[11] DONSEL AAR WOENS EL BR OEKMEULEN FRANS OO –
2005
•
Large percentage (78%) of young female associates
[8] COOPER BAR ON L EVY SWISHER GOGOS – 1999
Title: Improvement opportunities in Retail Logistics
An overview is given of improvement opportunities in Retail Logistics (specifically,
inventory replenishment in stores), which can be used to enhance Automated Store
Ordering (ASO) systems.
Title: PromoCast: A new Forecasting Method for Promotion Planning
Abstract:
This article describes the implementation of a promotion-event forecasting system,
PromoCast', and its performance in several pilot applications and validity studies. Pilot
studies involved retail grocery chains with 95 to 185 stores per trading area. The goal was
to provide short-term, tactical forecasts useful for planning promotions from a retailer's
perspective. Thus, the forecast system must be able to handle any of the over 150,000
UPCs (Universal Product Codes) in each store's item master file, and must be scalable to
produce approximately 800,000,000 forecasts per year across all the retailers served by
efficient marketing services, inc. (EMS). This is a much different task than one that
confronts a manufacturer, even one with a broad product line. Manufacturers can benefit
from custom modeling in a product line or category. Retailers need a production system
that generates forecasts that help promotion planning. Marketing scientists have typically
approached promotion analysis from the manufacturer's perspective. The objective is to
encourage marketing scientists to rethink promotion analysis from a different
perspective.
Logistic decisions taken by the retailer can be improved by increasing:
 Level of differentiation when controlling the operations,
 Level of sophistication in the Decision Support Systems,
 Level of integration of multiple decisions (made by the retailer or its supply chain).
Level of differentiation when controlling the operations
Five main product categories are distinguished for the level of differentiation, with
opportunities for improvement per category summarized:
1) Phasing in / out items,
2) Promotional items,
3) Purchasing driven items,
4) Capacity driven items,
5) Regular items.
Improvements could be made at each of the five product categories:
1) Phasing in / out items,
Items with a short product life cycle.
 Using similarity in forecasts made by different individual people as an indicator of
forecast accuracy when no sales data are available yet,
 Using early sales data to improve demand forecasts in the case of style goods,
 Using repeat rate information from customer cards to improve demand forecasts
when new products are introduced; (compare info with similar product launches)
 Using optimal markdown policies (for leftovers) to reduce the risk of obsolescence.
2) Promotional items
Items that are part of the regular assortment, but either offered temporarily at a reduced
price or offered at the regular price but with additional visibility (e.g. more facings in the
main aisle (gang) of the supermarket).
 Using marketing intelligence and/or econometric models to forecast demand for the
promotion items and their substitutes (instead of exponential smoothing or moving
average which is typical for non-promotion items); take into account price-elasticity
 Using a push-strategy with two waves (alpha policy = two waves of items pushed in
the store: first wave is normally around 70-80% of stock, second wave is variable due
to the early sales data and repeated buying-data of the first wave)
 Coordinating the promotion with the supplier (more promotion products, less
substitution products)
3) Purchasing driven items
One-time-items that are not part of the regular assortment, bought by the procurement
departments: they spotted a special buying or selling opportunity (Eastern, Xmas, etc).
 For the distribution of these items to the stores, a push-strategy with two waves, like
the alpha-policy, may be adopted.
4) Capacity driven items
Items used by the Operations Department to smooth handling and/or transportation
capacities.
 Review period for items with sufficient excess shelf space may be increased by
decreasing the delivery frequency. Lower ordering-frequency (for example weekly),
leads to higher lot sizes and therefore higher handling efficiency (lower costs)
 Walking distance for order pickers at the DC could be reduced substantially, with the
prerequisite that the item has excess shelf space in the relevant stores.
5) Regular items
Items that are not phasing in or out, not on promotion nor
purchasing or capacity driven.
 Trade-off between inventory holding costs and customer service; handling costs
outweigh inventory holding costs for regular items usually
 ASO: (R,s,nQ), Review period, service level, n*Q items with Q is case pack size
 Differences in Review period for perishables and non-perishable items: the waste of
perishables can be reduced by decreasing the review period, i.e. increasing the
delivery frequency.
 Other options to reduce waste: reduction of lead-time (e.g. cross docking), keeping
average sales per item relatively high, using customer willingness to substitute.
 ASO (=Automatic Store Ordering) systems, are preliminary designed for nonperishables and cannot easily cope with substitution effects: e.g. products like bread:
there is a high substitution effect, since you choose ‘one of five varieties of wheat
bread’ instead of e.g. backordering your absolute favorite type of bread.
Level of Sophistication in Reorder Systems
Five levels of sophistication are distinguished with respect to:
1) Level of Automation (some products are still ordered manually),
2) Quality of Input Data (one of the main problems, is that sales data (and so also
inventory data), is highly inaccurate, e.g. the cashier may scan a banana yoghurt
twice, when one banana yoghurt and one strawberry yoghurt of the same brand and
price are bought by the customer. This can be improved by register rules or
electronic identification),
3) Intelligence in setting logistic parameters in the reorder system (reorder level and
order quantity; can be fixed or varies because of f.e. seasonality or substitution
effects),
4) Ability to visualize economic tradeoffs,
5) Ability of the personnel to make decisions or to evaluate proposed decisions of the
system.
Note that inserted parameters in an ASO are fixed. For instance, the demand of ovenbuns increases just before eastern: a seasonality effect in ASO does not take into account
without interference of personnel (or a programmed historical learning curve over
multiple years in the source code of course).
Level of integration of multiple decisions (made by the retailer or its supply chain)
Decisions with respect to inventory and capacity management often affect many different
performance indicators or organizational units. Often only partial effects are taken into
account. The quality of decision making can be improve by increasing the level of
integration, three types:
Integration of all relevant performance indicators in the supply chain (previously:
EOQ, now found that handling costs are far more important, also on DC-level)
Integration of decisions made at different organizational units (decisions of
Marketing and Operations sometimes interdependent while not taken into account:
allocated shelve space versus reorder level)
Integration or coordination of decisions made at different hierarchical levels
(different strategies in retail chain if for example on higher level low cost strategy is
important while a store reorders a lot for a high customer service level)
Conclusion
Customer service and capacity utilization in retail chains can be increased by improving
the logistic decisions of the retailer. New technologies help to improve decisions, by
increasing the three mentioned levels.
A final remark: importance of labor costs, since they outweigh holding costs; major focus
of top management should be on how to improve labor efficiency; little research is done
in this area.
Mechandise
assortment
Stores in High-end shopping
streets
Large # cat’s, few #
SKU per cat.
Limited # cat’s, few #SKU per
cat.
Low; EDLP
Affordable exclusivity; high, but
rel. mod. High.
Limited 𝑃2
Limited 𝑃2: OOS may lead to
scarcity-perception
Same as Zara
Basic, special
products
Pricing
Customer Service
Store & design
display
Communication
Mix
-
-
Zara
Freestanding stores
Location Strategy
TV & Newspaper ads.
CBLSG’99 show:
 The value of using promotion-event data,
 How tactical forecasts based on these data can directly impact the bottom line of
grocery retailers,
 How store by store forecasts can help retailers with problems of running out of stock
or overstocking.
Introduction:
The rapid diffusion of scanner technology over the past two decades has helped foster
the belief that this vast information resource can be harnessed to make accurate
promotion planning a routing endeavor. The most sophisticated practice for an upcoming
promotion was to order the quantity that was ordered chain-wide for the last like
promotion. Even if management could accurately forecast aggregate sales for an
upcoming promotion, the absence of a store-by-store forecast would be costly. Our
model captures store-specific information for an item that is valuable in developing not
just chain-level forecasts, but store-by-store allocation policies. Fundamental planning
simply involves being able to do a short-term, tactical forecast of how much each store in
a grocery chain’s trading area will sell under a given combination of marketing efforts for
an item. Promotion-event data: most useful because it provides a complete census of
store data that directly apply to the managerial decision, while shopping-trip data provide
sample data that have to be dramatically transformed to answer the simple question of
how much product to order for an upcoming event. With a great deal of effort, one can
make store-tracking data look more like promotion-event data. Since promotion-event
data are available there is no need to bother transforming store tracking data. The unit of
brand aggregation is also an issue. The basic task is to forecast the results of a planned
promotion for any of the over 150,000 UPCs in any store (within a chain), for any
particular Start Date in the year, using the information available from over 20,000,000
historical promotion events in a retail chain in a trading area. Note that we sample
promotion events (the basic unit for which we wish a tactical forecast) rather than sample
items.
