a stable and constant demand [10].
In shared storage assignment, different SKUs are permitted to be stored in the
same location successively [5]. This means that if all pallets, cases, or items of a SKU
are picked from a location so the location is empty, any SKU can be granted permission
for assignment in this location. Once a location is empty, it is available for reassignment.
This differs from dedicated storage assignment because the location assignments in the
dedicated storage assignment policy exist for the duration of the planning period. Classbased storage includes an example of a shared storage assignment policy [5]. Groups of
SKUs can be formed based on a factor like CPO index or demand. The SKUs are then
randomly assigned a location within their respective groups like that in a shared storage
assignment policy.
The DTF allocation strategy requires a shared storage assignment policy in order
to reduce the number of replenishments. This assignment policy permits successive
storage of different SKUs in the same storage location. A SKU is assigned to an empty
17
pick face and moved directly from the receiving dock to this location, bypassing the
reserve storage and eliminating additional handling from replenishment.
2.1.2
Operating Strategy
The operating strategy of a warehouse or DC depends on the order-picking policy.
Petersen [20] identifies and defines five different order-picking policies: strict-order,
batch, sequential zone, batch zone, and wave picking. With the strict order policy an
individual employee travels from the I/O point, picks all lines of a single order, and then
returns to the I/O point before picking the next order. While this policy does maintain
order integrity, it may require the picker to travel long distances. In batch picking, an
individual employee picks all lines for more than one order before returning to the I/O
point. Although the order integrity is not maintained, the travel efficiency is much better
than that of strict-order policy.
In zone picking, all employees are assigned to zones (areas) within the
warehouse or DC in order to reduce travel distances. For sequential zone picking, all line
items for an order within a particular zone are picked and then those items travel to the
remaining zone(s) until the order is complete. While order integrity is maintained and
sorting is eliminated, order pickers may be blocked or starved, similar to stations in a
transfer assembly line. Orders are batched together in batch zone picking and employees
pick the items in their zone with all items sorted downstream. Order integrity is lost with
this policy but employees pick more of each SKU making trips more efficient.
18
The fifth policy, wave picking, is an adaptation of batch zone picking that
increases the number of each SKU picked per trip further increasing efficiency. The
difference in wave picking is that the batches are based on duration rather than quantity.
Selection of an order picking policy is based primarily on two performance measures:
total picking time and utilization of pickers [13].
Hinojosa [11] discusses order-picking operations for distribution centers that
require minimal capital investments. In order to evaluate these options, Hinojosa [11]
defines a typical DC’s demand distribution as well as the basic operations such as the
number and length of shifts. In this typical DC, 5% of SKUs account for 50% of the
DC’s total orders. Also, 20% of the SKUs make up 80% of the total orders showing the
demand distribution follows Pareto’s 80/20 rule.
Hinojosa [11] compares several piece-picking operations to a baseline operation
in which an order picker travels the entire picking loop to complete a single order. There
are three distinct elements of the order picking operation: travel, transaction (retrieval),
and setup.
The average time for each of these elements is used to calculate the
productivity of an order picker as well as the labor required for each order picking option.
In this work Hinojosa [11] shows that a wide variety of technologies, or lack
thereof, may be used to implement the operating strategy of a DC. The exploration of the
entire range of order picking technologies with the different types of operating strategies
will provide a DC operating options with a low capital cost.
19
2.1.3
Routing
Routing is simply the path selection for the order picker and is generally
performed by the WMS.
Petersen [21] defines and discusses six possible routing
strategies to determine the order-picking path. The first strategy, traversal, is a path
similar to that of a customer in a grocery store in which the order picker starts on one end
of an aisle and finishes on the opposite end for all aisles. In the return strategy, the picker
travels up one side of the aisle and back down the other for each aisle with required
items.
In the midpoint strategy, a picker only travels as far as the middle of the aisle
before returning to the side of the aisle entered. Later the picker accesses the aisle from
the other end to retrieve items on the half of the aisle. Similar to the midpoint strategy,
the picker in the largest gap strategy travels to a point in the aisle and then returns to the
side of the aisle originally entered. The difference is that the turn-around point is the pick
with the largest gap to the next pick. The composite strategy is a hybrid of the traversal
and return routing strategies. In this hybrid the strategy, traversal or return, with the
shortest distance to the next pick is chosen. Petersen [21] also presented an optimal
routing developed by Ratliff and Rosenthal as a possible strategy in which a heuristic
develops the order-picking route.
Petersen [21] tested all six routing strategies in a random storage environment. In
this case the optimal strategy provides the shortest route. However, the optimal strategy
is not prevalent in industry because there is no repeating pattern for routes and many
times it requires backtracking. Since the optimal strategy is not necessarily practical,
20
Petersen [21] presents a guideline for the random storage assignment based on the size of
the pick list: composite and traversal strategies are better for larger pick lists while largest
gap and midpoint result in shorter routes for smaller pick lists.
2.2
Cross Docking
According to Gue [7], cross docking is a logistics technique in which a warehouse
or distribution center does not store items or pick orders. Instead items are sorted and
consolidated into orders upon receipt. The items are then shipped to customers within a
matter of hours [8]. This eliminates both the operating costs of order picking and the
inventory costs of storing SKUs.
The basic principle of cross docking is the identification of the customer before
receipt of a SKU. General characteristics of cross-docked SKUs are a high demand with
low variance (of demand) and volumes large enough to make frequent shipments
economically feasible [8]. Opportunistic cross docking, one type of cross docking, is the
transfer of an item from the receiving dock to the shipping dock to fill an order in a
warehouse or DC. Not all SKUs received in a warehouse or DC satisfy the variance and
volume requirements of cross docking, thus the selection of SKUs to cross dock is not
trivial. Similarly the forward-reserve problem exists because the allocation of SKUs to
the forward pick area is not a trivial decision either.
In the DTF strategy, the customer identified upon receipt of a SKU is an empty
pick face in the forward pick area of the warehouse or DC. This does not constitute a
cross dock operation because the SKU does not move directly to the shipping dock from
21
the receiving dock to fill an order. However, this does exemplify the main principle of
cross docking, which is identifying a customer upon receipt. In this strategy, the pseudocustomer is an empty pick face in the forward pick area.
2.3
Forward-Reserve Problem
Frazelle, Hackman, Passy, and Platzman [4] develop a model to determine the
size of the forward area and the resulting picking costs. This model initially solves the
assignment–allocation problem, determining the items to be stored in the forward area as
well as the quantity of each item. Frazelle, et al. [4] rank each item based on a ratio they
term the Economic Assignment Quotient (EAQ), the relationship between an item’s
demand and its cubic size. The authors use an algorithm to rank all items and make
assignments and allocations to the forward area.
Frazelle, et al. [4] consider the problem with no existing facility or constraints on
the size of the forward area. By solving the assignment–allocation problem, the items to
be located in the forward area and the quantity of each are now known. This determines
the necessary storage capacity of the forward reserve area and thus determines its size
while minimizing the picking costs.
While Frazelle, et al. [4] attempt to minimize the total order picking and
replenishment costs through the assignment-allocation problem, their method does not
reflect standard industry practice. Their ranking and assignment method does not require
that all order picking occur in the forward area. However, for many distribution centers
22
such as Dollar General [15], picking is not done in the reserve area. This eliminates the
assignment decision from consideration.
Frazelle, et al. also [4] make the assumption that demand is stable and that the
assignment-allocation to the forward pick area is static (i.e. it is only done during the
design or redesign of the distribution center).
This is also not the case for many
distribution centers of products with short life cycles or with products of high seasonal
fluctuation of demand [2]. The DTF strategy assumes that empty pick faces are available
for an increase or decrease in demand (compared to inventory).
Van den Berg, Sharp, Gademann, and Pochet [19] evaluate the FRP with a known
capacity for the forward pick area and reserve storage area. The authors consider an
order picking system with both busy and idle periods. In this system there exists a direct
relationship between minimizing the order picking cost in the forward area and
minimizing that of the reserve storage area during the busy period. Since order picking is
required during the busy (picking) period, the authors turn their focus to minimizing
replenishment costs during this time. Previous work does not consider the fact that
replenishment may occur in a unit load that is less than the quantity required to fill the
allocated space in the forward pick area storage for the particular SKU. The authors also
consider replenishment prior to picking as well as simultaneous with picking.
Replenishment resources may be limited during picking and may also cause congestion
during picking.
Van den Berg, et al. [19] also develop a model to minimize the amount of labor
required during the picking period, thus reducing the operating costs during this period
23
and increasing the throughput of the order picking system. Their binary programming
model of the FRP assigns SKUs to the forward pick area, considering the unit loads, to
minimize the replenishment labor during picking.
The authors’ greedy knapsack
heuristic is capable of finding a feasible solution to the binary programming model. The
authors also develop a binary programming model to consider a constraint on capacity
(replenishment resources) during the picking period. A feasible solution is found on this
binary programming model using a Relaxation Improvement Heuristic.
The research of Van den Berg, et al. [19] does not encompass research of the DTF
strategy for many reasons. The authors clearly state that they do not see any advantages
to storing more than one unit-load of a SKU in the forward pick area. Their model
minimizes the number of replenishments during the busy period to reduce operating costs
(and increase throughput) in that period. However, they do not consider total operating
costs across all periods nor do they consider minimizing the total number of
replenishments during all periods. The DTF strategy considers both the total operating
costs as well as the total number of replenishments. The DTF strategy does this by taking
advantage of empty pick faces in the forward area and assigning more than one unit-load
(or pick faces) to SKUs.
Hackman and Rosenblatt [9] develop an assignment-allocation method for a
problem similar to the FRP. In this case, all items are received and stored in a central
storage. All items are then assigned to a primary location for order picking, which is the
automated storage and retrieval system (AS/RS) for some SKUs.
Central storage
represents the reserve area while the AS/RS represents the forward area in the FRP.
24
There exists a cost to replenish items in the AS/RS. However, there also exists a savings
in order picking time (and thus cost) for picking items from the AS/RS rather than
picking from the central storage. The authors assign and allocate items to the AS/RS
using a cost-benefit analysis.
Two major differences separate the research of Hackman and Rosenblatt [9] from
the DTF allocation strategy. The first major difference is found in the model used by
Hackman and Rosenblatt [9], which does not require all items to be picked from the
AS/RS, the forward pick area. As mentioned previously, many distribution centers do
not pick from reserve storage. This research considers all items picked from the forward
pick area. The second major difference is in their decision for assignment and allocation.
Hackman and Rosenblatt [9] consider the savings in order picking costs achieved through
assignment and allocation to the forward area (as compared to the replenishment costs).
The DTF assignment-allocation strategy does not consider savings in order picking costs
because of its assumption that order picking costs are not affected, since it only considers
items picked from the forward pick area. Instead the DTF allocation strategy makes
decisions based on the total replenishment costs.
Bartholdi and Hackman [1] discuss two typical methods for allocating SKUs in
the forward pick area: the Equal Space Allocation (ESA) and the Equal Time Allocation
(ETA). The ESA method allocates an equal amount of space in the forward pick area to
each SKU. While this allocation method simplifies adding and removing SKUs from the
forward pick area it fails to acknowledge that SKUs vary in demand, and thus in the
number of replenishments they require. The ETA method allocates SKUs to the forward
25
pick area such that there is a sufficient quantity of each for a specific time period. This
method provides the opportunity for batch replenishments but it does not necessarily
minimize the total number of replenishments.
Bartholdi and Hackman [1] use a fluid model to design a fast-pick area, a.k.a. the
forward pick area, and develop an optimal assignment and allocation strategy. In this
model, each SKU is considered an incompressible, continuous fluid that is divisible into
any size. The flow of this fluid is the number of cubic feet picked per year and the
number of replenishments per year for a SKU is the flow divided by the stock volume.
Bartholdi and Hackman [1] assign SKUs to the forward pick area based on their
viscosity, the number of picks divided by the square root of the flow. SKUs with a high
viscosity are picked more often relative to their total demand than those SKUs with a low
viscosity. The estimate for the number of total replenishments for a SKU is used to
determine the quantity of the SKU allocated to the forward pick area. The optimal
strategy minimizes the sum of the pick costs and replenishment costs, which are
dependent on the number of total replenishments.
The initial difference between the optimal strategy proposed by Bartholdi and
Hackman [1] and this research is assignment; this research only considers SKUs that are
assigned to the forward pick area. Their optimal strategy allocates SKUs to the forward
pick area based on the sum of pick costs and replenishment costs. While this strategy
does minimize the number of total replenishments, it does not necessarily minimize the
total replenishment costs. Also, this research considers the DTF technique to further
minimize replenishment costs, which is not discussed by Bartholdi and Hackman.