Method:
The obvious strategy is to ask “What information is relevant to any promotion event?”
and then to save and use that information. Three perspectives help us understand what
information is relevant:
1. Promotional mix (combination of price-cuts, ads and displays)
2. Item itself as viewed by its promotion history (average same-store sales of the item
on matching ad and display conditions, average same-store sales of the item on all
promotions, average chain-wide sales of the item on matching ad and display
conditions, and average chain-wide sales of the item on all promotions)
3. Store’s historic relation with a particular style of promotion. (as historical average
sales increased, so did the residuals, therefore we added indicators of these
conditions and the interactions of them; the review of residuals also revealed a
within-store pattern) One natural benchmark is how much better our forecasts are
than the historical averages for matching ad and display conditions. We will first go
through the model specifications and then use this benchmark to evaluate our
tactical forecasting model.
Seasonality:
Our seasonality adjustment operates at the sub-commodity level. The approach to special
seasonal influences used in this forecasting model involves leaving out specific weeks
when special events tend to boost sales. Slow moving items: Slow moving items simply
do not respond as strongly to the promotional effort as do faster-moving items. To avoid
the damping of promotion sensitivity that might result from using a single model to
reflect such a heterogeneous response pattern, we decided to calibrate different
parameters for slow movers versus standard movers. The effect of duration: We expect
to sell more on a promotion of longer duration. However, retailers have policies on how
they promote and which items they place on what style of promotion. We should look at
the data before we form our expectations. The possible endogeneity between duration
and promotion policy was one of the factors which persuaded us to set up separate
models for the four primary planning periods. As a result, instead of one promotionresponse model, we now have eight (four planning periods by fast-versus-slow movers).
The separation into eight models also makes it easier to detect when not to make a
forecast.
Model and results:
CBLSG99 used many historical averages from these databases to build a 67-variable,
regression-style model. The forecast incorporates a simple bias correction needed when
using a log-transformed dependent variable (the natural log of total unit sales). They
argue that the historical averages matching the planned ad and display conditions provide
a benchmark superior to the widely used "base-times-lift" method. When aggregated into
case units (the natural unit for product ordering), 69% of the forecasts in our first
validation study were within ± one case compared to 39% within ± one case using the
appropriate historical averages. We report the results of two over-time validity studies
that reflect the value of our model for retailers. Model assumption: all historical
information available.
Discussion:
CBLSG99 compared the forecast accuracy with the historical averages that best match the
promotional conditions for each particular item. Since ordering is generally done in case
units, an absolute yardstick for assessing forecast accuracy is the number of case errors
incurred. A case error means, If one misses a forecast by a single unit, but that unit error
requires ordering another case (resulting in ordering one too many cases), then one has a
one case error. If one misses a forecast by 11 units, but still has the correct case order,
then no case error is incurred.
Longitudinal cross-validation: Two cross-validations were undertaken to assess forecast
accuracy in contexts closer to real application:
1. forecasts across trading areas and over time.
2. longitudinal cross-validation as a worst case scenario.
[26] ZARA CASE – INDITEX
Title: Zara Case Description
Walmart
From the retailer's point of view the "planning unit" is the promotion event. Neither
weekly store-tracking data nor shopping-trip data from consumer panels are easily
aggregated to reflect total sales during a promotion event. We describe the promotionevent databases and the statistical model developed using these databases. The data are
the strategic asset. Our goal is to help retailers use their data to increase the profitability
of promotions. We have data on the performance of each UPC in each store under a
variety of promotion conditions, on each store's adeptness at executing various styles of
promotions, as well as on chain-wide historical performance for each UPC.
displays
for
TV & Newspaper ads
Inditex is owner of Zara; international competitors are H&M, GAP and Benetton
compression of cycle times is enabled by improvements in information technology
and encouraged by shorter fashion cycles and deeper markdowns, particularly in
women’s wear
Zara shows that strategic imperatives depends on how a retailer wants to create and
sustain a competitive advantage through its cross-border activities
Zara limits the number of markdowns (= prijsreductie) by only having 1 DC (400,000m2),
although their stores are located in every continent. By thus pooling the central inventory
and by keeping most production as close as possible to the DC, the lead times are short,
thus limiting the markdowns. By only opening stores in high‐end high‐traffic shopping
streets, items can be sold relatively easy, thus limiting the markdowns. By not aiming for
very high target fill rates for the fashionable part of the assortment, also the markdowns
are limited.
Brands mapped at dimensions Fashion x Price:
Er worden van Inditex alleen cijfers en informatie over het boekjaar 2001 gegeven:
 Founded in ’63 (Zara sinds ‘75 in La Coruña)
 €3250 MLN operating revenues, €340MLN net Income. (Note: H&M, Gap of
Benneton hebben een hogere omzet, maar een negatieve winst zelfs: doen ze best
goed dus).
 Mutatie van market value in een jaar: +47%.
 26,724 employees, 78% women, 10,919 of 26,724 abroad.
 Operational in 39 countries (1300 stores of Inditex).
Workforce distribution: Over 80% of Inditex’ employees are engaged in retail stores,
8.5% in manufacturing, the remainder for operations, i.e. design, logistics, distribution,
and headquarter activities.
Capital Expenditures: 80% on new-store openings, 10% on refurbishing, 10% on
operations. Planning for the year 2002 requests for capital expenditures of 510-560
million euros, for which 230-275 stores could be opened. (snelle rekensom: 80% *
€535MLN/252.5 = €1.7 MLN capital expenditures for opening 1 new store: rough
averages).
The founder of Zara, i.e. Amancio Ortega Gaona, was a gadgeteer by inclination. He
already bought his first computer in 1976, to optimize operations regarding sales and
refurbishments. With just four factories and two retail stores, he saw that his store data
‘requested’ other goods, than what was being produced and shipped from the factories
to the stores. This characteristic of his personality made him found Inditex in 1963, after
he experienced how costs are allocated and what production times are present
throughout the supply chain of a regular apparel shop.
After having penetrated every city in Spain with more than 100,000 inhabitants with at
least one Zara store (1989), Zara began expanding outside of Spain.
The global apparel chain, a prototype of a buyer-driven global chain (apparel=kleding), in
which profits derived from “unique combinations of high-value research, design, sales,
marketing, and financial services that allow retailers, branded marketers, and branded
manufacturers to act as strategic brokers in linking overseas factories” with markets.
Differences between Zara and close competitors. Zara versus: (yes: Zara is being
compared, not Inditex).
Gap: big player in Japan: 86% of international expansion of all store locations outside
North America. Three clothing formats (banana republic, Old Navy, The Gap), without a
clear fashion positioning had started to take toll globally.
H&M: all production outsourced to European suppliers, resulting in relatively long lead
times compared to Zara’s. Single format clothing business versus Inditex’ multiple
formats. 60% less clothing designers compared to Zara, less refurbishments in stores, and
H&M has slightly lower prices.
Benetton: Very controversial advertising, production sold through licensees instead of
normal product sales. Over 5500 third party stores sold Benetton products, and 100 own
Benetton Megastores, in 2001.
Zara’s business system:
Overall: Zara maintains 11,000 (internally produced!) distinct items (hundreds of
thousands unique SKU’s when size and color are taken into account), whilst key
competitors maintain about 2,000 – 4,000 distinct items. Quick recap: Zara is part of
Inditex, which has over 60 companies with several brands as displayed in the Figure with
four quadrants above! Also, Zara spends just 0.3-0.4% of total revenues on media
advertising, whereas the three above spends about 3-4%.
Operations & Distribution:
Zara is almost finished with building a second DC, with an extra 120,000m2 of capacity.
Location: Zaragoza, (northeast of Madrid, Spain). Close to the airport, with ample
possibilities w.r.t. the railway and road network available.
Most important according to lecture slides 2012: ‘Quick to adapt to new trends’ and
‘Affordable exclusivity’ Pricing strategy implies a moderate-cost-fast-supply-chain:
•
1 DC, Regional production near DC and frequent parcel distribution to avoid long
leadtimes -> high responsiveness and less markdowns
•
Only stores in high-end high-traffic shopping areas (to limit markdowns)
•
Low customer service level (to create ‘sense of scarcity/exclusivity’ and to limit
markdowns)
Limitations and Implications:
The limitations and implications of this planning tool for managerial decision making
concerning stocking levels are discussed. Whenever historical data are the strategic asset
we face inherent limitations. Our model does not forecast new products. The forecast
error increases when an existing product is promoted in a new way. Over 99.5% of the
time, we have full data from which to create a forecast. However, with a database for a
typical chain market containing over 20 million promotion events in the 30-month time
frame we use, 100,000 events have less than ideal data. The breadth of the database
(typically 150,000 UPCs) makes it impractical to in-corporate data on competitive
offerings.
CBLSG99 finds that regression-style modeling is not adept at incorporating in-formation
on the 1,200 sub commodities managed in our pilot stores or the 1,000 manufacturers
who supply those stores.
[9] CORSTEN GRUEN 2003
Title: Desperately seeking shelf availability: an examination of the extent, the causes,
and the efforts to address retail out-of-stocks
Abstract:
With all the hype around efficient consumer response (ECR) and the brave new world of
technologies, one would believe that retail out-of-stocks have gone down over the last
ten years. That is wrong. Retailers have been struggling with considerable out-of-stocks
for decades – with little evidence of improvement. A similar wrong belief is that shoppers
are also still unwilling to accept low service levels. In fact, increasingly, consumers switch
brands when they do not find the brand they wanted. But retailers must be wary,
because the results of our research show that increasingly shoppers switch stores quickly
and may never come back. So, who is to blame? The supply chain. And where to tackle it?
On the shop floor. Over the past two years, we have conducted a major, worldwide study
of the extent, causes, and consumer responses to out-of-stocks in the fast moving
consumer goods industry. In this article, we report these findings and provide insight to
solving this chronic industry problem.
Introduction:
Availability of products to the customer is the new battleground in the FMCG industry.
What is the extent of shelf out-of-stocks?
Northwest Europe showed the lowest OOS rates of any region in the world, while
Southeast Europe showed the highest. Regarding promotional effects, the studies
consistently show OOS rates to be higher on promoted items than on non-promoted
items.
What are the consumer reactions to shelf out-of-stocks?
Academic research has identified and categorized up to 15 possible consumer responses
to an OOS, though typically, managerial researchers measure five primary responses:
1. store switch
2. buy later at same store
3. substitute – same brand
4. substitute – different brand
5. lost sale
European consumers are almost 50% more likely to switch to a competing brand when
faced with an OOS on the desired item. US consumers are more likely to substitute a
different package size or variation within their preferred brand. Consumer responses vary
considerably per category. To present a generalized approach, we found that there are
three primary drivers that interact and cause the consumer to take one action over
another:

Opportunity cost (of not being able to immediately
consume the product)

Substitution cost (of using a less preferred brand)

Transaction cost (time and effort required to obtain the
preferred item)
What is the cost of shelf out-of-stocks to the retailer?
The total cost of OOS affects the entire supply chain and can be divided into four areas:
1. Retailer shopper loss risk (shopper permanently switches stores due to OOS)
2. Retailer sales loss risk (consumer buying the item at another store, consumers
cancelling their purchase, and consumers substituting a smaller and/or lower priced
item).
3. Manufacturer shopper loss risk (when shoppers switch to a competitor’s brand)
4. Manufacturer sales loss risk (when consumers substitute a competitor’s item or
cancel a purchase)
The areas of loss are independent. Other implications of OOS include logistics and
information inefficiencies in the supply chain.
What are the root causes of shelf out-of-stocks?
Previous studies have placed most of the responsibility for OOS on retailer store ordering
and forecasting practices. Our research confirms this. Causes of OOS tend to be assigned
to one of the following three general processes:
 Ordering: ordered too little or too late / forecast may have misjudged
 Replenishment practices: product in store but not on shelf when the consumer
comes to buy the product
 Planning practices: For example manufacturer has not shipped enough or the
manufacturer is unable to produce enough.
How can shelf availability be improved?
Ideally, a sustainable on shelf availability management process consists of a set of linked
decisions on category tactics and shelf-space allocation, as well as the mode, frequency
and quantity of ordering and replenishment.

Remedy 1: process improvements
 Assortment planning and space allocation: Given continuously changing and growing
assortments, most stores end up in the dilemma where they allocate relatively too
little shelf space for fast movers and too much shelf space for slow movers. While
shelf replenishment remains, even today, a predominantly manual process,
automatic or computer-assisted store ordering has emerged as a key lever for better
on-shelf availability.
 EDI, Internet, and real-time ordering: To address the bullwhip effect (batching orders
that disrupt the product flow to the shelf) many retailers have already increased
their ordering frequency, implemented EDI and Internet ordering, introduced mixed
truckloads, adapted minimum pack sizes, reworked delivery schedules and
automated ordering to break batches.
 Inventory control: Higher supply-chain inventory actually correlates with higher outof –stock rates. This apparent paradox can be explained by the fact that retailers with
lower inventory levels tend to manage their supply chains better and have their
inventories in the appropriate places.

Supply network/store flow replenishment: the overall design of the supply and
distribution network does make a big difference.

Remedy 2: improve operational accuracy
 Automatic availability measurement: Shelf-availability monitor (SAM) tracks the sales
transaction data (rather than the inventory) for a store’s top 2000 products and can
be used to flag items that may be out of stock. The “item velocity monitor” predicts
with 90 percent accuracy the out-of-stock status for items that move four or more
times per day. These new solutions all share the ability to utilize technology (as
opposed to inventory or manpower) to address out-of-stocks items in a rapid basis.
 Inventory record accuracy: presents a major obstacle to on-shelf availability and
needs to be addressed. This is crucial since ordering and inventory models assume
that inventory records are accurate.
 Automatic Identification: For example RFID, where intelligent tags will be attached to
each stock-keeping unit, providing truly accurate inventory control.

Remedy 3: Improve incentive alignment
 Ordering incentives: Rather than penalizing inventory, stores should focus on onshelf availability.
 Incentive system: category management teams operating at retail headquarters
need to have a way to incorporate the local store needs.
 Roles and responsibilities: Retailers must communicate that the introduction of new
store technologies does not threaten jobs.
 Flexible staffing: Align staff scheduling to replenishment peaks, as well as to shopper
peaks.
 Change culture: by setting tough targets, aligning incentives and controlling the
process, they have achieved step change in employee attitude to availability.
Conclusion:
 OOS is a problem.
 OOS is costly
 Not all OOS are the same
 Duration of OOS is important
 Most of the responsibility for lowering OOS rests in the retail store
 Important to understand the limits of projections
 Consumers are indeed localized in their choices.
[5] BR OEKM. &DONSEL AAR – 2009
Title: A heuristic to manage perishable inventory with batch ordering, positive leadtimes, and time-varying demand.
Abstract:
So far the literature on inventory control for perishable products has mainly focused on
(near-) optimal replenishment policies for a stylized environment, assuming no lead-time,
no lot-sizing, stationary demand, a first in first out withdrawal policy and/or product life
time equal to two periods. This literature has given fundamental insight in the behavior
and the complexity of inventory systems for perishable products. In practice, many
grocery retailers have recently automated the inventory replenishment for nonperishable products. They recognize they may need a different replenishment logic for
perishable products, which takes into account e.g. the age of the inventory in the system.
Due to new information technologies like RFID, it now also becomes more economically
feasible to register this type of information. This paper suggests a replenishment policy
for perishable products, which takes into account the age of inventories and which
requires only very simple calculations. It will be shown that in an environment, which
contains important features of the real-life retail environment, this new policy leads to
substantial cost reductions compared with a base policy that does not take into account
the age of inventories. We will evaluate the different replenishment policies for both the
FIFO and the LIFO customer withdrawal behavior.
Introduction:
Controlling the inventories of perishable products is increasingly important because:
 Margins on non-perishable products are relatively small and decreasing.
 Customers are asking for higher product variety in perishable product categories,
leading to less predictable demand per product and to more outdating, and for new
product categories with a short shelf life, such as fresh ready-to-eat meals.
ASO (automated store ordering) system: It might be useful to extend the ASO system
using the information on the age of the inventory.
Literature review: Their paper differs from other papers in two ways:
 Their replenishment policy takes into account all information about the age distribution.
 The assumptions on the withdrawal policy (both LIFO and FIFO) and the inventory
system are different (think of assumptions for week pattern/lot-sizing/continuous
reviewing or not)
Model:
Single echelon perishable inventory system with stochastic demand and fixed lifetime.
Replenishment policy that assumes a constant safety stock and which does not use
information on the demand distribution other than the expected demand.
Assumptions:
• Single perishable product with fixed lifetime of m days.
• Demand is probabilistic with a time-varying demand pattern during the week.
• The inventory is controlled with a periodic review system with review period equal to R
days.
• The inventory in the store at the start of day t consists of one or more batches
(batch=items with same age).
• Replenishment orders arrive with a fixed lead-time equal to L days. We assume that the
supplier has ample stock.
• Predetermined lot size Q.
• Shelf has ample capacity.
• Customers withdraw items with positive remaining shelf life from the batches on the
shelf.
• When the inventory on the shelf is insufficient to satisfy the demand, the excess
demand is lost.
• In the replenishment policies we apply the same safety stock SS for each weekday.
Replenishment policy: EWA policy. It will be compared with a base policy.
 Base policy: (R,s,nQ) policy. A replenishment order is created only when the
inventory position at a periodic review moment is strictly below the dynamic reorder
level st. In that case a number of case packs (𝑛𝑡 ), each with size 𝑄, is ordered which is
necessary to bring the inventory position back to or just above the reorder level s.