26
Sadiq and Landers [15] present the need for an algorithm that considers
assignment, allocation, and location of SKU within the forward pick area. The authors
cite warehouse and DC operations for products with either short life cycles or seasonal
spikes in demand. These types of operations create additional challenges to the forward
reserve problem such as re-warehousing and re-assigning products to the forward pick
area.
Due to their rapidly changing nature, these challenges need to be addressed
continuously justifying the need for an algorithm that considers assignment, allocation,
and location dynamically.
Sadiq, Landers, and Taylor [17] present an algorithm to provide the continuous
assignment, allocation, and location assignment for the forward pick area.
This
algorithm, the Dynamic Stock Location Assignment Algorithm (SLAA), is a heuristic
method to manage the forward pick area.
This method, which considers demand
correlation between SKUs for location assignment, appears to outperform the traditional
location assignment strategies like Heskett’s CPO index [10].
The continuous (dynamic) approach to assignment, allocation, and location
assignment in the forward pick area makes assumptions different from those in this
research. Both the work of Sadiq and Landers [15] and that of Sadiq, et al. [17] address
the assignment part of the FRP assuming that not all SKUs are picked from the forward
pick area. However, this research considers only SKUs picked from the forward pick
area. These two papers consider re-warehousing costs as part of the objective function
but these costs are not considered in this research since SKUs remain in a pick face until
its inventory is depleted from this location. The dynamic SLAA developed by Sadiq,
27
Landers, and Taylor [17] also assigns locations within the forward pick area to minimize
order-picking costs.
This research assumes order-picking costs are independent of
location and thus does not consider the location within the forward pick area.
In a working paper, Kuo [12] presents methods for solving the allocation problem
within the forward-reserve problem. Kuo defines this allocation problem as the decision
of which SKUs to assign to the forward pick area and in what quantities. Two distinct
types of methods exist for solving this allocation problem: static and dynamic. The
objective of the static allocation methods is to maximize the difference between pick
savings and replenishment costs, also discussed by Hackman and Rosenblatt [9]. Static
allocation methods assume a constant demand. The objective of the dynamic allocation
methods is to minimize the difference between the sum of replenishment and rewarehousing costs and pick savings, like that of Sadiq and Landers [15]. Dynamic
allocation methods do not assume demand is constant and account for possible rewarehousing costs, the cost to move a SKU out of the forward pick area and back into the
reserve storage.
There is a distinct difference between the definition of the allocation problem
given by Kuo [12] and the definition used in this research. Frazelle, et al. [4] defines the
FRP as an assignment-allocation problem, assigning SKUs to forward pick area and
allocating quantities of assigned SKUs. In Kuo’s research, allocation is determining the
set of SKUs and the quantity of each of these SKUs to store in the forward pick area.
The allocation method in this research is neither static nor dynamic based on the
definitions given by Kuo [12]. The allocation method in this research does not assume a
28
constant demand as in a static method. However, the allocation does not consider rewarehousing costs like a dynamic method since all SKUs are picked from the forward
pick area and replenishment is demand based.
2.4
Duration of Stay
The turnover rate is generally used to describe the movement of a product (SKU)
through a warehouse or DC. This rate is typically defined as the total inventory of the
SKU divided by the demand. Goetschalckx and Ratliff [5] cite a major difference
between a SKU and its individual unit loads. The turnover rates for all individual unit
loads of the same product are the same. However, the time spent in storage by each
individual unit load of a product varies by unit load. The authors term the time spent in
storage as the “duration of stay” stating that this is a unit characteristic while turnover
rate is a product characteristic.
The inventory-to-demand ratio (used by the DTF allocation strategy in this
research) is the turnover rate for SKUs in the forward pick area. This ratio is not the
turnover rate discussed by Goetschalckx and Ratliff [5] because it only uses the forward
pick area inventory, not the entire storage inventory and is thus not reflective of the
product’s movement throughout the entire facility.
In order to reduce the total number of replenishments from reserve, the DTF
allocation strategy depends on the number of empty pick faces in the forward pick area.
This number is dependent upon the rate at which pick faces become open (empty). There
is an inverse relationship between the rate pick faces open and the duration of stay of the
29
unit loads in the forward pick area: the shorter the duration of stay the faster the rate at
which empty pick faces open. However, the inventory-to-demand ratio is reflective of
the duration of stay in this research since SKUs with multiple pick faces will be picked
from one pick face at a time.
30
3
METHODOLOGY
3.1
3.1.1
Situation
Replenishment
The forward-reserve storage strategy utilizes two unique storage areas: the
forward pick area and the reserve storage area. Incoming SKUs enter the DC at the
receiving dock and from this point must be moved to one of these two areas for storage.
In this research, replenishment included the activities required to move a SKU from the
receiving dock’s staging area to reserve and then retrieve the SKU from reserve until the
SKU is located in the forward pick area. Each activity required a trip and these activities
were broken down into three distinct types of possible trips for replenishment:
DR = trip from the receiving dock to the reserve storage area
RF = trip from the reserve storage area to the forward pick area
DF = trip from the receiving dock to the forward pick area
A trip from the receiving dock to the reserve storage (DR) is a put away operation
in which a unit load of a SKU is moved from the receiving dock to its designated location
in reserve storage. A trip from the reserve storage area to the forward pick area (RF) is
both a retrieval and put away operation in which a unit load of a SKU is moved from
reserve storage to a pick face in the forward pick area. A trip from the receiving dock to
the forward pick area (DF) is a put away operation in which a unit load of a SKU is
moved from the receiving dock to a pick face in the forward pick area. Each trip from
the dock directly to the forward pick area eliminates the additional retrieval and put away
operations as well as the travel of a trip from reserve storage to the forward pick area.
31
There are other tasks that may affect replenishment costs. For example, a worker
may be required to record each transaction or remove a pallet from an empty storage face.
These other tasks clearly affect the time required for replenishment. It was assumed that
these tasks were a routine part of every replenishment trip. Since the three types of
replenishment trips account for all replenishment activities, replenishment costs are
therefore dependent on the number of trips.
Any pick faces remaining open after replenishments have been made to fulfill the
current period’s demand are discretionary. These pick faces are available for trips from
the dock to the forward area or for replenishments from the reserve area at the discretion
of management. The decision of which SKUs to allocate to these “extra” pick faces has
clear implications on the number of pick faces available for similar allocation in the
future. For example, a lower demand (unpopular) SKU allocated to a discretionary pick
face may require more time, compared to a higher demand SKU, until the pick face is
available for a new SKU. The relationship between a SKU’s demand, current forward
inventory, and the time until a pick face becomes open is the key to minimizing the
number of total replenishment trips.
3.1.2
Assumptions
The fundamental assumption for this research was that the decision strategy only
considered items assigned to the forward pick area. Items not picked from this area were
ignored because there were no possible replenishment trips from the dock-to-forward.
This reflects standard industry practice found in distribution centers, based on interviews
32
with DC managers at Dollar General, AutoZone, and Worthington Foods. Since this
research only considers SKUs picked from the forward pick area, each SKU occupies at
least one pick face in the forward pick area. Therefore the assignment portion of the
Forward Reserve problem (FRP) is unnecessary. The only portion of the FRP left
unsolved is the allocation of SKUs to the forward pick area. The decision strategies
evaluated in this research focus solely on the allocation of each SKU to the forward pick
area, i.e. the quantities of each SKU in the forward pick area.
The allocation of SKUs to the forward pick area is typically determined by a
demand-based strategy. The quantity of each SKU allocated to the forward pick area is
determined by the SKU’s demand relative to the overall demand. However, this strategy
may not minimize the replenishment costs because it does not consider the relationship
between the inventory of in the forward pick area and the demand for each SKU.
The model in this research assumes that the warehouse utilizes a shared storage
assignment policy rather than a dedicated storage policy. In shared storage assignment,
different SKUs are permitted to be stored in the same location successively [5]. This
policy permits the decision strategy to assign a SKU to a discretionary pick face
regardless of the last SKU stored in that pick face. This assumption is imperative to
utilize open pick faces in order to reduce replenishment costs.
A facility that utilizes dedicated storage assigns SKUs to pick faces in the forward
pick area for a planning period. The planning period may be a month, a quarter, or a
year. Since pick faces are designated for specific SKUs they cannot be utilized for
replenishment from the dock for any other SKU when open, only for their SKU.
33
Generally every SKU is not received on every day of the week and thus many
opportunities to make replenishments from the dock are lost with this policy.
To simplify the problem, it is assumed that the capacity of each pick face is one
replenishment-load and that every replenishment-load received in the forward area fills
the pick face. In other words, if the replenishment-loads were pallets, then all pallets
received in the forward pick area would be a full pallet of a single SKU. This assumes
that any partial pallets received at the dock are used to build full pallets in reserve
storage.
Two requirements must be met in order to coordinate replenishments from the
receiving dock directly to the forward area: scheduled orders to be filled and scheduled
receipts must be known in advance. These must be known for at least the next period
(e.g. shift, day) in order to use the decision strategies. All replenishments to meet the
next period’s demand must be planned to determine the number of discretionary pick
faces available.
It is assumed that the long-term schedule for both receipts and orders are known
in the tests of the different strategies. In essence, the demand for the next period is
known. While this assumption may not hold true for all warehouses and DCs, the
popularity of cross docking in this industry shows that it is typical to have comparable
information. Warehouses and DCs must have scheduled receipts and shipments to meet
the basic principle of cross docking, which is the identification of the customer upon
receipt of a SKU [8].
34
3.2
Objective Function
The primary objective of this research is to develop a method of identifying the
best DTF candidates to minimize replenishment costs. The replenishment costs are
dependent upon the number of trips made for replenishment activities:
•
TDR = number of trips from the receiving dock to the reserve storage
•
TRF = number of trips from the reserve storage area to the forward pick area
•
TDF = number of trips from the receiving dock to the forward pick area
Replenishment costs (C) are calculated as the total number of replenishment trips
(T0) multiplied by a constant value for the cost per trip, K. The objective function, shown
in equation 1, is to minimize the replenishment costs (C).
min C = T0 × K
(1)
The total number of replenishments trips (T0) is the only variable in the objective function
since the cost per trip, K, is assumed to be a constant. While this cost is not necessarily
constant, the cost for a DTF trip is typically less than the sum of the costs for a dock to
reserve trip and a reserve to forward trip. Thus, K is assumed to be a constant
The sum of the three types of replenishment trips makes up the total number of
replenishment trips. In order to minimize the replenishment costs and meet the objective,
the total number of replenishment trips must be minimized. This secondary objective is
shown in equation 2.
min T0 = (TDR + TRF + TDF )
(2)
35
A DC has a finite storage capacity requiring a balance between receiving and
demand. In the long run, the number of units received must equal the number of units
shipped. If this balance does not exist, there are two possible consequences: (1) the
facility’s receiving will exceed maximum storage capacity and eventually fill up or (2)
the orders will deplete the inventory to zero, incapacitating the facility. This balance
leads to the constraint, shown in equation 3, that the number of trips for put away from
the receiving dock must equal the number of trips for put away in the forward pick area.
TDR + TDF = TRF + TDF
(3)
The receiving dock area in a warehouse or DC is a collection of truck docks with
an area for temporary storage. Since the storage is only temporary, receipts must be
moved from this area quickly. Assuming no SKUs are cross-docked, receipts must be
stored in either the reserve storage or the forward pick area. The types of trips to move
receipts from this area are trips to from the dock to the reserve area (DR) and trips from
the dock to the forward pick area (DF). Therefore, the sum of the number of these two
types of trips equals the number of unit loads received at the facility, ND. Equation 4
represents this constraint on the secondary objective function.
TDR + TDF = N D
(4)
SKUs are moved to the forward pick area through two types of replenishment
trips: trips from the reserve area and trips from the dock. The third constraint placed on
the secondary objective function, equation 5, is that the sum of the these two types of
trips equals the number of unit loads received in the forward pick area, NF.
TRF + TDF = N F
(5)
36
NF is a constant that is determined by demand. In other words, NF reflects
demand with no other influences on its value. Due to its relationship with TRF and TDF,
NF is easily substituted into the secondary objective function from equation 2 as shown in
equation 6.
min T0 = TDR + (TRF + TDF ) = TDR + N DF
(6)
The secondary objective function now has one variable (TDR) and one constant (NF). The
number of unit loads received in the forward area (NF) is constant based on demand.
Therefore, in order to minimize T0, TDR must be minimized.
The relationship between TDR and TDF is seen in equation 4. TDR is the difference
between the number of unit loads received at the dock (ND) and the number of trips from
the dock to the forward area (TDF). The greater (TDF), the less the number of trips from
the dock to reserve storage (TDR) that are needed. Therefore, TDF must be maximized in
order to minimize TDR and thus minimize T0.
The one constraint on the number of trips from the dock to the forward area (TDF)
is the number of discretionary pick faces in the forward area on day i (Pi) after the current
demand is met. Clearly a replenishment trip from the dock to the forward area is not
feasible if no open pick faces are available in which to store the unit load. The choice of
which SKUs to allocate to these open pick faces is made after replenishment assignments
to meet the current day’s demand are considered. The number of discretionary pick faces
in the forward area (Pi) is the number of empty pick faces once the current demand is
met. The more pick faces available in the forward area, the greater the number of
opportunities for trips from the dock to the forward area that exist.
37
The rate at which pick faces become open (available) is inversely related to the
average time SKUs spend in the forward area. The less time a SKU spends in a pick
face, the sooner the pick face becomes available. This rate multiplied by a time is the
number of open pick faces for that period of time. As the rate increases, the number of
open pick faces in the time period also increases. Therefore, increasing the rate that pick
faces become available increases the number of trips from the dock to the forward area
(TDF).
In order to maximize the rate at which pick faces become available, the time until
the pick face j is open (Ej) must be minimized. The time until a pick face is open is
dependent on the rate at which the inventory of the SKU in a pick face is depleted, which
is depleted is the demand for that SKU. The demand, in terms of unit loads per time
period, appears to be the sole factor that determines the time a SKU spends in a pick face.
However, in many warehouses and DCs a SKU may occupy more than one pick face in
the forward area. In this case, demand is not the only factor determining the time until a
pick face is open. For example if the SKU with the highest demand is located in pick
face j, then pick face j will open first.
However, if this same SKU is also stored in other pick faces which are picked
first, the time until pick face j is depleted will be increased. The relationship between the
time until a pick face is open and the objective function follows a clear, straight path as
shown in Figure 3-1. Therefore it is both demand and total inventory in the forward pick
area that determines Ej.
38
Figure 3-1: Relationships for Objective Function
Reducing the time until a pick face opens increases the total number of empty
pick faces which maximizes the number of trips for dock-to-forward. By maximizing the
number of trips from dock-to-forward, the number of dock to reserve trips is minimized
which minimizes the total number of replenishment trips. Minimizing the total number
of replenishments trips minimizes the total replenishment costs, the objective of this
research.
3.3
Inventory versus Demand
The time until a pick face is open is determined by both the demand for a SKU
and the SKU’s current inventory in the entire forward area. Demand (Ds) is the rate at
which SKU s is picked from inventory in the forward area, per time period. The current
inventory in the forward area (Ls) is the number of unit loads stored in this area for SKU
s. Equation 7 shows the relationship between demand and forward inventory determines
the time periods until a SKU’s inventory is depleted.
39
Ls
= time periods until depletion
Ds
(7)
The result of equation 8 is the time at which the demand will deplete all of the
current forward inventory of SKU s. The SKU’s inventory will need replenished no later
than the end of this time period in order to continue meeting demand. Since this ratio
includes the entire current forward inventory, the resulting time period is the amount of
time until all pick faces occupied by the particular SKU become available (assuming no
replenishments are made during this period).
It is assumed that a SKU is picked from a single pick face until that pick face is
depleted and once a pick face is depleted, the SKU is then picked from the next occupied
pick face. In this case, pick faces occupied by the SKU with the lowest time period to
depletion (i.e. the smallest value for the ratio) will be the first pick faces to become
completely available.
Since the inventory-to-demand ratio shown in equation 7 provides a measure of
the time until a pick face becomes open for a particular SKU, it can be utilized to make
an intelligent decision with regards to the SKU(s) to allocate to the discretionary pick
faces. One drawback of using the inventory-to-demand ratio to make allocation decisions
is the fact that it does not consider the SKUs’ inventory in the forward area after the
allocation is made. The more of these faces that are available, the greater the number of
trips that can be made from the dock to the forward area, minimizing replenishment costs.
40
3.4
Decision Strategies
A comparison of four decision strategies will be made in order to develop and
identify the best strategy for making the intelligent DTF allocation decision. These four
decision strategies are: random, demand-based, inventory-to-demand-based, and futureinventory-to-demand-based decisions. Management can use these strategies to fill all
discretionary pick faces from dock-to-forward replenishments in order to minimize the
number of trips from the dock to reserve storage to minimize replenishment costs.
3.4.1 Random
The random strategy makes allocation decisions for discretionary pick faces based
on randomly chosen SKUs. A SKU is randomly selected from those being received on
that day for a dock-to-forward replenishment until all discretionary pick faces are full.
There is no expected pattern for the allocation in this strategy. This decision will not
consider the implications on the time until a pick face opens which clearly affects the
total number of replenishment trips from the dock to the forward pick area. This strategy
is included in the testing to help show the allocation decision is not trivial.
3.4.2
Demand-Based
The demand-based strategy allocates SKUs from the dock to discretionary pick
faces based on each SKU’s individual average demand. The SKUs in the highest demand
class that are received on that day are selected for a dock-to-forward replenishment to the
discretionary pick face(s) until either all discretionary pick faces are full or no more unit
41
loads of the SKU are available at the dock. This process moves to the next highest
demand class and iterates until all discretionary pick faces are full.
The demand-based strategy attempts to maximize the depletion rate of the SKUs
allocated to the discretionary pick faces since it places SKUs with the highest demand in
these pick faces. However, the depletion rate of the SKUs in these discretionary pick
faces, Ej, is dependent on the inventory in the forward area.
3.4.3
Inventory-to-demand Ratio
As discussed in Section 3.3, the ratio between a SKU’s total inventory in the
forward area to its demand determines the time until all of its current pick faces become
open. The inventory-to-demand strategy makes the allocation decision based on this
ratio. The SKU that is received on that day with the minimum ratio is selected for a
dock-to-forward replenishment to the discretionary pick face. After each individual
allocation, the ratios are updated to reflect the inventory change and this process is
iterated until all discretionary pick faces are full.
The inventory-to-demand strategy considers the relationship between a SKU’s
current inventory in the forward area and its demand. This strategy attempts to maximize
the depletion rate of the SKUs allocated to the discretionary pick faces. Since it considers
both factors that affect Ej, this strategy appears to provide more opportunities for DTF
trips than the previous two strategies.
42
3.4.4
Future Inventory-to-demand Ratio
The inventory-to-demand strategy fails to consider the effect of the unit-load
replenishment (from the dock to the forward area) on this ratio. Since the time until pick
faces open directly relates to replenishment costs (See Figure 3-1), the future-inventoryto-demand decision strategy is tested because it considers the actual time until the pick
face being assigned opens. The strategy allocates SKUs to discretionary pick faces based
on a ratio of a SKU’s forward inventory plus one replenishment-load to its demand. The
SKU with the minimum ratio that is received that day is selected for a dock-to-forward
replenishment in a discretionary pick face. The ratios are updated and the process is
repeated until all discretionary pick faces are full.
43
4
RESULTS
4.1
Implementation
The test for each of the four decision strategies was executed in a Microsoft Excel
workbook. This spreadsheet included seven worksheets that were used to store data and
perform calculations: demand, receiving schedule, forward inventory level, ratio, number
of dock-to-forward replenishments, number of reserve-to-forward replenishments, and
number of occupied pick faces. Each of these worksheets provided a column for the
SKU numbers and enough columns for 250 days worth of data. Assuming the facility
worked fifty weeks of the year and five days a week, the spreadsheet provided the
capacity to store an entire year of data.
4.1.1
Excel Worksheets
The demand for each SKU in this experimentation was randomly generated using
a Poisson distribution. The Poisson distribution is a discrete probability distribution with
a single parameter, λ [22]. This parameter is the inverse of the expected mean value for
the demand. The Poisson distribution was used to generate a daily demand value for each
SKU. These values could be replaced by actual demand values for a distribution center,
if available for additional testing.
The forward inventory level worksheet calculated the forward inventory Is,n, for
SKU s on day n, as shown in equation 8, by subtracting the SKU’s demand for day n, Ds,n
from the previous day’s inventory and then added both the replenishments for the SKU
from the dock to the forward area and from the reserve to the forward area for that day.
44
I s ,n = I s ,n−1 − Ds ,n + TRF ,s ,n + TDF ,s ,n
(8)
This equation assumes that the replenishment occurs after the picking is
completed on day n. The ratio worksheet was used to compare the current forward
inventory to the demand. The ratio calculation is the forward inventory for the day
divided by the day’s demand with the exception of the future-ratio. For the future
inventory-to-demand strategy the ratio calculation for discretionary pick faces is the sum
of the forward inventory for the day plus one pallet load divided by the day’s demand.
The occupied pick faces worksheet calculated the number of occupied pick faces
for a SKU on a particular day, which is the forward inventory for that SKU rounded up to
the next integer. The sum of the occupied pick faces for each day is subtracted from the
total number of pick faces to determine the number of open pick faces available.
The dock-to-forward replenishment worksheet was used to collect the number of
DTF replenishments to the forward pick area for each SKU on each day. The reserve-toforward replenishment worksheet was used to collect the number of replenishments from
reserve for each SKU on each day.
4.1.2
Macro
A macro within the Excel spreadsheet performed the execution and made the
decisions based on the desired strategy. For all four decision strategies, the first two
steps of the execution were the same. In the first step, the macro checked the inventoryto-demand ratio only for SKUs being received on that day. For any SKUs with a ratio
45
less than one, dock-to-forward replenishments were scheduled until the ratio for each
SKU was greater than or equal to one, or the supply on the receiving dock was depleted.
In the second step, reserve-to-forward replenishments were scheduled for until the
ratios for all SKUs were greater than or equal to one. The first two steps insured that the
inventory for each SKU was sufficient to meet the demand for the day. It was at this
point, when all required replenishment was complete, that decisions regarding the
remaining open pick faces were discretionary. This was where the decision strategies
differed.
The third step of the macro function was the allocation of SKUs to the
discretionary pick faces and was dependent upon the decision strategy. For the random
decision strategy, a random number was generated from the list of SKU numbers
received that day. A number was generated for each discretionary pick face and the
corresponding SKU was scheduled for a dock-to-forward replenishment to the pick face.
For the demand-based decision strategy, the SKUs in the highest demand class
received that day were scheduled for dock-to-forward replenishments until all of the
discretionary pick faces were full. The replenishments are distributed evenly among all
SKUs in the demand class. If no unit loads remained on the dock and discretionary pick
faces remained, SKUs in the next highest demand class were scheduled for dock-toforward replenishments until all of the discretionary pick faces were full.
For the inventory-to-demand ratio, a dock-to-forward replenishment was
scheduled for the SKU with the minimum ratio. This was iterated until replenishments
were scheduled for all discretionary pick faces. After each discretionary pick face was
46
assigned, the ratios were recalculated. For the future inventory versus demand strategy, a
dock-to-forward replenishment was scheduled for the SKU with the minimum ratio of
inventory plus one to demand.
Once step three was completed, the steps were repeated for the next day until
dock-to-forward replenishments were scheduled for all days in the study. The Visual
Basic code for the macro is shown in Appendix A.
The decision strategies were compared based on the average number of
discretionary pick faces available per day during the 250 days studied, which determined
the average number of trips from the dock to the forward pick area. The decision strategy
that produced the most discretionary pick faces per day minimized the total
replenishment costs for the DC.
4.2
Trial Experiment
Before developing a macro to execute the decision strategies, a pilot experiment was
performed by executing the strategies manually. For the trial experiment demand
data was randomly generated for fifty SKUs, in four demand classes, over ten days.
The results of this trial experiment are shown in
Table 4-1. This trial experiment provided evidence that there may be a difference
between the four decision strategies and showed that further testing was necessary.
47
Table 4-1: Trial Average Number of DTF Trips
Decision Strategy
Random
Demand
Current-ratio
Future-ratio
Number of DTF Trips
90% Confidence Interval
Average
Upper
Lower
23.4
25.36
21.44
23.1
25.12
21.08
26.7
29.95
23.45
26.3
29.09
23.51
The confidence intervals for each strategy overlapped showing that there were no
statistically significant differences between the average number of DTF trips for any of
the strategies in this experiment. However, both ratio strategies had an average greater
than the random and the demand-based strategies showing that they outperformed these
other strategies in this experiment. The sample size for the experiment was only ten days
and by increasing the sample size, the confidence intervals are subject to less variation in
the mean. This could lead to a statistically significant difference between strategies.