 EWA policy: the inventory position is first corrected for the estimated amount of
outdating and an orders is placed if this revised inventory position drops below the
reorder level 𝑠𝑡 . The estimated amount of outdating is the only difference between
the EWA policy and the base policy. The outdating quantities are calculated for
consecutive periods 𝑖, the withdrawal, the remaining batches and the outdating in
period i under the assumption that in period 𝑖 demand is equal to the expected
demand. Procedure: determine withdrawal by customers, then determine remaining
batches at end of period and then determine outdating (eventually place orders).
Simulation experiments:
In order to compare the performance of the replenishment policies, we measured the
long-term average costs. We did a factorial experiment in which we tested several levels
for each of the 10 input parameters. To test the sensitivity of the results for the week
pattern we also simulated each scenario with demand having no week pattern.
Simulation experiments are done for four scenario’s: differentiating on base policy
(R,s,nQ) or EWA policy and on FIFO withdrawal or LIFO withdrawal. For each scenario the
optimal safety stock level SS is determined, which minimize average simulated costs.
Performance: In only a small number of cases, 2% of the cases with FIFO withdrawal and
only 0.1% of the cases with LIFO withdrawal, the EWA policy performs worse than the
base policy. Under FIFO, the EWA policy gives the largest improvements for a short
remaining shelf life, long lead time, long review period, high outdating cost ration and/or
high lost sales cost ratio. Still, larger benefits with EWA can be reached under LIFO
compared to FIFO. Under LIFO the largest improvements are for products with a short
remaining shelf life, long lead-time, high outdating cost ration and/r a high lost sales cost
ration. The EWA policy performs well when lost sales ratio is high, since then SS is high
and therefore large amount of outdating. Under both FIFO and LIFO withdrawal, the fill
rate increases and the average inventory decreases, the reduction of the average
outdating is substantial, the effect on the freshness for the customers is relatively small.
Conclusions:
One main insight from this research is that taking into account the age distribution in the
replenishment decision for perishable items often gives a large cost reduction. This
reduction can be taken into account by managers while looking at costs of additional
registration of data by, for example, RFID. It turned out that with FIFO withdrawal and
with a daily delivery frequency the cost benefit of the EWA policy is much smaller. This
indicates that if the costs for the registration of full age information are high, managers
may opt for an alternative scenario to prevent high costs in such an environment if
customers are inclined to use LIFO withdrawal (try to direct customers towards FIFO, for
example by price discounts). Next, an advantage of the EWA policy is its simplicity: to
determine the estimated outdating quantities, only very simple calculations are needed
and easy to explain the logic. Using the complete age vector of the inventory, the EWA
policy can lead to substantial cost reductions for a retailer selling perishable products.
The cost reductions are especially large for products with a short remaining shelf life,
when customer withdrawal is LIFO, the lead-time is large, the review period is large,
outdating is expensive and/or when the retailer aims for a high product availability.
Formulae:
𝑡+𝐿+𝑅
(1) 𝑠𝑡 = 𝑆𝑆 + ∑ 𝐸[𝐷𝑖 ]
𝑖=𝑡+1
(2) 𝑛𝑡(𝑅, 𝑠, 𝑛𝑄):
𝑠𝑡 − 𝐼𝑃𝑡
𝑖𝑓 𝐼𝑃𝑡 < 𝑠𝑡 ; 𝑛𝑡 = ⌈
⌉
𝑄
𝑡+𝐿+𝑅−1
(3) 𝑛𝑡(𝐸𝑊𝐴):
𝑖𝑓 𝐼𝑃𝑡 −
̂𝑖 < 𝑠𝑡 ; 𝑛𝑡 = ⌈
∑ 𝑂
𝑖=𝑡+1
̂𝑖
𝑠𝑡 − 𝐼𝑃𝑡 + ∑𝑡+𝐿+𝑅−1
𝑂
𝑖=𝑡+1
⌉
𝑄
𝑟−1
(4) 𝑊𝑡𝑟 (𝐹𝐼𝐹𝑂) = 𝑀𝑖𝑛{𝐵𝑡𝑟 , 𝐷𝑡 − ∑ 𝑊𝑡𝑖
𝑚
(5) 𝑊𝑡𝑟 (𝐿𝐼𝐹𝑂) = 𝑀𝑖𝑛{𝐵𝑡𝑟 , 𝐷𝑡 − ∑ 𝑊𝑡𝑖
𝑖=1
(6) 𝑂𝑡 = 𝐵𝑡,1 − 𝑊𝑡,1
𝐶(𝐵𝑎𝑠𝑒) − 𝐶(𝐸𝑊𝐴)
(7) Δ𝐶 = 100
𝐶(𝐵𝑎𝑠𝑒)
𝑖=𝑟+1
[12] DONSEL AAR BR OEKMEUL EN – 2008
Title: Inventory replenishment in retail: The Efficient Full Service Strategy; BETA
working paper.
Abstract: In this paper we compare two inventory replenishment strategies for retailers
and evaluate their effect on service levels, average inventory and the number of order
lines. The first inventory replenishment strategy we consider is the Full Service strategy
which is currently applied by many retailers and orders at a review period if either a case
pack fits onto the shelves or the minimum reorder level is reached. This strategy is
compared to an Efficient Full Service strategy where an order is placed only if at a review
period the inventory position drops below the minimum reorder level; then as many case
packs are ordered as possible taking into account the limited shelf space. This modified
strategy will be compared with the current strategy. We will derive approximations for
the key performance indicators and use simulation based on empirical data for thousands
of SKU’s at multiple stores from a European retailer to quantify the improvement
potential of the new strategy and to evaluate our approximations. The results show that,
on average, inventory can be reduced with 22% and the number of handled order lines
can be reduced with 17% when applying the Efficient Full Service strategy, (see table 2)
while guaranteeing the same target customer service level. The approximations for the
average inventory and the number of order lines perform very well at the store level and
perform well at the SKU level. We also show that these approximations can be used as
good indicators for the improvement potential of the new replenishment strategy.
Full service strategy:
𝑉 − 𝐼𝑃
𝑠 − 𝐼𝑃
(1) 𝑞 = max { ⌊
⌋𝑄 ,⌈
⌉𝑄 ,0 }
𝑄
𝑄
The first term on the right-hand side reflects the basic idea behind the FS strategy: at a
review period we order as many case packs that fit on the shelf, given the current
inventory position 𝐼𝑃. The second term on the right-hand side is needed in order to
satisfy the requirement that the fill rate 𝑃2 is at least equal to the target fill rate 𝑃2 for a
SKU. So if the inventory position 𝐼𝑃 is less than the reorder level 𝑠 , which is based on
the target fill rate, we need to order the minimum number of case packs which is needed
to raise 𝐼𝑃 back to or above the reorder level. Finally the third term reflects the notion
that the order quantity should always be non-negative (due to the dynamic 𝑠 the 𝐼𝑃 may
sometimes be larger than 𝑠 + 𝑄).
Efficient Full Service Strategy:
Aims to minimize the number of order lines per year, while guaranteeing 𝑃2∗
𝑉 − 𝐼𝑃
𝑠 − 𝐼𝑃
(2) 𝑞 = max { ⌊
⌋𝑄 ,⌈
⌉ 𝑄 , 0 } , 𝑖𝑓 𝐼𝑃 < 𝑠
𝑄
𝑄
The Efficient Full Service strategy (EFS) is similar to the FS strategy, but aims to minimize
the number of order lines per year, while still guaranteeing the target service level. Only
If at a review period the inventory position is strictly below the reorder level 𝑠 , we order
the maximum number of case packs such that the 𝐼𝑃 just after ordering is less than or
equal to the shelf capacity 𝑉 . Unless this 𝐼𝑃 is still below 𝑠 , i.e., the shelf is not large
enough to accommodate all units, then we order as many case packs as needed to bring
the inventory position after reordering to (or just above) 𝑠 .
KPIs for comparison of FS and EFS:
There are various KPIs that are important when comparing the FS to the EFS strategy, i.e.
the percentual difference Δ(𝑋) (3), the average inventories 𝐼̂ (4), and the average number
̂ . (5). We know there are costs involved for holding inventories and
of Order Lines 𝑂𝐿
placing orders, since these handling costs normally incurs a large extent of operational
expenditures.