The macro discussed in section 4.1.2 was validated using the results of this trial
experiment. The macro was tested for all four decision strategies with the same demand
values and receiving schedule used in the trial experiment. The macro produced the
exact same results as the trial experiment.
4.3
4.3.1
Experiment
Experiment Setup
According to Hinojosa [11], many distribution centers utilize piece picking rather
than pallet or case picking in order to service retail stores with just-in-time inventory.
48
Hinojosa [11] states that the demand for SKUs in these types of DCs follows Pareto’s
80/20 rule. In other words, 80% of the orders in the DC are for 20% of the SKUs.
Hinojosa [11] further describes the demand for SKUs in a DC with piece picking
by defining fast moving SKUs as the 5% of the product line that account for 50% of the
orders. With Hinojosa’s definition of a fast moving SKU and the application of Pareto’s
law, the distribution of product demand for a typical piece picking DC was derived and is
shown in Table 4-2.
Table 4-2: Demand Distribution
Percentage of SKUs
5%
15%
30%
50%
Percentage of Orders
50%
30%
15%
5%
The demand data for the experiment were randomly generated to model a DC
with piece picking operations by following the distribution in Table 4-2.
This
distribution has four demand classes, shown in Table 4-3. Five Hundred SKUs were
stored in the DC over a time period of 250 days, approximately one year. The average
number of SKUs ordered per day was 16,000, which is a similar volume to the 18,000
SKUs per day ordered in the DC described by Hinojosa [11].
Table 4-3: Demand Classes for Experiment
Demand Class
1
2
3
4
Number of SKUs
25
75
150
250
Avg Number of Each SKU Ordered/Day
320
64
16
3.2
49
The initial inventory for each SKU was one and a half of the average daily
demand. It was assumed that order picking occurred before replenishment. While 250
days of demand were generated, there were only 249 days of receiving following a day
with order picking. Therefore only 249 days or samples of DTF trips were available for
each trial.
4.3.2
Experiment Results
The demand data were generated for five different trials and are shown in
Appendix B. Each of the four decision strategies was tested for all five trial sets of
demand data. There are a total of twenty observations with the four strategies and five
trials. Table 4-4 shows the average number of DTF trips for each observation.
Decision
Strategies
Table 4-4: Observed Average Number of DTF Trips per day
Random
Demand-Based
Current-ratio
Future-ratio
1
382
434
503
495
2
386
435
500
490
Trial
3
386
438
501
492
4
384
439
501
491
5
384
421
486
480
Average
384.3
433.3
498.2
489.6
% Increase
12.75
26.93
27.40
The strategy using the current-ratio to make the decision of what items to allocate
to the discretionary pick faces outperformed all three other decision strategies in every
trial run. On average the current-ratio strategy showed a 14.95% increase in the number
of DTF trips per day. The performance for each strategy, in terms of average number of
DTF trips, is plotted in the graph Figure 4-1.
50
Average No. DTF Trips per day
525
500
475
Random Strategy
Demand-based Strategy
Current Ratio Strategy
Future Ratio Strategy
450
425
400
375
1
2
3
4
5
Trial
Figure 4-1: Average Number of DTF Trips
The future-ratio strategy provided more DTF trips on average than the random
strategy and the demand-based strategy. The demand-based strategy also outperformed
the random strategy in every trial run, providing a 12.75% increase in DTF trips on
average. Further analysis is required to determine if there is any statistical difference
between decision strategies.
4.3.3
Experiment Analysis
Typically methods like ANOVA are used to test experiment results for statistical
difference between treatments like the strategies in this case [14]. However, single factor
ANOVA only determines whether all treatments are the same or whether there is some
statistical difference. With four different strategies from which to choose, it is also
51
important to compare the difference in the results. The paired t-test compares one
strategy versus another strategy to determine if there is a difference between the two and
if there is, it shows which strategy produces better results [14].
Since the input (the demand data) was different for each trial, the means of the
average number of DTF trips are not compared. Instead the paired t-test compares the
average difference in the number of DTF trips between each pair of decision strategies
for each trial [14]. The null hypothesis for each paired t-test was that the mean difference
between the average number for DTF trips equals zero while the alternate hypothesis is
that the mean difference is not equal to zero, shown in equation 9.
H0: µd = 0; H1: µd ≠ 0
(9)
The equation for the test statistic in the paired t-test, t0, is shown in equation 10.
t0 =
d
Sd
(10)
n
For this equation, d is the average difference in the average number of DTF trips per day
between two strategies while Sd is the sample standard deviation and n is the number of
trials.
The T-value for a two-tailed test with an alpha value of 0.01 (99% confidence)
and four degrees of freedom is 4.604. Table 4-5 shows the mean difference in the
average number of DTF trips between each pair of decision strategies as well as the tstatistic calculated for the pair. The t statistic for each pair is greater than the value from
the T distribution. This test shows that the difference in the average number of DTF trips
for each pair of decision strategies is statistically significant.
52
Table 4-5: Paired T-Test Results
Decision Strategy 1
Demand-Based
Future-ratio
Future-ratio
Current-ratio
Current-ratio
Current-ratio
Decision Strategy 2
Random
Random
Demand-Based
Random
Demand-Based
Future-ratio
d
49.37
105.71
56.34
113.97
64.60
8.26
t0
16.20
38.57
35.55
35.14
54.59
11.06
To better understand the precision of the confidence in each paired t-test, the twotailed p-value for each test was calculated. The p values for each paired t-test are shown
in Table 4-6 as well as the actual percent confidence in the test. The p values for these
tests show the limit of confidence for each test, which are all greater than 99.95%.
Table 4-6: Paired T-Test p Values
Strategy 1
Demand-Based
Future-ratio
Future-ratio
Current-ratio
Current-ratio
Current-ratio
Strategy 2
Random
Random
Demand-Based
Random
Demand-Based
Future-ratio
p Value
4.0 x 107
4.2 x 105
4.0 x 106
3.0 x 106
3.0 x 106
3.8 x 10-4
Percent Confidence
99.99%
99.99%
99.99%
99.99%
99.99%
99.96%
Figure 3-1 shows the relationship between the number of discretionary pick
faces and the number of DTF trips. According to this figure, the number of DTF trips
should increase as the number of discretionary pick faces increases. This logic holds true
for this experiment as shown in Figure 4-2.
53
Avg No. DTF Trips per day
525
500
475
Random Strategy
Demand-based Strategy
Current Ratio Strategy
Future Ratio Strategy
450
425
400
375
175
200
225
250
275
300
325
Avg No. Discretionary Pick Faces
Figure 4-2: Average DTF Trips Versus Discretionary Pick Faces
The objective function of this research is to minimize the total replenishment
costs by minimizing the total number of trips. Derivations in chapter 3 show that
maximizing the number of DTF trips minimizes the total number of trips. The results of
this experiment, shown in Figure 4-3, show that as the number of DTF trips increases, the
number of total trips decreases. Thus, the assumption in the methodology appears to be
true.
The total number of replenishment trips, shown in equation 2 in section 3.2, is the
sum of the dock-to-forward trips, the dock-to-reserve trips, and the reserve-to-forward
trips. The Excel workbook used in the experiment recorded the number of DTF trips, the
number of trips from reserve-to-forward, and the number of pallets received per day. The
difference between the number of pallets received and the number of DTF trips is the
54
number of dock-to-reserve trips. The total number of trips for each decision strategy in
each trial are shown in Table 4-7.
Avg Total Trips per day
1680
1660
1640
Random Strategy
Demand-based Strategy
Current Ratio Strategy
Future Ratio Strategy
1620
1600
1580
1560
1540
375
400
425
450
475
500
525
Avg No. DTF Trips per day
Figure 4-3: Total Trips versus Average Number of DTF Trips
Decision
Strategies
Table 4-7: Average Number of Total Trips per Day
4.4
Random
Demand-Based
Current-ratio
Future-ratio
1
2
1672 1667
1619 1618
1551 1553
1558 1563
Trial
3
1668
1615
1553
1562
4
1669
1615
1552
1561
5
1669
1631
1567
1572
Avg % Decrease
1669
1620
2.94%
1555
6.83%
1563
6.35%
Differences in Ratio-Based Decision Strategies
Two of the four decision strategies tested in this experimentation used a ratio to
make the decision for allocating SKUs to discretionary pick faces. The inventory-to-
55
demand ratio strategy allocates each discretionary pick face to the SKU with the
minimum ratio, in which the inventory is the current inventory in the forward pick area
for the SKU.
The future-inventory-to-demand ratio adds a pallet load to the current inventory in
the forward pick area for the SKU. By doing this, the future-ratio looks ahead to see
which SKU will use all of the extra inventory the fastest. It was expected that the futureratio would increase the average number of discretionary pick faces and thus the average
number of DTF trips because it allocates to SKUs that use the extra inventory the fastest.
However, the experiment results show this theory is not the case. Instead the inventoryto-demand ratio strategy has a greater average number of DTF trips per day than the
future-inventory-to-demand ratio strategy in each trial. While the inventory-to-demand
ratio strategy had a better average number of DTF over the entire year, though there are a
significant number of days that the future-inventory-to-demand ratio produced more DTF
trips.
In the experiment there are 249 days of data in each trial for a total of 1245 days.
The future-ratio strategy outperforms the current-ratio strategy, in terms of the total
number of DTF trips, on 411 of these days, approximately 33% of the time.
Interestingly, these days are not spread out randomly through the week. For each trial,
there are two days of the week that account for 75% or more of the times the future-ratio
strategy outperforms the current-ratio strategy.
Understanding what is common among the days that the future-inventory-todemand ratio outperforms the inventory-to-demand ratio may lead to an improved
56
decision strategy. The two days of the week from each of the five trials makes a total of
ten days of the week in which the future-ratio performs its best. On seven of these ten
occasions the number of different SKUs received on the previous day was less than that
of the current day. This shows that the future-ratio strategy may perform better than
inventory-to-demand ratio with less SKUs from which to choose.
The type of SKUs allocated provides another interesting observation regarding the
performance of the future-ratio strategy. The future-ratio strategy always allocates more
SKUs from the most popular demand class (those with the greatest average demand) than
the current-ratio strategy. This is expected since the future-ratio strategy makes the
allocation decision based on the current-ratio plus one divided by demand. While many
SKUs may have similar current-ratios, those with higher demand have a smaller futureratio and are more likely to be selected. Likewise the current-ratio strategy always
allocates more SKUs from the two least popular demand classes. However, it is not clear
how this pattern can improve the performance of the decision strategy.
There are many observations for the performance of the future-ratio strategy with
respect to that of the current-ratio strategy. In certain cases the future-ratio outperforms
the current-ratio strategy on a day-to-day basis but the not over the long run. However,
there are no clear or obvious patterns to explain this unexpected behavior.
4.5
Comparison with other DC Strategies
Two additional strategies were tested in order to compare the performance of the
DTF technique and the various decision strategies with typical DC operations. The first
57
strategy replenishes the forward pick area using reserve-to-forward trips and DTF trips.
However, this strategy does not utilize discretionary pick faces, i.e. no more trips are
made once the inventory of the forward pick area is sufficient to meet the next day’s
demand.
The second strategy replenishes the forward pick area from reserve storage only
and it does not utilize the DTF technique. A FIFO inventory system would require this
strategy but other inventory systems could also use it also. The average total number of
trips per day for all strategies is shown below in Table 4-8. This table also shows the
difference between the two baseline strategies and the four decision strategies utilizing
discretionary pick faces. In the “No DTF” column of Table 4-8, strategies are compared
to the strategy that does not use DTF. The strategies are also compared against the
strategy that does not use discretionary pick faces in Table 4-8.
Table 4-8: Baseline Comparison of the Average Total Number of Trips per day
Strategy
No DTF
No Discretionary Pick Faces
Random
Demand-based
Current Ratio
Future Ratio
Trips
2051
1851
1669
1620
1555
1563
No DTF
9.73%
18.62%
21.03%
24.18%
23.78%
Percent Decrease
No Discretionary Pick Faces
9.85%
12.51%
16.00%
15.56%
The strategy that uses the DTF technique for replenishment and does not use
discretionary pick faces reduces the average total number of trips per day by more than
9% compared to a strategy that does not use the DTF technique. This result shows that
58
simply utilizing the DTF technique to replenish the forward pick area reduces the total
replenishment costs.
All four decision strategies that use discretionary pick faces show a decrease in
the average total number of trips per day of at least 9% compared to a strategy that uses
the DTF technique for replenishment and does not use discretionary pick faces. The
current ratio shows a 16% decrease in the average total number of trips per day over this
strategy and it also shows a 24% decrease versus a strategy that does not use DTF trips.
Thus, the use of discretionary pick faces for DTF trips reduces replenishment costs.
Also, the method of allocating SKUs to the forward pick area has clear implications on
the potential cost reductions. This allocation method determines the extent to which
average total number of replenishment trips per day are further reduced by using
discretionary pick faces for DTF trips.
59
5
5.1
CONCLUSIONS
Review of Results
The purpose of this research was to minimize replenishment costs in a distribution
center with a forward reserve storage strategy through an improved method of allocating
SKUs to the forward pick area. The replenishment costs are dependent upon the total
number of replenishment trips. By maximizing the number of dock-to-forward (DTF)
trips, the total number of trips is minimized. The allocation of SKUs to the forward pick
area affects the number of pick faces available for DTF trips. In this research, four
decision strategies for allocating SKUs to the forward pick area were tested using the
demand data for a typical case picking distribution center.
The experiment results show there is a statistically significant difference between
the average number of DTF trips per day between all four decision strategies. The
strategy that used the current inventory-to-demand ratio to make the allocation decision
had a higher average number of DTF trips per day than the three other strategies. The
demand-based decision strategy, similar to what is used in industry, only performed
better than the random-based decision strategy.
The current inventory-to-demand ratio strategy reduced the average number of
overall trips per day by 6.83% compared to the random decision strategy. This strategy
reduced the average number of overall trips per day by 24% compared to a strategy that
does not use the DTF technique and by 16% compared to a strategy that uses DTF but
does not use discretionary pick faces. These results shows the significance of the DTF
60
technique and the benefits of discretionary pick faces in terms of reducing replenishments
costs.
The future-ratio strategy was expected to have a greater average number of DTF
trips than the current-ratio strategy but the results show the opposite. There do exist dayto-day scenarios in which the future-ratio strategy outperforms the current-ratio strategy.
However, the current-ratio strategy has more DTF trips over the course of the year and
there are no apparent patterns to explain this phenomenon.
5.2
Application
A logical medium for a decision strategy to allocate SKUs to the forward pick
area is through a facility’s Warehouse Management System (WMS). In order to make
the decision about which SKUs to allocate to the forward pick area, only the following
data is required: the day’s orders, the day’s expected receipts, and the current inventory.
The WMS generally tracks all orders, inventory quantities, inventory locations, and
receipts in the DC to coordinate activities such as order picking and replenishment, thus
the WMS has all of the information required to make allocation decisions and is typically
used to determine the location of items received. A modification in the WMS source
code to make the allocation decision would be necessary to implement the decision
strategy.
The implementation of this decision strategy has clear potential for the
improvement of DC operations. The total number of replenishment trips is minimized by
61
the decision strategy meaning less labor is required to perform this operation. Labor is an
operating cost for the DC, which has a direct impact on the company’s profits [6].
In this experiment it was assumed that the capacity of all pick faces was a single
replenishment load or one pallet. While this is not a correct assumption for many DCs
like Dollar General that have pick face capacities of three a pallets, the decision strategy
presented in this research is still applicable. To implement the decision strategy, the
WMS would direct all picking for a specific SKU to occur from a single pick face until
that inventory is depleted. This prevents more than one partially depleted pick face for a
single SKU from blocking potential DTF trips.
The results of this research also show the potential for reduction of replenishment
costs by using shared storage.
This storage policy allows the decision strategy to
consider all forward area pick faces to fully utilize the DTF technique. In this experiment
the inventory-to-demand based strategy reduced the average total number of trips per day
by 15% compared to a decision strategy that only uses the DTF technique for dedicated
storage. While the shared storage policy may require careful planning, it has the potential
to reduce replenishment costs significantly.
5.3
Future Work
The decision strategy introduced in this research considers only those SKUs
assigned to the forward pick area. This assignment is the first of the two important
aspects of the forward-reserve problem. It is in the assignment aspect that SKUs with the
greatest pick savings (compared to replenishment costs) are selected to be stored in the
62
forward pick area, which leads to the minimization of the order picking costs.
A
potential improvement in the decision strategy is including the assignment to the forward
pick area as part of the decision.
In section 4.4 the difference in performance of the current-ratio and future-ratio
strategies is discussed. In this discussion there is no pattern to explain the fact that the
current-ratio strategy produces a greater average number of DTF trips than the futureratio strategy over a period of a year. However, the future-ratio strategy performs well on
days when there are less SKUs to choose from on the receiving dock. A combination of
these strategies into a hybrid strategy may lead to an increase in the average number of
DTF trips over the course of a year.
63
BIBLIOGRAPHY
[1] Bartholdi, John J. III and S.T. Hackman. Warehouse and Distribution Science
Release 0.30, 1998 pp. 89-120. http://www.isye.gatech.edu/~jjb/wh/book/wh-sci.pdf
[2] Beavers, Melinda Kay. “An Automated System for Dynamic Reconfiguration of
Forward Picking Areas” M.S. Thesis, University of Arkansas 1993.
[3] Frazelle, E.H. World-Class Warehousing and Material Handling McGraw Hill, 2002.
[4] Frazelle, E.H., S.T. Hackman, U. Passy, and L.K. Platzman. “The Forward Reserve
Problem” in: T.A. Ciriani, R.C. Leachmen (Eds) Optimization in Industry 2 1994,
Wiley, pp 43-61.
[5] Goetschalckx, Marc and H. Donald Ratliff. “Shared Storage Policies Based on the
Duration Stay of Unit Loads” Management Science 36 (9) 1990 pp. 1120-1132.
[6] Goldratt, Eliyahu M. and Jeff Cox. The Goal: a process of ongoing improvement
North River Press: NY, 1992.
[7] Gue, Kevin R. “Crossdocking: Just-In-Time for Distribution” Graduate School of
Business & Public Policy, Navy Postgraduate School 2001 pp 1-7.
http://web.nps.navy.mil/~krgue/Teaching/xdock-mba.pdf
[8] Gue, Kevin R., John J. Bartholdi III, and Keebom Kang. “Throughput Models for
Unit-Load Crossdocking” 2001 pp. 1-23.
http://web.nps.navy.mil/~krgue/Publications/tput.pdf
[9] Hackman, S.T., and Meir Rosenblatt. “Allocating Items to an Automated Storage
and Retrieval System” IIE Transactions Vol. 22 (1) 1990 pp. 7-14.
[10] Heskett, J.L. “Cube-Per-Order Index- A Key to Warehouse Stock Location”
Transportation and Distribution Management (3) 1963 pp. 27-31.
[11] Hinojosa, Arturo. “Picking Up the Pieces” Industrial Engineer Vol. 35 (2) 2003 pp.
39-44.
[12] Kuo, Po-Hsun. Georgia Tech “Dynamic Allocation” Working paper 2003.
64
[13] Lin, Che-Hung and Iuan-Yuan Lu. “ The procedure of determining the order picking
strategies in distribution center” International Journal of Production Economics 6061 1999 pp. 301-307.
[14] Montgomery, Douglas C. Design and Analysis of Experiments John Wiley & Sons,
Inc. 2001.
[15] Ron Dennis. Dollar General. Personal interview. Oct. 2002.
[16] Sadiq, Malik and Thomas L. Landers. “An Approach To Dynamic Reconfiguration
Of The Forward Picking Area” Progress In Material Handling Research: 1994 pp.
277-296.
[17] Sadiq, Malik, Thomas L. Landers, and G. Don Taylor. “An assignment algorithm for
dynamic picking systems” IIE Transactions Vol. 28 1996 pp. 607-616.
[18] Tompkins, James A., John A. White, Yavuz A. Bozer, and J.M.A. Tanchoco.
Facilities Planning John Wiley & Sons, 2003.
[19] Van den Berg, Jeroen P., Gunter Sharp, A.J.R.M. Gademann, and Yves Pochet.
“Forward-reserve allocation in a warehouse with unit-load replenishments”
European Journal of Operational Research (111) 1998 pp. 98-113.
[20] Petersen, Charles G. “An Evaluation of Order Picking Policies for Mail Order
Companies” Production and Operation Management Vol. 9 (4) 2000 pp. 319-335.
[21] Petersen, Charles G. “An Evaluation of Order Routeing Policies” International