The percentual difference between FS and EFS:
(𝑋𝐵𝐴𝑆𝐸 − 𝑋𝐴𝐿𝑇 )
(3) Δ(𝑋𝐵𝐴𝑆𝐸 , 𝑋𝐴𝐿𝑇 ) = 100
𝑋𝐵𝐴𝑆𝐸
̂ 𝑳:
Average Inventory 𝑰̂ average number of order lines 𝑶
𝑄−1
𝑅−1
(4) 𝐼̂
− (𝐿 +
)𝜇
= max{𝑉 − 𝑄 + 1 , ⌈(𝐿 + 𝑅)𝜇 + 𝑠𝑠𝐹𝑆 ⌉}
𝐹𝑆 = 𝑠𝐹𝑆 +
2
2
𝐼̂
𝐸𝐹𝑆 = 𝑠𝐸𝐹𝑆 +
𝑄−1
𝑅−1
+
− (𝐿 +
)𝜇
2
2
̂𝑄 − 1
̂𝑄 − 1
𝑁
𝑅−1
𝑁
− (𝐿 +
) 𝜇 = ⌈(𝐿 + 𝑅)𝜇⌉ + 𝑠𝑠𝐸𝐹𝑆 +
2
2
2
𝑅−1
− (𝐿 +
)𝜇
2
̂ 𝑳:
Average number of order lines 𝑶
𝑃2∗ 𝜇
̂
(5) 𝑂𝐿
𝐹𝑆 =
max{𝑅𝜇 , 𝑛𝑈 𝑄𝑝𝑈 + (𝑛𝑈 + 1)𝑄(1 − 𝑝𝑈 )}
̂
𝑂𝐿
𝐸𝐹𝑆 =
𝑃2∗ 𝜇
̂ 𝑄}
max{𝑅𝜇 , 𝑛𝑈 𝑄𝑝𝑈 + (𝑛𝑈 + 1)𝑄(1 − 𝑝𝑈) , 𝑁
1+𝐸[𝑈]
𝑤𝑖𝑡ℎ 𝑛𝑈 = ⌈
𝑄
⌉
; 𝑝𝑈 = 𝑃(𝑈 ≤ 𝑛𝑈 𝑄) ; denominators are 𝑞̂
̂
𝐹𝑆 resp. 𝑞
𝐸𝐹𝑆 .
Simulated results
Theoretically, the potential improvement of the new suggested replenishment strategy is
sound. Therefore, empirical tests with 184,901 SKUs have been performed at 44 stores.
The results are displayed in tables 2 and 3 below. Table 2 displays the descriptive
statistics for all relevant parameters on a store level, and table 3 on a SKU level.
Key assumptions: (1) delivery moments are equidistant, and (2) demand is stationary. In
the test environment, i.e. the stores, these assumptions are actually not valid!
Table 2 shows a very large performance improvement when changing from a FS strategy
to an EFS strategy: inventories per store are reduced by 22.0% on average, while the
number of order lines per store are reduced by 16.7% on average. The performance
improvement varies per store, particularly for the reduction in number of order lines. This
variation is no surprise, since the stores are quite different; e.g. the maximum daily
demand per store is almost four times as large as the minimum daily demand and some
stores are delivered only twice per week (𝑅 = 3), while others are delivered five times
per week (𝑅 = 1.2). Despite this variation, all stores clearly benefit from the EFS strategy.
Table 3 shows the descriptive statistics of the same variables as in Table 2, but now at the
SKU level: It confirms our store level insights: the EFS strategy results in less inventory and
less order lines with a reduction of 16.80% in inventories and 13.78% in order lines
respectively. These numbers are slightly different than the ones reported above, but this
is due to the different level of analysis (stores versus SKU). Table 3 also shows that the
performance improvement varies strongly between SKUs, as is evident from the large
standard deviation (17.86 resp. 23.47) relative to the mean performance improvement
(16.80 resp. 13.78) for the reduction in inventories resp. the number of order lines. This
variation is again explained by the large differences between SKU's. The highest average
daily demand per SKU e.g. is more than 60,000 times the lowest average daily demand.
Also the available shelf capacity and the case pack size differ greatly per SKU. The reason
for a relatively high percentage for the inventory reduction is due to the fact that a
substantial reduction in number of order lines can only be achieved if the difference
between the shelf capacity and the EFS reorder level is at least equal to two case packs,
while the inventory can already be reduced with the EFS strategy when this difference
is approximately equal to one case pack.
FS strategy is actually a discrete (R,s,nQ)-strategy with:
(6) 𝑠𝐹𝑆 = max{ 𝑉 − 𝑄 + 1 , ⌈(𝐿 + 𝑅)𝜇 + 𝑆𝑆⌉ }
𝑠𝐸𝐹𝑆 = ⌈(𝐿 + 𝑅)𝜇⌉ + 𝑠𝑠𝐸𝐹𝑆
𝑄−1
(7) 𝐸[𝐼𝑃] = 𝑠 +
,
𝑤𝑖𝑡ℎ ∀ 𝐼𝑃: 𝑠 − 1 < 𝐼𝑃 < 𝑠 − 1 + 𝑄
2
And with the mean and Variance of the Undershoot equal to:
1
1
1
(8) 𝐸[𝑈] = (1 + 𝑐𝑅2 )𝜇𝑅 ; 𝑉𝐴𝑅[𝑈] = (1 + 𝑐𝑅2 )(1 + 2𝑐𝑅2 )𝜇𝑅2 − (1 + 𝑐𝑅2 )2 𝜇𝑅2
2
3
4
Further research should / could derive formulas for the safety stock norms, and its impact
on overall operational efficiency.
[3] BLANCO, FRANSOO (2013)
Title: Reaching 50M nanostores: retail distribution in emerging megacities
Introduction
In this paper, the authors define and characterize nanostores (very small, family-owned
and operated stores), and the associated logistics and channel strategies to reach them as
the next opportunity in global retailing. With the growth in emerging markets, a
significant change in the retail landscape is happening. The structures and characteristics
of retail in megacities are fundamentally different of the developed economies organized
big-box retail, which is in contradiction to retail in megacities a well-studied, welldocumented field of research and practice. The market share of nanostores in many
countries is around half of the total retail market. The authors estimate that there are at
least 50 million nanostores in the developing world.
Urbanization in developing economies drives retail landscape
The speed at which urbanization is happening has increased on the past decade,
especially in developing economies. In 2025, the top 600 cities of the world will cover 22%
of the world population and more than half of the world’s GDP. Multinationals in
Consumer Packaged Goods are already realizing more than half of their revenues in
emerging markets, and their growth ambitions need to be realized completely in
emerging markets.
Most definitions of megacities take the population size as a criterion, with both 5 and 10
million inhabitants as the cut-off point. From a logistic point of view, it is the high
population density in combination with the size that makes megacities in emerging
markets very different from the large cities in Europe or the United Sates. Many of the
megacities are more or less permanently congested. Moreover, these cities are
characterized by unprecedented income disparities. Unfortunately, large income
disparities are often associated with security problems and other problems of crime.
Why is retailing in emerging megacities different: the nanostore
In retail, a distinction can be made between the traditional and modern channel. The
modern channel is the organized (corporate) retail channel, where the traditional retailer
is usually a family-operated business, with in most cases only one store in the retail
company. One of the main challenges in the logistics planning and execution is to time
the delivery at nanostores such that cash is available to pay for the delivery. This because
nanostores have the ability to provide informal credit to consumers which means that
nanostore operators are usually short of cash. The plateauing of the growth of the
modern channel is most likely affected by the limited access of lower income groups to
the modern channel. Therefore, in most of the developing economies the market share of
the traditional channel is still substantial. Beyond money and time, also the format of
nanostores is an important contributor to their continued market dominance. In
nanostores, the operation of the stores, the merchandising of the suppliers, and the
distribution toward the stores is substantially different from the modern channel.
Table 1: Comparing the modern channel supermarket with the traditional channel
nanostore
Reaching the nanostores: channel strategies
Supplying nanostores faces the same choices as in the traditional manufacturer-retail
environments, namely the choice between direct store deliveries and indirect service
models. Due to the unique characteristics of the nanostore there are deeper
implementations for the manufacturer and a wider range of strategic and operational
choices between both models. Figure 1 shows the key functions that need to be
considered when serving nanostores. When serving the modern retail channel, these
functions are usually split among various departments within the retailer and
manufacturer. If a manufacture chooses an indirect service model (via a wholesaler or a
distributor), the key functions are simply considered transactional elements and are
evaluated in pure logistics efficiency terms. Except for demand generation, these
activities are usually maintained within the manufacturer.
In case of nanostores, these key functions work in a very different way. First physical
distribution is much more complex. When looking at logistics efficiency metrics,
manufacturers often conclude that a wholesaler or a distributor will achieve higher
economies of scale and select an indirect service model to reach nanostores.