Journal of Operations and Production Management Vol. 17 (1) 1997 pp. 1096-1111.
[22] Walpole, Ronald, Raymond Myers, Sharon Myers, and Keying Ye. Probability &
Statistics for Engineers & Scientists Prentice Hall: NJ, 2002 pp 135-136.
65
APPENDIX A: VISUAL BASIC MACRO CODE
66
Sub replenish()
Dim y As Integer 'Number of SKUs
Dim x As Integer 'Number of Days
Dim z As Integer 'Number of Discretionary Pick Faces
Dim j As Integer ' Current Day
Dim i As Integer 'Current SKU
Dim SKU As Integer 'SKU number
Dim num_classes As Integer 'Number of demand classes
Dim current_dtf As Integer 'Number of DTF trips for a SKU on a particular day
Dim strategy As Integer 'Decision Strategy
Sheets("Test_Parameters").Activate
Range("A1").Select
strategy = ActiveCell.Offset(1, 1).Value
y = ActiveCell.Offset(2, 1).Value
x = ActiveCell.Offset(3, 1).Value
num_classes = ActiveCell.Offset(10, 1).Value
Range("C20").Select
ActiveCell.Value = Now()
ActiveCell.Offset(0, -1).Value = ActiveCell.Value
ActiveCell.Value = ""
Sheets("STF").Activate
Range("A1").Select
ActiveCell.Offset(13, 0).Value = 1 'Day of the week is one initially
ActiveCell.Offset(1, 5).Value = 1 'Current Day is one initially
If strategy = 3 Then
For random_setup = 1 To y
Range("A1").Select
this_day = ActiveCell.Offset(random_setup + 1, 3).Value
If this_day = 1 Then
ActiveCell.Offset(510 + one_total, 3).Value = ActiveCell.Offset(random_setup + 1, 4).Value
one_total = one_total + 1
End If
If this_day = 2 Then
ActiveCell.Offset(510 + two_total, 5).Value = ActiveCell.Offset(random_setup + 1, 4).Value
two_total = two_total + 1
End If
If this_day = 3 Then
ActiveCell.Offset(510 + three_total, 7).Value = ActiveCell.Offset(random_setup + 1, 4).Value
three_total = three_total + 1
End If
67
If this_day = 4 Then
ActiveCell.Offset(510 + four_total, 9).Value = ActiveCell.Offset(random_setup + 1, 4).Value
four_total = four_total + 1
End If
If this_day = 5 Then
ActiveCell.Offset(510 + five_total, 11).Value = ActiveCell.Offset(random_setup + 1, 4).Value
five_total = five_total + 1
End If
Next random_setup
End If
For j = 1 To x
For i = 1 To y
Sheets("STF").Activate
Range("A1").Select
If ActiveCell.Offset(i + 1, 3).Value = ActiveCell.Offset(13, 0).Value Then
Range("G1").Select ' Select STF for Day 1 Column
ActiveCell.Offset(i + 1, j - 1).Select 'Activate STF cell for SKU i on day j
Do Until ActiveCell.Offset(0, -j).Value >= 1 'Loop until SKU i's ratio greater than 1 on day j
ActiveCell.Formula = ActiveCell.Value + 1
Loop
Else
Sheets("RTF").Activate ' Activate RTF sheet
Range("C1").Select ' Select RTF Column on day 1
ActiveCell.Offset(i + 1, j - 1).Select 'Activate RTF cell for SKU i on day j
Do Until ActiveCell.Offset(0, -j).Value >= 1 'Loop until SKU i's ratio greater than 1 on day j
ActiveCell.Formula = ActiveCell.Value + 1
Loop
End If
Next i
Sheets("STF").Activate
Range("B1").Select
z = ActiveCell.Value
If z > 0 Then
ActiveCell.Offset(y + 4, j + 4).Value = z 'select cell below sum of DTF trips for day j & write
number of discretionary pick faces on day j
'Demand-based decision
If strategy = 1 Then
Range("A14").Select
day_num = ActiveCell.Value
68
For class = 1 To num_classes
Sheets("STF").Activate
Range("B1").Select
If ActiveCell.Value > 0 Then
Sheets("Test_Parameters").Activate
Range("C13").Select
lower = ActiveCell.Offset(class, 0).Value
upper = ActiveCell.Offset(class, 1).Value
decision_sum = 0
For g = lower To upper
Sheets("STF").Activate
Range("D2").Select
If ActiveCell.Offset(g, 0).Value = day_num Then
current_dtf = ActiveCell.Offset(g, j + 2).Value
Sheets("Receiving").Activate
Range("IV2").Select
If current_dtf < ActiveCell.Offset(g, 0).Value Then
diff = ActiveCell.Offset(g, 0).Value - current_dtf
decision_sum = decision_sum + diff
End If
End If
Next g
Sheets("Test_Parameters").Activate
Range("F13").Select
ActiveCell.Offset(class, 0).Value = decision_sum
Do While ActiveCell.Offset(class, 1).Value > 0
For h = lower To upper
Sheets("STF").Activate
Range("B1").Select
If ActiveCell.Value > 0 Then
Range("D2").Select
If ActiveCell.Offset(h, 0).Value = day_num Then
current_dtf = ActiveCell.Offset(h, j + 2).Value
Sheets("Receiving").Activate
Range("IV2").Select
If current_dtf < ActiveCell.Offset(h, 0).Value Then
Sheets("STF").Activate
Range("B1").Select
ActiveCell.Offset(h + 1, j + 4).Value = ActiveCell.Offset(h + 1, j + 4).Value +
1
End If
End If
End If
Next h
69
decision_sum = 0
For p = lower To upper
Sheets("STF").Activate
Range("D2").Select
If ActiveCell.Offset(p, 0).Value = day_num Then
current_dtf = ActiveCell.Offset(p, j + 2).Value
Sheets("Receiving").Activate
Range("IV2").Select
If current_dtf < ActiveCell.Offset(p, 0).Value Then
diff = ActiveCell.Offset(p, 0).Value - current_dtf
decision_sum = decision_sum + diff
End If
End If
Next p
Sheets("Test_Parameters").Activate
Range("F13").Select
ActiveCell.Offset(class, 0).Value = decision_sum
Loop
End If
Next class
ElseIf strategy = 2 Then
total_allocated = 0
Do While total_allocated < z
Sheets("STF").Activate
Range("B1").Select
SKU = ActiveCell.Offset(2, 0).Value 'SKU number with mininimu ratio = SKU
ratio_check = ActiveCell.Offset(SKU + 1, j + 4).Value 'SKU's current # of STF
Sheets("receiving").Activate
Range("IV1").Select
ratio_on_dock = ActiveCell.Offset(check_sku + 1, 0).Value '# of pallets for SKU received
If ratio_check < ratio_on_dock Then
Sheets("STF").Activate
Range("B1").Select
ActiveCell.Offset(SKU + 1, j + 4).Value = ActiveCell.Offset(SKU + 1, j + 4).Value + 1 'Add
one to SKU's STF
total_allocated = total_allocated + 1
End If
Loop
ElseIf strategy = 3 Then
Range("A1").Select
easy = ActiveCell.Offset(13, 0).Value + 1
If ActiveCell.Offset(13, 0).Value = 1 Then
70
received_skus = one_total
End If
If ActiveCell.Offset(13, 0).Value = 2 Then
received_skus = two_total
End If
If ActiveCell.Offset(13, 0).Value = 3 Then
received_skus = three_total
End If
If ActiveCell.Offset(13, 0).Value = 4 Then
received_skus = four_total
End If
If ActiveCell.Offset(13, 0).Value = 5 Then
received_skus = five_total
End If
For generate_ran = 1 To received_skus
Range("A1").Select
ActiveCell.Offset(509 + generate_ran, easy * 2).Value = Rnd
Next generate_ran
total_allocated = 0
Do While total_allocated < z
Sheets("STF").Activate
Range("A1").Select
ActiveCell.Offset(10, 0).Value = Rnd
random_number = ActiveCell.Offset(10, 0).Value
current_num = 0
current_sku = 0
For num_check = 1 To received_skus
Sheets("STF").Activate
Range("A1").Select
If ActiveCell.Offset(509 + num_check, easy * 2).Value < random_number And
ActiveCell.Offset(509 + num_check, easy * 2).Value > current_num Then
check_sku = ActiveCell.Offset(509 + num_check, easy * 2 - 1).Value
check_dtf = ActiveCell.Offset(check_sku + 1, j + 5).Value
Sheets("receiving").Activate
Range("IV1").Select
on_dock = ActiveCell.Offset(check_sku + 1, 0).Value
If check_dtf < on_dock Then
Sheets("STF").Activate
Range("A1").Select
current_num = ActiveCell.Offset(509 + num_check, easy * 2).Value
current_sku = ActiveCell.Offset(509 + num_check, easy * 2 - 1).Value
71
End If
End If
Next num_check
If current_sku > 0 Then
Sheets("STF").Activate
Range("A1").Select
ActiveCell.Offset(current_sku + 1, j + 5).Value = ActiveCell.Offset(current_sku + 1, j +
5).Value + 1
total_allocated = total_allocated + 1
End If
Loop
End If
End If
Sheets("STF").Activate
Range("B1").Select
ActiveCell.Offset(y + 4, j + 4).Value = z 'write number of discretionary pick faces on day j
Sheets("STF").Activate
Range("F2").Select
ActiveCell.Formula = ActiveCell.Value + 1 'Increment the current Day by one
Range("A14").Select
If ActiveCell.Value = 5 Then 'If day of week = 5, then reset to one
ActiveCell.Value = 1
Else
ActiveCell.Value = ActiveCell.Value + 1 ' Increment Day of week by one
End If
Sheets("forward_inv").Activate
Range("A1").Select
For Forward = 1 To y
Range("A1").Select
ActiveCell.Offset(Forward + 1, j + 1).Activate
Selection.Copy
ActiveCell.Offset(0, 1).Activate
ActiveSheet.Paste
ActiveCell.Offset(0, -1).Activate
ActiveCell.Value = ActiveCell.Value
Next Forward
Sheets("empty_pick_faces").Activate
Range("A1").Select
For Pick_Faces = 1 To y + 2
72
Range("A1").Select
ActiveCell.Offset(Pick_Faces + 1, j).Activate
Selection.Copy
ActiveCell.Offset(0, 1).Activate
ActiveSheet.Paste
ActiveCell.Offset(0, -1).Activate
ActiveCell.Value = ActiveCell.Value
Next Pick_Faces
Sheets("ratio").Activate
Range("A1").Select
For C_ratio = 1 To y
Range("A1").Select
ActiveCell.Offset(C_ratio + 1, j).Activate
Selection.Copy
ActiveCell.Offset(0, 1).Activate
ActiveSheet.Paste
ActiveCell.Offset(0, -1).Activate
ActiveCell.Value = ActiveCell.Value
Next C_ratio
Next j
Sheets("Test_Parameters").Activate
Range("C21").Select
ActiveCell.Value = Now()
ActiveCell.Offset(0, -1).Value = ActiveCell.Value
ActiveCell.Value = ""
End Sub
73
APPENDIX B: DC DEMAND AND RECEIVING DATA
74
Average Daily Demand per Trial
SKU
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
1
322
320
321
321
321
320
319
321
321
322
322
320
320
320
319
321
317
319
319
321
321
319
322
320
320
64
64
65
64
64
64
64
65
64
63
64
64
64
64
64
64
64
64
64
65
64
64
64
64
63
64
64
63
64
64
2
321
318
320
320
319
320
319
319
321
321
320
321
321
320
321
322
322
320
320
320
319
320
319
319
320
65
64
63
63
64
64
64
64
64
64
63
63
64
64
64
63
64
64
64
64
64
65
64
64
63
64
63
65
64
64
3
320
322
321
319
320
322
320
320
321
321
319
321
320