Furthermore, nanostores are often part of the ‘informal’ economy or work with limited
assets and no access to credit by financial institutions. As a consequence, cash is usually
collected on-delivery. Depending on the risk profile and relationship with its distribution
activities, this sometimes means that the vehicle driver is directly responsible for the
product during the transportation operations and responsible for its value throughout the
distribution process. With regard to demand generation, and given the limited shelf space
and low technological level of nanostores, the sales organizations have an interest in
having direct contact with nanostore owners. The combined demand generation with
order processing activity is usually referred to as ‘pre-sales’. Manufactures can also opt to
completely merge the functions into a single operations referred as ‘on-board sales’,
where the delivery vehicle carriers inventory and performs all the activities as part of its
order processing is effectively eliminated and demand generation, product delivery,
payment and after-sale service are combined in a single interface to the nanostore.
Leading companies in emerging markets have been using direct service models. They are
using a wide variety of presales, direct store and on-board sales supply schemes to
nanostores. This has enabled higher levels of execution in terms of merchandising and
control. On the downside, it may results in higher transportation and service costs for the
manufacturer. Multinational manufactures (MNCs) often rely on indirect service models
to reach the nanostores. A major reason for this is that MNCs prefer safety to developing
the business opportunity. Regional and local manufacturers tend to depend on indirect
service models when they face capital and scale constraints.
Table 2: Supply str
𝑃1 (𝑆𝐴 , 𝑆𝐵 ) = [(𝜆𝐴) 𝑥1 ∗ 𝑒 −𝜆𝐴∗𝑇 ] ∗ [(𝜆𝐵 ) 𝑦1 ∗ 𝑒 −𝜆𝐵 ∗𝑇 ], two data values to enter.
Sit.2 Only product A runs out: Likelihood function =
𝑃1 (𝑆𝐴 , 𝑆𝐵 ) = [(𝜆𝐴) 𝑆𝐴 ∗ 𝑒 −𝜆𝐴 ∗𝑇𝐴 ] ∗ [(𝜆𝐵 ) 𝑧2 ∗ 𝑒 −𝜆𝐵 ∗𝑇𝐴 ] ∗ [(𝜆𝐴̅𝐵 )𝑤2 ∗ 𝑒 −𝜆𝐴𝐵 ∗(𝑇−𝑇𝐴) ], three data
values to enter.
Sit.3: only product B runs out:
𝑃1 (𝑆𝐴 , 𝑆𝐵 ) = [(𝜆𝐵 )𝑆𝐵 ∗ 𝑒 −𝜆𝐵 ∗𝑇𝐵 ] ∗ [(𝜆𝐴)𝑧3 ∗ 𝑒 −𝜆𝐴 ∗𝑇𝐵 ] ∗ [(𝜆𝐴𝐵̅ )𝑤3 ∗ 𝑒 −𝜆𝐴𝐵∗(𝑇−𝑇𝐵 ) ], three data
values to enter.
Sit.4: A runs out, then B runs out: Likelihood function:
𝑃1 (𝑆𝐴 , 𝑆𝐵 ) = [(𝜆𝐴) 𝑆𝐴 ∗ 𝑒 −𝜆𝐴 ∗𝑇𝐴 ] ∗ [(𝜆𝐵 ) 𝑧4 ∗ 𝑒 −𝜆𝐵 ∗𝑇𝐴 ] ∗ [(𝜆𝐴̅𝐵 )𝑆𝐵 −𝑧4 ∗ 𝑒 −𝜆𝐴𝐵∗(𝑇𝐵−𝑇𝐴) ], three
data values to enter.
Sit.5: B runs out, then A runs out. Likelihood function:
𝑃1 (𝑆𝐴 , 𝑆𝐵 ) = [(𝜆𝐵 )𝑆𝐵 ∗ 𝑒 −𝜆𝐵 ∗𝑇𝐵 ] ∗ [(𝜆𝐴)𝑧5 ∗ 𝑒 −𝜆𝐴 ∗𝑇𝐵 ] ∗ [(𝜆𝐴𝐵̅ )𝑆𝐴 −𝑧5 ∗ 𝑒 −𝜆𝐴𝐵∗(𝑇𝐴−𝑇𝐵) ], three
data values to enter.
Then, estimators of 𝒑𝒂, 𝒑𝒃, 𝒂𝑨𝑩, 𝒂𝑩𝑨 are found via: max ℒ = ∏5𝑖=1 𝑃𝑖 (𝑆𝐴 , 𝑆𝐵 ), such that
0 ≤ 𝑎𝐴𝐵 ≤ 1, and 0 ≤ 𝑎𝐵𝐴 ≤ 1.
Empirical Application in the Vending Industry
Application of the model to most real settings entails dealing with more than two goods.
One possibility is to assume that choice probabilities are subject to the Independence of
Irrelevant Attributes (IIA), does not hold for soft drinks. Therefore, focused on the case of
one-stage substitution. Under this choice restriction, demand for a product that is out-ofstock is (partially) transferred or spilled-over to another product. However, if that product
is also out-of-stock then this spilled over demand is lost.
Further research
Further research should strive to check for an approximation using the negative binomial
distribution, for a possible improved fit. The process is non-homogeneous with time, i.e.
the arrival rate could be lower in the early mornings than during lunch, yet the model has
not been corrected for this behavior. Furthermore, now it is assumed that the aggregate
arrival rates and the substitution probabilities matrices are identical across machines, this
can be modified to the problem to pool data from machines with varying assortments. In
this case, assume that spillovers rates from product C to A under temporary stock-outs
are the same as under assortment unavailability.
The models presented in this paper are relevant in numerous (nonvending) retail
environments in which stock-outs occur and customers may partially substitute. If
customers’ preferences are not observed, only their choices are, the problem of
estimating core demand rates and substitution probabilities has to be solved.
Enhancements might need to be made to the model to take account of changes in the
retail environment (for example, promotional changes).
0 0.3
Example: 𝐴 = [
] , 𝑝1 = 0.4 , 𝑝2 = 0.3 , 𝑠𝑒𝑡 𝑁 = {1,2} (e.g. denk aan automaat
0.9 0
met alleen Coca cola of Pepsi). Also, note that the set 𝑆 ⊆ 𝑁.
Question: What is the purchase probability for product 1, 𝑃1 (𝑆), with 𝑆 = {1,2} ?
𝑷𝟏 (𝟏, 𝟐) = 𝒑𝟏 = 𝟎. 𝟒
Question: What is the purchase probability for product 1, 𝑃1 (𝑆), with 𝑆 = {1} ?
𝑷𝟏 (𝟏) = 𝒑𝟏 + ∑(𝒑𝟐 ∙ 𝒂𝟐𝟏 ) =
𝟎. 𝟒 + (𝟎. 𝟗 ∗ 𝟎. 𝟑) = 𝟎. 𝟒 + 𝟎. 𝟐𝟕 = 𝟎. 𝟔𝟕
[20] GUANDAGNI LITTL E – 1983
Title: A logit model of brand choice calibrated on scanner data.
Multinomial Logit Model:
The multinomial logit (MNL) model of brand choice, is a utility-based model that is
commonly used in economics and marketing literatures, that gives a ‘nice’ formula for
𝑃𝑗 (𝑆), though with the disadvantage of the IIA assumption (explained below). Idea of the
paper: The customer 𝑖 chooses that product 𝑗 with the highest utility 𝑢𝑗 = 𝑣𝑗 + 𝜖𝑗 from a
set of alternatives 𝑆. 𝜖𝑗 displays the random component of the utility, which are
independently distributed random variables.
Two main assumptions are applied at the MNL model:
 The deterministic component 𝒗𝒋 for a customer can be expressed as a linear
𝑖
function of attributes of both product 𝑗, as also the customer 𝑖: 𝑣𝑗𝑖 = ∑𝑏𝑘𝑗 𝑥𝑘𝑗
𝑖
𝑖
With: 𝑏𝑘𝑗
= utility weight of attribute 𝑘 for alternative 𝑗 , 𝑥𝑘𝑗
= observed value of
attribute 𝑘 for alternative 𝑗 for consumer 𝑖., 𝑇 = set of attributes.
 IIA assumption = Independence of Irrelevant Alternatives. The ratio of the
probabilities of picking two alternatives remains the same independently of which
𝑷 (𝑺)
𝑷 (𝑻)
other alternatives are available, 𝒋 (𝑺) = 𝒋 (𝑻) for any two alternatives j and k and 𝑆 ⊆
𝑷𝒌
𝑷𝒌
𝑇.  adding one small product to a certain space of products that are small or big,
decrease the probability of all products, whether small or big (FALSE of course). This
will result in systematic errors in predicted choice probabilities. (Kun je testen of dit
aanwezig is via ingewikkelde 𝑋 2 verdeelde testen: de IIA assumption moet
voorbehouden blijven)
Formula to determine 𝑃𝑗 (𝑆) =
𝑒 𝑣𝑗
∑𝑘∈𝑆 𝑒 𝑣𝑘 +𝑒 𝑣0
, where 𝑣0 is the utility of the no-purchase
option. This formula of 𝑃𝑗 (𝑆) is increasing in 𝑣𝑗 , i.e. the measure of popularity, but it is
decreasing in 𝑣𝑘, for 𝑘 ≠ 𝑗, 𝑘 ∈ 𝑆 (including 𝑣0).
Example:
𝑆 = {𝐶𝑎𝑟, 𝐵𝑢𝑠}, 𝑣𝐶 = 2, 𝑣𝐵 = 1, 𝑣0 = 0.
Question: what is 𝑃𝐶𝑎𝑟 (𝑆) ? Answer: 𝑷𝑪𝒂𝒓({𝑪, 𝑩}) =
Question: what is 𝑃𝐵𝑢𝑠 (𝑆) ? Answer: 𝑷𝑩𝒖𝒔 ({𝑪, 𝑩}) =
𝒆𝟐
𝒆𝟐 +𝒆𝟏 +𝒆𝟎
𝒆𝟏
𝒆𝟐 +𝒆𝟏 +𝒆𝟎
= 𝟎. 𝟔𝟕
= 𝟎. 𝟐𝟒
Great problem with the model, according to next article [19] Kök & Fisher (2007): “(…) it is
not possible to have two categories with the same penetration rates but different
substitution rates!”
Explanation of the IIA assumption, following the Car&Bus example above:
𝑆 = {𝐶𝑎𝑟, 𝑏𝑙𝑢𝑒 𝐵𝑢𝑠, 𝑟𝑒𝑑 𝐵𝑢𝑠}, 𝑣𝐶 = 2, 𝑣𝐵𝐵 = 1, 𝑣𝑅𝐵 = 1, 𝑣0 = 0.
Then, 𝑷𝒄 = 𝟎. 𝟓𝟑 ,
𝑷𝑩𝑩 = 𝑷𝑹𝑩 = 𝟎. 𝟐𝟎
Now,
𝑆 = {𝐶𝑎𝑟, 𝑏𝑙𝑢𝑒 𝑏𝑢𝑠, 𝑟𝑒𝑑 𝑏𝑢𝑠, 𝑔𝑟𝑒𝑒𝑛 𝑏𝑢𝑠}, 𝑣𝐶 = 2, 𝑣𝐵𝐵 = 1, 𝑣𝑅𝐵 = 1, 𝑣𝐺𝐵 =
1, 𝑣0 = 0
Then, 𝑷𝒄 = 𝟎. 𝟒𝟒,
𝑷𝑩𝑩 = 𝑷𝑹𝑩 = 𝑷𝑮𝑩 = 𝟎. 𝟏𝟔
The behavior of the IIA-assumption is now easy to understand: In a state space with a car
and three colours of buses, versus a state space with only a car or a bus, the differences
are too big. 3 x 0.16=0.48 >> 0.24. “In plain English: If there are three buses versus one
car, to choose your transportation. Would your choice be very different if there would be
one car or one bus, to choose from?”
[21] KÖK FISHER (2007)
Title: Demand Estimation and Assortment Optimization Under Substitution:
Methodology and Application
Abstract
Assortment planning at a retailer entails both selecting the set of products to be carried
and setting inventory levels for each product. We study an assortment planning model in
which consumers might accept substitutes when their favourite product is unavailable.
We develop an algorithmic process to help retailers compute the best assortment for
each store. First, we present a procedure for estimating the parameters of substitution
behaviour and demand for products in each store, including the products that have not
been previously carried in that store. Second, we propose an iterative optimization
heuristic for solving the assortment planning problem. In a computational study, we find
that its solutions, on average, are within 0.5% of the optimal solution. Third, we establish
new structural properties (based on the heuristic solution) that relate the products
included in the assortment and their inventory levels to product characteristics such as
gross margin, case-pack sizes, and demand variability. We applied our method at Albert
Heijn, a supermarket chain in The Netherlands. Comparing the recommendations of our
system with the existing assortments suggests a more than 50% increase in profits.
Introduction
Retail assortment planning: specifying the set of products carried at each store and
setting their inventory levels so as to maximize a profit function subject to fixed shelf
space and possibly other constraints, which vary by context.
Substitution: consumer settle for another similar product instead of favourite one.
Substitution takes place within subcategories, but not across subcategories.
Hierarchy: groups (chilled products, dry goods, and groceries), (merchandising)
categories, subcategories, and finally SKU’s.
Replenishment system: products within a category have the same delivery schedule.
Shelves are derived in facings (per SKU) within a shelf area. The capacity of a facing
depends on depth of the shelf and size of a unit.
Inventory model: periodic review, stochastic demand, lost sales, positive constant
delivery lead time.
Objective: maximize expected gross profit, with gross profit = margin * sales – selling
price * disposed inventory
𝑓𝑗 : number of facings allocated to product 𝑗
𝑐𝑗 : capacity of facing
𝑑𝑗 : original demand rate to product 𝑗 (i.e., first choice if product is present)
𝑓𝑗 𝑐𝑗 : maximum level of inventory. (no back room)
𝑏𝑗 : batch size (integral number of case-packs is ordered to be as close as possible to
𝑓𝑗 𝑐𝑗 )
𝑁 = {1, … , 𝐽}: set of potential variants in subcategory
𝑆: store’s assortment
𝑤𝑗 : width of a facing of product 𝑗
𝐷𝑗 : effective demand rate to product 𝑗, depends on facing allocation of all products in
the subcategory 𝑓 = (𝑓1 , 𝑓2 , … , 𝑓𝐽 ) and the demand rates of all products in the
subcategory 𝑑 = (𝑑1 , 𝑑2 , … , 𝑑𝐽 )
𝐺𝑗 : average gross profit of product 𝑗 given 𝑓𝑗 and 𝐷𝑗
Loss associated with disposing a unit is approximately equal to the selling price
We assume that the original demand for a product is not affected by the number of
facings assigned to it.
Decision process: allocating a discrete number of facings to each product to maximize
total expected gross profits subject to a shelf space constraint:
In the introduction, the structure of the article is given and the main contributions:
Provide empirical information about how assortment planning works in practice and
evaluate a process against real data in the rapidly growing literature on assortment
planning. (validity and applicable)
Present a novel substitution estimation approach that works even when only sales
summary data are available.
Develop an iterative optimization heuristic for the assortment planning problem and
establish new structural properties based on the heuristic solution.
Substitution model
Stockout-based substitution: switch to an available variant by a consumer when her
favourite product is carried in the store, but is stocked out at the time of her shopping.
Assortment-based substitution: switch to an available variant by a consumer when her
favourite product is not carried in the store.
Assumptions:
Every customer chooses her favourite variant from set N.
If for any reason this favourite is not available, with probability 𝛿 she chooses a
second favourite, and with probability 1 − 𝛿 she elects not to purchase. The
probability of substituting product 𝑗 for 𝑘 is 𝛼𝑘𝑗 .
o
𝛿: probability of substitution  sum 𝛼𝑘𝑗 , k=1,..,n.
Either the substitute product is available and the sale is made, or the sale is lost. No
more attempts to substitute occur.  single-attempt model
The effective demand rate function is (sum of incremental demand for product 𝑗 of
assortment-based and stockout-based substitution):
With:
𝐿𝑘 : lost sales of product 𝑘
Assumption: stockouts are negligible. (AH: 99,5% service level for non-perishable
products)
After-Substitution Demand Estimation (ASDE): estimation of effective demand, using
above models, per customer for product at particular store, might include substitution
demand.
Original Demand Estimation (ODE): we estimate the original demand for the products by
calibrating the above models with data from all full-assortment stores.
For full-assortment stores, both ODE and ASDE models estimate the original demand;
however, ASDE models are store specific and therefore more accurate than ODE.
A combination of results from many regression models to estimate a substitution rate
(i.e., purchase
incidence, choice, and quantity models for each ASDE model and the ODE model) is used
to estimate the substitution rate.
Then the original demand rate is computed by doing two tasks:
Deflating the demand rate of the variants already in the assortment.  The true
demand rates of products in the assortment are lower than their ASDE estimates
because the substitution demand is removed.
Estimating a positive demand rate for the variants that are not in the assortment.
The ratio of the demand for these variants to the total subcategory demand is the
same as this ratio in the ODE models.
Assumption: negligible level of stockout-based substitution was occurring.
Estimation of Demand for Products Carried in a Store
If the store carries less than a full assortment, then these demand estimates include the
demand due to assortment-based substitution.
Assumption: the stockout rate is very low, stockouts and stockout-based substitution is
negligible.
The model is based on the number of customers visiting the store and three related
decisions:
Daily number of customers. (Hours of sunshine, humidity, day of the week, holiday)
Purchase-incidence: whether or not to buy from a subcategory.  binary choice
(temperature, promotion level of subcategory)
Choice: which variant to buy given purchase-incidence. (product characteristics,
marketing, and environmental variables)
Quantity: how many units to buy.