320
320
320
319
318
322
319
320
321
319
320
320
64
64
64
64
64
63
64
63
64
64
64
64
64
63
64
65
64
64
64
65
64
64
63
64
63
64
64
64
64
64
4
320
322
321
319
320
322
320
320
321
321
319
321
320
321
320
320
319
318
322
319
320
320
319
320
320
64
64
64
64
64
63
64
63
64
64
64
64
64
63
64
65
64
64
64
65
64
64
63
64
63
64
64
64
64
64
5
320
322
321
319
320
322
320
320
321
321
319
321
320
320
320
320
319
318
322
319
320
321
319
320
320
64
64
64
64
64
63
64
63
64
64
64
64
64
63
64
65
64
64
64
65
64
64
63
64
63
64
64
64
64
64
1
4
5
5
2
3
4
1
1
1
2
5
3
3
1
5
3
3
4
4
1
4
4
2
3
5
2
5
5
2
3
3
5
1
3
2
5
3
5
3
3
3
2
1
2
2
4
5
4
4
2
1
1
2
4
4
Receiving Day per
Trial
2
3
4
5
3
1
4
1
5
2
2
4
3
3
4
3
1
5
5
1
4
4
2
2
4
4
1
1
2
1
5
2
5
4
2
5
1
3
5
5
5
2
2
3
1
2
3
4
1
1
5
1
1
4
3
1
3
5
2
1
1
1
4
3
5
2
5
5
2
1
1
1
1
2
5
3
3
1
5
2
5
1
2
2
1
4
5
2
2
3
2
2
2
2
1
3
4
5
3
3
4
3
1
3
2
4
5
1
3
5
4
4
1
5
4
5
2
2
3
3
5
4
3
5
4
1
4
4
5
4
1
5
3
5
2
5
5
2
4
3
2
1
4
5
5
5
1
5
4
4
1
5
4
5
3
4
1
5
5
2
3
4
1
3
4
5
3
1
Qty of Receipt per Trial
5
1
4
4
5
5
1
5
4
1
4
2
5
2
3
2
5
1
3
4
5
5
5
2
2
5
5
2
4
2
5
2
4
1
2
1
3
2
4
1
3
4
4
2
2
2
4
3
1
1
2
1
1
2
5
5
1
1613
1602
1604
1604
1603
1600
1595
1607
1605
1609
1609
1600
1601
1602
1595
1607
1587
1597
1596
1603
1606
1593
1613
1598
1602
319
322
323
318
319
321
321
324
323
316
323
321
322
319
321
319
322
318
319
323
322
320
323
321
315
319
319
314
322
320
2
1604
1593
1599
1603
1594
1600
1598
1594
1603
1604
1600
1607
1604
1599
1605
1608
1609
1602
1599
1601
1596
1601
1593
1594
1601
325
322
316
318
321
320
320
321
322
320
318
318
321
321
322
317
322
319
318
321
323
324
320
322
317
318
315
325
321
320
3
1600
1609
1607
1598
1598
1612
1599
1601
1603
1604
1595
1604
1601
1603
1600
1601
1596
1588
1608
1594
1599
1603
1597
1599
1602
320
319
320
320
318
317
319
318
323
320
322
321
322
318
320
324
322
323
320
324
319
322
317
319
317
321
321
321
322
321
4
1600
1609
1607
1598
1598
1612
1599
1601
1603
1604
1595
1604
1601
1603
1600
1601
1596
1588
1608
1594
1599
1603
1597
1599
1602
320
319
320
320
318
317
319
318
323
320
322
321
322
318
320
324
322
323
320
324
319
322
317
319
317
321
321
321
322
321
5
1600
1609
1607
1598
1598
1612
1599
1601
1603
1604
1595
1604
1601
1603
1600
1601
1596
1588
1608
1594
1599
1603
1597
1599
1602
320
319
320
320
318
317
319
318
323
320
322
321
322
318
320
324
322
323
320
324
319
322
317
319
317
321
321
321
322
321
75
Average Daily Demand per Trial
SKU
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
1
64
64
64
64
64
64
65
65
63
64
64
63
64
65
64
64
63
64
64
64
65
64
64
64
63
64
63
64
64
64
64
63
65
65
63
63
63
65
63
64
64
63
64
65
64
16
16
16
16
16
16
16
16
16
16
16
16
16
2
63
64
63
64
64
64
64
64
64
64
64
63
65
65
64
64
65
65
64
64
66
64
63
64
64
64
63
63
63
65
64
64
64
63
64
64
64
64
64
64
65
64
64
65
64
16
16
15
16
16
16
16
16
16
16
16
16
16
3
64
63
64
63
64
63
64
64
64
65
64
64
63
64
66
64
63
64
64
64
64
63
64
64
64
64
64
64
64
64
64
65
64
64
64
64
63
64
64
64
64
64
64
63
63
16
16
16
16
16
16
16
16
16
16
16
16
16
4
64
63
64
63
64
63
64
64
64
65
65
64
63
64
66
64
63
64
64
64
64
63
64
64
64
64
64
64
64
64
64
65
64
64
64
64
63
64
64
65
64
64
64
63
63
16
16
16
16
16
16
16
16
16
16
16
16
16
5
64
63
64
63
64
63
64
64
64
65
64
64
63
64
66
64
63
64
64
64
64
63
64
64
64
64
64
64
64
64
64
65
64
64
64
64
63
64
64
64
64
64
64
63
63
16
16
16
16
16
16
16
16
16
16
16
16
16
1
5
1
1
1
4
3
4
3
5
5
1
4
4
1
2
5
4
2
2
4
4
5
4
4
2
3
4
2
2
1
2
1
5
1
5
3
3
5
3
1
2
3
5
1
3
1
1
4
4
4
1
5
1
2
4
5
1
5
Receiving Day per
Trial
2
3
4
1
3
5
5
4
4
1
2
2
2
1
1
4
2
4
4
4
4
5
4
5
5
5
2
1
4
3
3
1
5
1
4
3
4
5
1
3
1
3
1
4
4
3
3
1
2
4
3
1
5
1
2
4
1
2
4
2
2
2
1
4
4
2
2
2
5
4
2
1
1
2
2
3
3
1
5
4
5
3
3
1
1
4
3
1
3
3
1
2
3
4
3
1
4
3
1
1
4
5
2
2
3
1
5
1
2
4
5
5
1
1
3
2
3
5
4
3
4
5
4
4
1
2
5
2
1
4
5
5
5
4
1
3
4
3
5
2
1
5
5
4
4
3
3
2
4
5
4
2
2
1
2
4
1
4
3
2
5
3
2
2
2
2
4
1
5
1
2
1
3
1
3
3
2
Qty of Receipt per Trial
5
3
1
3
2
4
4
1
4
5
1
5
1
4
4
1
5
2
4
5
2
3
3
1
3
2
2
1
2
3
2
4
4
2
5
2
4
1
5
1
3
1
4
1
5
1
2
3
4
3
5
2
4
1
2
1
4
1
1
1
319
321
322
319
321
323
324
324
317
320
322
315
320
325
323
323
316
320
321
321
323
321
322
320
316
321
316
322
319
321
322
316
324
324
317
315
316
324
316
321
322
318
321
323
323
82
79
80
82
80
81
83
79
80
80
80
82
81
2
315
319
316
321
323
323
320
320
321
318
319
317
327
323
321
320
325
323
319
321
328
321
316
321
321
323
316
317
317
324
323
320
320
317
322
321
319
319
323
320
323
321
320
323
318
80
78
78
79
82
80
80
81
83
80
80
81
82
3
319
317
323
315
319
315
321
320
321
325
323
322
317
323
329
321
316
321
320
318
322
317
323
321
322
322
322
319
319
319
320
324
320
321
322
319
317
323
320
323
319
321
321
316
318
81
81
82
81
80
79
80
80
80
79
82
81
82
4
319
317
323
315
319
315
321
320
321
325
323
322
317
323
329
321
316
321
320
318
322
317
323
321
322
322
322
319
319
319
320
324
320
321
322
319
317
323
320
323
319
321
321
316
318
81
81
82
81
80
79
80
80
80
79
82
81
82
5
319
317
323
315
319
315
321
320
321
325
323
322
317
323
329
321
316
321
320
318
322
317
323
321
322
322
322
319
319
319
320
324
320
321
322
319
317
323
320
323
319
321
321
316
318
81
81
82
81
80
79
80
80
80
79
82
81
82
76
Average Daily Demand per Trial
SKU
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
1
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
17
16
16
16
16
16
15
16
16
16
16
16
16
16
16
16
17
16
17
16
16
16
16
16
16
15
16
17
16
16
16
16
16
17
16
16
16
16
2
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
17
16
16
16
16
16
16
16
16
16
16
16
16
15
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
15
3
16
16
16
16
16
16
15
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
17
16
16
16
16
16
16
16
15
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
17
16
16
16
16
16
16
16
16
16
16
4
16
16
16
16
16
16
15
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
17
16
16
16
16
16
16
16
15
16
15
16
16
16
16
16
16
16
16
16
16
16
16
16
16
17
16
16
16
16
16
16
16
16
16
16
5
16
16
16
16
16
16
15
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
17
16
16
16
16
16
16
16
15
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
17
16
16
16
16
16
16
16
16
16
16
1
3
1
1
1
4
1
5
5
5
1
5
4
4
1
1
1
1
3
3
2
1
3
4
3
3
2
1
3
2
4
2
2
4
2
1
2
4
4
3
1
2
2
1
3
3
4
4
3
5
2
5
1
2
5
1
2
3
5
Receiving Day per
Trial
2
3
4
5
1
3
3
2
2
3
1
2
5
3
1
1
3
3
4
3
1
5
2
2
3
1
3
5
2
5
1
2
4
3
2
2
4
2
1
1
5
2
3
1
4
1
4
5
5
5
4
3
3
1
4
5
1
5
5
2
1
4
5
5
2
5
4
2
3
3
1
3
5
4
5
5
4
3
2
2
4
2
3
5
2
4
1
1
5
3
4
2
1
5
3
2
4
3
3
3
1
4
1
3
4
5
5
2
3
4
5
2
3
5
2
5
3
1
5
4
2
2
3
2
2
3
3
5
5
1
1
2
3
3
3
4
2
5
3
1
2
5
4
4
2
3
4
2
4
2
2
3
1
4
1
2
4
5
1
4
5
2
3
4
2
3
4
2
3
1
3
4
1
1
2
2
2
Qty of Receipt per Trial
5
1
1
3
3
1
1
1
2
5
4
1
4
2
5
5
3
5
3
2
2
1
2
1
5
2
4
1
4
1
2
5
5
4
4
3
3
4
2
4
5
2
1
5
3
5
4
1
2
2
3
1
3
4
5
1
2
3
4
1
80
80
82
80
80
81
80
80
81
81
80
82
81
82
79
81
81
80
83
81
85
82
82
81
82
81
77
80
81
80
82
79
80
83
82
80
83
82
84
80
81
82
82
82
81
77
79
84
81
80
80
80
81
83
81
80
82
81
2
79
79
82
81
80
80
82
80
80
82
81
80
82
82
79
81
79
83
81
81
80
81
79
80
81
84
80
82
79
80
82
80
81
78
81
81
81
81
78
82
81
81
79
81
80
82
81
83
78
80
81
81
78
79
79
81
81
78
3
80
82
81
81
80
78
78
81
80
81
80
82
82
80
81
81
80
80
83
80
82
80
83
79
79
83
81
80
81
82
77
81
78
82
80
83
80
80
81
79
82
80
81
81
81
80
82
83
78
80
79
80
82
81
80
79
80
80
4
80
82
81
81
80
78
78
81
80
81
80
82
82
80
81
81
80
80
83
80
82
80
83
79
79
83
81
80
81
82
77
81
78
82
80
83
80
80
81
79
82
80
81
81
81
80
82
83
78
80
79
80
82
81
80
79
80
80
5
80
82
81
81
80
78
78
81
80
81
80
82
82
80
81
81
80
80
83
80
82
80
83
79
79
83
81
80
81
82
77
81
78
82
80
83
80
80
81
79
82
80
81
81
81
80
82
83
78
80
79
80
82
81
80
79
80
80
77
Average Daily Demand per Trial
SKU
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
1
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
15
16
16
16
16
16
16
16
16
16
16
15
16
2
16
16
16
16
16
16
17
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
3
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
4
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
5
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
1
1
1
3
4
2
5
2
4
1
5
1
2
5
3
4
4
1
2
1
2
1
5
1
2
2
1
1
4
4
2
1
2
2
3
1
5
1
4
4
4
5
2
1
4
4
4
3
3
4
1
3
3
5
1
5
3
5
4
Receiving Day per
Trial
2
3
4
4
5
3
3
4
5
3
4
2
5
3
5
5
5
2
2
5
1
5
5
5
5
5
5
5
2
3
3
1
1
3
1
3
5
3
4
3
4
2
1
3
1
4
5
1
3
3
1
5
1
3
4
2
5
3
3
1
4
3
2
4
4
2
1
1
5
4
5
1
5
4
5
4
2
5
3
2
4
2
2
2
3
5
4
5
1
1
5
1
1
1
5
3
5
4
3
5
5
3
5
2
2
4
4
5
1
4
2
1
4
3
5
5
5
4
3
4
2
3
1
5
3
5
2
4
3
2
3
2
4
3
3
5
2
3
1
3
5
1
3
3
3
3
2
2
4
2
1
1
1
1
4
5
2
4
4
2
2
3
5
4
1
4
3
1
1
5
4
3
2
3
2
4
3
Qty of Receipt per Trial
5
2
1
2
2
4
2
2
3
2
1
5
1
2
2
1
4
1
1
5
3
2
1
4
3
3
2
3
1
2
1
3
3
3
2
3
4
3
4
1
5
2
2
2
4
5
5
3
5
1
3
3
5
5
1
3
4
4
3
1
80
80
81
78
81
81
79
81
82
80
79
80
79
82
78
81
78
80
79
79
80
81
81
82
81
78
82
81
81
81
81
79
81
81
80
80
81
80
80
81
80
83
82
80
81
78
80
80
79
82
83
79
80
83
80
82
77
79
2
80
83
81
79
81
78
83
81
79
81
82
80
83
82
81
81
81
80
81
81
83
82
81
80
82
83
78
80
82
81
82
83
80
80
80
79
80
80
81
81
81
82
81
81
81
79
81
82
79
81
81
82
82
81
81
82
83
81
3
80
80
79
82
83
80
80
81
79
79
80
81
82
82
80
80
78
81
81
80
80
81
82
80
81
82
82
82
82
83
80
79
81
80
81
80
80
78
80
80
80
81
79
80
81
82
81
81
81
81
80
81
79
82
81
83
81
80
4
80
80
79
82
83
80
80
81
79
79
80
81
82
82
80
80
78
81
81
80
80
81
82
80
81
82
82
82
82
83
80
79
81
80
81
80
80
78
80
80
80
81
79
80
81
82
81
81
81
81
80
81
79
82
81
83
81
80
5
80
80
79
82
83
80
80
81
79
79
80
81
82
82
80
80
78
81
81
80
80
81
82
80
81
82
82
82
82
83
80
79
81
80
81
80
80
78
80
80
80
81
79
80
81
82
81
81
81
81
80
81
79
82
81
83
81
80
78
Average Daily Demand per Trial
SKU
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
1
16
16
16
17
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
2
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
16
17
16
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
16
16
17
16
16
16
16
16
16
16
16
16
16
16
17
16
16
16
16
16
16
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
4
16
16
17
16
16
16
16
16
16
16
16
16
16
16
17
16
16
16
16
16
16
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
5
16
16
17
16
16
16
16
16
16
16
16
16
16
16
17
16
16
16
16
16
16
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
1
4
5
2
1
5
5
2
2
2
1
3
4
5
5
1
4
4
1
5
1
3
4
5
3
5
1
2
4
2
3
4
3
1
1
3
2
3
1
2
5
4
1
2
3
2
4
3
4
1
5
4
3
3
5
3
Receiving Day per
Trial
2
3
4
2
2
3
1
1
4
3
4
5
3
5
2
3
1
2
4
3
3
3
1
5
3
2
3
3
4
5
4
3
4
1
5
2
4
1
2
1
4
3
4
1
2
3
3
1
4
1
2
3
3
5
5
1
1
1
4
4
1
1
2
5
2
4
4
2
3
2
3
2
3
1
2
5
3
3
3
2
1
2
3
1
4
2
1
2
4
1
1
4
1
1
1
4
1
5
3
1
5
4
2
4
5
2
3
3
4
4
2
1
2
1
5
2
5
5
5
4
3
1
4
5
2
2
3
5
1
3
5
5
5
3
1
3
5
5
1
5
5
3
3
2
5
4
2
1
2
1
2
3
5
5
2
3
4
3
2
5
4
2
4
1
3
5
2
3
Qty of Receipt per Trial
5
3
2
1
4
4
3
4
2
5
5
3
5
5
1
5
3
5
3
5
1
3
5
4
1
4
2
5
4
5
2
5
2
1
2
4
3
1
5
5
4
2
3
1
2
1
1
5
4
2
4
4
5
5
4
4
1
80
81
81
83
80
82
81
82
82
80
79
81
80
81
81
81
81
80
81
79
81
17
17
16
16
17
17
16
16
17
16
16
16
18
16
16
16
16
16
16
16
17
17
17
17
16
17
17
16
17
16
17
16
17
17
2
82
80
82
80
79
80
79
80
79
80
83
82
79
78
82
83
81
83
82
83
81
17
16
17
16
16
16
16
18
17
16
16
16
16
17
16
18
17
17
16
16
17
17
17
16
16
16
16
16
17
16
17
16
17
16
3
82
79
83
80
80
79
81
81
81
81
80
82
81
82
84
81
81
82
81
80
80
16
17
16
15
17
17
16
17
17
16
17
15
17
16
17
16
17
17
15
16
17
17
17
16
16
17
16
17
17
16
17
16
17
16
4
82
79
83
80
80
79
81
81
81
81
80
82
81
82
84
81
81
82
81
80
80
16
17
16
15
17
17
16
17
17
16
17
15
17
16
17
16
17
17
15
16
17
17
17
16
16
17
16
17
17
16
17
16
17
16
5
82
79
83
80
80
79
81
81
81
81
80
82
81
82
84
81
81
82
81
80
80
16
17
16
15
17
17
16
17
17
16
17
15
17
16
17
16
17
17
15
16
17
17
17
16
16
17
16
17
17
16
17
16
17
16
79
Average Daily Demand per Trial
SKU
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
1
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
2
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
4
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
5
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
1
4
5
5
5
5
3
2
4
3
1
1
3
5
2
3
1
3
3
1
4
4
2
1
1
5
4
1
2
1
3
4
4
3
2
5
1
3
1
4
4
1
1
5
5
5
2
2
5
4
3
5
4
5
4
4
1
Receiving Day per
Trial
2
3
4
2
2
4
5
2
3
3
3
2
1
5
5
3
3
1
3
3
2
1
2
1
2
4
3
5
3
4
4
1
3
5
2
4
5
3
2
2
5
5
3
3
2
3
2
3
1
5
5
2
3
5
1
2
5
2
5
5
1
3
5
2
2
4
3
2
3
4
3
3
2
3
2
2
2
4
2
3
4
3
1
2
2
2
4
3
5
1
3
4
2
2
3
4
5
3
3
2
2
3
1
5
4
3
3
2
1
3
3
3
4
5
2
5
2
3
2
2
1
4
4
4
5
2
3
3
5
5
2
2
3
1
2
4
5
5
1
3
2
4
4
3
3
4
4
5
2
4
5
2
3
3
1
2
5
4
2
2
5
1
2
4
4
5
1
1
5
2
1
Qty of Receipt per Trial
5
5
5
3
2
2
3
5
3
1
1
5
1
5
2
2
1
1
3
4
3
2
3
4
4
1
3
2
5
3
5
3
2
5
1
3
4
1
4
3
1
1
1
1
3
5
5
4
5
5
5
2
2
5
5
2
4
1
16
16
15
17
16
16
16
17
17
16
15
16
16
17
16
16
16
18
16
16
17
15
16
16
17
17
17
17
16
17
16
16
17
17
16
16
15
16
16
16
16
17
17
17
16
16
17
17
16
17
16
16
17
17
16
17
2
17
18
16
16
16
17
17
17
16
16
16
16
16
16
17
16
17
16
17
16
17
16
16
17
17
16
17
17
16
17
17
17
17
16
17
17
17
17
16
17
17
17
17
15
16
16
17
16
16
16
16
16
17
17
16
16
3
16
16
16
18
17
17
17
17
17
17
15
16
17
16
17
17
16
17
15
16
17
15
15
16
16
16
18
17
16
15
17
17
16
17
18
16
17
17
16
17
17
16
17
17
16
16
17
16
16
16
18
17
16
16
16
17
4
16
16
16
18
17
17
17
17
17
17
15
16
17
16
17
17
16
17
15
16
17
15
15
16
16
16
18
17
16
15
17
17
16
17
18
16
17
17
16
17
17
16
17
17
16
16
17
16
16
16
18
17
16
16
16
17
5
16
16
16
18
17
17
17
17
17
17
15
16
17
16
17
17
16
17
15
16
17
15
15
16
16
16
18
17
16
15
17
17
16
17
18
16
17
17
16
17
17
16
17
17
16
16
17
16
16
16
18
17
16
16
16
17
80
Average Daily Demand per Trial
SKU
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
1
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
2
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
4
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
5
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
1
2
5
3
3
3
4
3
2
3
4
3
3
5
2
3
4
3
5
2
2
4
5
1
5
3
4
5
1
2
4
4
3
4
1
2
5
2
4
2
4
4
1
3
3
4
5
2
1
2
2
1
4
2
3
4
Receiving Day per
Trial
2
3
4
1
2
1
1
3
1
2
5
4
5
5
1
3
3
1
1
2
4
2
5
3
5
2
4
4
2
4
1
2
4
5
4
2
3
5
1
3
4
3
4
3
2
3
3
3
2
2
5
4
2
2
5
2
5
3
1
5
4
4
3
5
4
3
4
2
1
1
3
3
5
3
4
5
4
4
5
3
4
1
5
1
2
3
4
1
5
5
4
3
3
3
5
2
4
1
3
2
2
2
5
5
5
5
1
1
1
4
1
3
1
4
1
1
4
4
5
1
3
2
1
1
1
4
3
4
1
1
4
5
3
3
5
1
5
4
2
5
3
1
4
1
2
5
4
2
4
4
3
3
2
1
5
1
4
5
2
3
5
5
2
3
2
1
4
2
Qty of Receipt per Trial
5
1
2
4
3
5
1
2
4
4
1
4
3
4
2
2
4
3
4
5
1
2
3
3
1
3
3
1
4
4
5
1
4
4
5
1
2
3
2
5
2
2
1
4
1
2
4
3
4
3
2
2
4
3
3
5
1
16
16
17
17
16
17
17
17
16
17
16
16
17
17
16
16
16
16
17
17
17
17
17
17
16
17
16
17
17
16
17
16
16
17
17
17
17
16
16
16
16
16
15
16
15
16
17
17
16
17
16
16
17
16
17
2
17
17
17
16
16
15
17
15
16
16
15
17
17
17
17
17
15
16
17
16
17
17
16
17
16
16
17
17
17
16
16
16
17
16
17
16
17
17
16
16
17
16
15
16
17
16
16
17
16
16
16
17
16
17
15
3
16
17
16
17
16
16
16
17
17
17
16
17
16
17
17
16
16
17
16
16
17
17
17
17
16
16
17
17
16
16
15
17
17
17
17
17
16
15
15
18
16
17
18
17
17
16
17
16
17
17
16
16
17
17
16
4
16
17
16
17
16
16
16
17
17
17
16
17
16
17
17
16
16
17
16
16
17
17
17
17
16
16
17
17
16
16
15
17
17
17
17
17
16
15
15
18
16
17
18
17
17
16
17
16
17
17
16
16
17
17
16
5
16
17
16
17
16
16
16
17
17
17
16
17
16
17
17
16
16
17
16
16
17
17
17
17
16
16
17
17
16
16
15
17
17
17
17
17
16
15
15
18
16
17
18
17
17
16
17
16
17
17
16
16
17
17
16
81
Average Daily Demand per Trial
SKU
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
1
3
4
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
2
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
4
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
5
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
1
4
5
3
2
1
5
4
2
1
3
3
5
3
3
5
4
5
4
3
1
1
4
3
1
1
3
1
1
3
2
3
3
3
2
3
5
3
2
5
3
3
2
1
1
4
3
3
2
3
3
3
5
2
4
5
1
2
Receiving Day per
Trial
2
3
4
1
3
3
5
1
4
1
1
4
3
4
4
3
4
3
1
4
2
2
1
5
1
4
2
3
4
2
1
4
5
3
3
1
2
5
4
3
2
3
2
1
3
1
3
5
3
1
1
2
4
3
2
3
5
3
1
3
1
4
1
4
3
5
2
5
5
2
4
1
1
5
3
3
1
1
4
1
5
5
1
1
1
1
3
2
2
3
4
5
4
3
4
4
4
2
2
4
3
4
1
3
4
2
4
2
2
1
2
5
1
4
2
1
2
1
3
2
4
5
5
1
4
3
2
3
2
4
4
2
5
4
4
2
2
1
5
4
4
1
1
1
2
4
2
3
4
1
1
3
1
1
4
1
3
3
4
1
5
5
3
2
5
1
3
5
2
1
1
2
5
2
Qty of Receipt per Trial
5
4
5
3
4
1
1
3
4
5
4
5
2
2
2
1
3
3
4
4
3
5
5
1
1
4
3
5
4
4
5
1
1
2
2
3
2
1
2
4
2
4
4
3
2
5
4
1
4
5
4
2
1
4
2
5
1
3
1
16
18
16
16
17
16
17
16
17
17
17
16
17
16
16
16
15
16
17
16
16
16
16
17
17
18
17
16
16
16
17
17
16
16
17
17
17
16
16
17
16
16
18
16
16
16
17
15
17
16
16
17
16
16
16
17
17
2
17
17
17
16
17
17
16
16
16
17
16
17
17
16
17
16
16
17
17
17
17
16
17
16
16
17
16
16
17
17
17
17
15
16
18
16
16
17
15
17
16
17
17
17
16
17
17
17
16
16
17
17
16
16
16
17
15
3
18
17
17
16
17
17
17
15
17
16
17
16
17
16
16
16
17
17
16
17
18
16
17
17
16
16
16
17
18
17
18
17
16
16
17
17
16
17
16
17
17
16
16
17
17
16
16
16
17
17
16
16
17
17
16
16
17
4
18
17
17
16
17
17
17
15
17
16
17
16
17
16
16
16
17
17
16
17
18
16
17
17
16
16
16
17
18
17
18
17
16
16
17
17
16
17
16
17
17
16
16
17
17
16
16
16
17
17
16
16
17
17
16
16
17
5
18
17
17
16
17
17
17
15
17
16
17
16
17
16
16
16
17
17
16
17
18
16
17
17
16
16
16
17
18
17
18
17
16
16
17
17
16
17
16
17
17
16
16
17
17
16
16
16
17
17
16
16
17
17
16
16
17
82
Average Daily Demand per Trial
SKU
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
1
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
2
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
4
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
5
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
1
4
1
4
2
4
2
4
1
1
5
3
4
2
4
3
1
4
4
1
1
3
4
2
4
5
3
1
5
2
5
5
2
1
4
1
1
1
1
5
3
2
3
4
2
1
3
1
2
Receiving Day per
Trial
2
3
4
5
2
5
5
5
4
2
2
3
4
1
5
5
1
2
3
5
3
3
4
3
4
2
2
2
3
5
5
4
4
1
5
1
5
4
4
5
2
3
1
5
5
1
5
2
3
2
5
4
4
3
5
2
4
2
3
1
1
4
1
4
3
5
3
1
2
3
1
5
1
5
4
5
1
2
2
4
2
3
5
4
4
1
3
3
4
1
2
5
1
1
2
2
4
3
3
1
3
5
4
4
1
2
1
1
4
3
1
5
4
3
3
2
2
4
5
1
4
1
2
1
1
5
1
2
1
5
2
4
1
4
1
5
2
3
3
1
1
5
1
5
2
4
3
Qty of Receipt per Trial
5
4
5
4
1
5
4
5
2
3
4
1
3
4
3
1
5
5
5
2
3
4
2
3
3
3
1
1
2
3
1
3
5
4
3
2
5
2
1
4
2
3
2
5
5
2
5
1
5
1
18
17
17
17
16
17
16
16
17
17
18
16
17
17
16
16
17
17
16
16
17
17
16
16
17
16
17
18
17
17
17
17
16
16
17
17
16
17
16
16
17
15
17
16
17
16
17
17
2
16
17
17
16
16
17
16
16
18
16
17
16
17
17
16
17
17
16
16
17
18
17
17
16
16
17
16
17
16
16
17
17
17
16
17
17
17
16
17
16
16
17
16
16
16
17
17
16
3
16
17
16
16
17
16
17
18
16
17
16
16
17
17
16
15
17
17
17
16
17
17
17
17
16
16
16
17
16
16
17
17
17
17
16
17
16
17
17
17
16
17
16
16
16
17
17
16
4
16
17
16
16
17
16
17
18
16
17
16
16
17
17
16
15
17
17
17
16
17
17
17
17
16
16
16
17
16
16
17
17
17
17
16
17
16
17
17
17
16
17
16
16
16
17
17
16
5
16
17
16
16
17
16
17
18
16
17
16
16
17
17
16
15
17
17
17
16
17
17
17
17
16
16
16
17
16
16
17
17
17
17
16
17
16
17
17
17
16
17
16
16
16
17
17
16