 Choice-based approach advantages versus direct approach (per SKU):
Imitates consumer behaviour in a subcategory of substitutable products
Can be generalized to estimate substitution behaviour
Nevertheless: this demand estimation module can be replaced with Albert Heijn’s
method or any other method without affecting the assortment-based substitution
procedure and the optimization module.
Possible ways to determine the parameters based on data are given in the article.
Estimation of Assortment-Based Substitution with Sales Summary Data
Estimating the assortment-based substitution rate using demand estimates from multiple
stores, and we use this procedure to estimate the original demand from sales data that
include assortment-based substitution.
Finding the 𝑆 ∗ :
The profit is maximized by either not adding any more variants or by adding the
variant with highest preference among those not included in 𝑆. The same holds for
the trend following demand case.
While the most profitable assortment of 𝑘 variants need not consist of the most
popular 𝑘 variants, the optimal assortment does consists of the most popular k
variants for some value of 𝑘.
Calculate profit and choose assortment which gives highest store profits (example in
slides).
-
-
Assumptions:
We assume that the number of customers who visited the store but did not purchase
anything is negligible.
Because only a single store is considered, we drop the subscript ℎ and assume that
𝑆 = 𝑁.
Data used are the inventory-transactions. These do not include all consumer behaviour.
Customers who are not interested in the subcategory or who cannot find an acceptable
substitute are not known. We deal with this missing data problem by using the
expectation-maximization (EM) algorithm. The E-step replaces the incomplete data with
their expectation using the current estimates. The M-step maximizes the complete-data
likelihood function to obtain new estimates.
-
-
-
Greedy heuristic: in each iteration compare the expected profit obtained when adding
one facing of each product. Add a facing of the product which gave the highest expected
profit and fits on the shelf.
-
Example: slides class 8, page 16 and 17.
In the case of multiple subcategories in (AP), the facing allocations for SKUs also
determine a shelf-space allocation between subcategories. This can be viewed as a
bottom-up approach to allocating shelf space in a store.
-
Structural Properties of the Iterative Heuristic
In this section, we characterize the properties of the resulting assortment from the
iterative heuristic. Products with higher demand, higher margin, or smaller physical size
should be included first in the assortment and should be assigned more inventory.
Products with lower demand variability and smaller case sizes should also be included in
the assortment first, but more inventory can be assigned to products with higher demand
variance and larger case sizes if the available shelf space is sufficiently high.
Application
Data
SKU-day-store level sales data: 20 weeks, 7 merchandises, 37 AH stores
Promotion and weather data is known.
Financial impact
Conclusion
Objective: develop an algorithmic process to help retailers determine the best assortment
for each store.
By means of:
Methodologies for estimating the parameters of the model for different sets of
available data.
Optimization algorithm: the retailer can add or delete products from stores that
carry less than full assortment and delete products from stores with full assortment.
Structural properties (suggested by heuristic optimization algorithm): higher
demand, higher margin, smaller physical size  included first in assortment and
assigned more inventory. Lower demand variability and smaller cases sizes  should
also be included first, but more inventory can be assigned to products with higher
demand variance and larger case sizes if the available shelf space is sufficiently high.
Impact:
Comparing the results of the recommendations of our system with the existing
assortments suggests a more than 50% increase in profits.
The method described here demonstrates that focusing on the right decisions (the
set of products and their stocking levels) and taking operational characteristics of
products into account in assortment planning can greatly improve a retailer’s
profitability.
Drawback:
The methodology is not suitable for seasonal product categories, because we do not
deal with a dynamic assortment problem. Still, the optimisation model can be used
within each season.
Further research:
At Albert Heijn, price and promotion are the variables influencing the utility of
product 𝑗. It is straightforward to incorporate variables other then these into the
approach.
[22] V RYZIN, MAHAJAN (1999)
Title: On the Relationship Between Inventory Costs and Variety Benefits in Retail
Assortments
Abstract
Consider a category of product variants distinguished by some attribute such as colour or
flavour. A retailer must construct an assortment for the category, i.e., select a subset
variants to stock and determine purchase quantities for each offered variant. We analyze
this problem using a multinomial logit model to describe the consumer choice process
and a newsboy model to represent the retailer’s inventory cost. We show that the
optimal assortment has a simple structure and provide insights on how various factors
affect the optimal level of assortment variety. We also develop a formal definition of the
level of fashion in a category using the theory of majorization and examine its
implications for category profits.
Introduction and Literature Review
Analytical study with the Multinomial logit model (MNL), under assortment based
substitution. The article addresses the costs and benefits of product variety (colours,
flavours, sizes) as analysed from a joint marketing-operations perspective. Our primary
aim is to obtain theoretical insights rather than to provide a decision support tool.
Variety costs:
Direct costs (few): set-up and change-over
Indirect costs: stock-outs and overstocking
Assumption: While the concept of a “category” of merchandise is not well defined in
general, we have in mind a specialized category of merchandise, consisting of alternative
variants, offered at identical retail prices and having identical unit costs. (= uniform
margins)
Variety trade-off: A retailer must decide which subset of variants should be offered and
how much inventory of each should be stocked. Adding variants to the assortment
increases the likelihood that consumers will purchase something from the assortment.
However, including more choice alternatives reduces the volume of demand for each
variant individually. This thinning—or fragmenting—of total demand increases the
variability of demand for each variant, which in turn tends to drive up inventory costs.
Model:
Demand: stochastic choice process, individual purchase decisions according
nulinomial logit random utility model (MNL)
Supply process: newsboy problem (stochastic inventory model)
Interpretations:
Short-run variety and inventory decisions for a specialized merchandise category
within a store (direct costs, variable, short-run opportunity costs for shelf space)
Stylized representation of the long-run, strategic assortment (entire range of
products) decisions of an entire specialty store (fixed costs of store space for
example)  uniform margins is rough estimation of the typical margins
Model Formulation
We formulate several versions of our assortment model for a single merchandise
category.
Assumptions:
Each variant is offered at identical retail price (𝑝) and had identical unit cost (𝑐)
𝑝 is exogenously determined (price competition, manufacturer suggests retail price)
𝑈𝑗 is unobservable  individual’s choice is uncertain
Utility values can vary from individual to individual due to heterogeneity of
preference among customers
Independence from irrelevant alternatives  MNL model should be restricted to
choice sets containing alternatives that are, in some sense, “equally dissimilar” (e.g.,
different colours or different sizes, but not different colour-size combinations).
Customers choose based only on knowledge of the set 𝑆, and they have no
knowledge of the inventory status of the variants in 𝑆.  static choice assumption.
If a customer selects a variant in 𝑆 and the store does not have it in stock, the
customer does not undertake a second choice, and the sale is lost.  static choice
assumption
Independent Population Model: aggregate demand is normally distributed.
Trend-Following Population Model: aggregate demand is Bernoulli random variable.
Multinomial Logit model: choice decision.
Each individual in the population associates a utility 𝑈𝑗 with the variants 𝑗 ∈ 𝑆.
There is a no purchase option (𝐽 = 0), with associated utility 𝑈0 .
An individual chooses the variant with the highest utility among the set of available
choices, (𝑈𝑗 : 𝑗 ∈ 𝑆 ∪ {0}).
Adding an option:
o More likely choice of purchase (only if max{𝑈𝑗 } ≥ 𝑈0 )
𝑗∈𝑆
-
-
o
o
-
o Switching between options (if 𝑈𝑖 > 𝑈𝑗 )
The selection of the set 𝑆 affects the choice decision of each consumer and hence
the total demand for each variant.
𝑈𝑗 is unobservable and varies from individual to individual. This variable is modelled
by summing nominal utility (𝑢𝑗 ) and a zero-mean variable (𝜉𝑗 ) with a Gumbel
distribution.  Higher value of μ for more heterogeneity.
Independence from irrelevant alternatives (IIA): not realistic if adding a new
alternative reduces the probability of choosing similar alternatives more than
dissimilar ones.
𝑣𝑗 = preference, high means higher expected utility.
(1) reflects that variants are choice alternatives. If we add variant:
Original probability certain choice decreases.
Overall probability increases (sum 𝑞𝑗 (=choice probabilities))
It is only a customer’s initial choice that is influenced by the set of alternatives that
are offered. (static choice assumptions  uninformed customer explanation, storevisit explanation, store-setting explanation and no stockouts explanation)
Independent Population Model: aggregate demand model I.
Aggregate demand is the result of a series of independent choices from a
heterogeneous population of consumers, assumed to be normally distributed.
The independent purchase model is useful for basic product categories, in which
aggregate consumer preference is relatively stable and the primary uncertainty is
over individual preferences for colour, size, or flavour that inherently vary from one
customer to the next.
Trend-Following Population Model: aggregate demand model II.
Aggregate demand is the result of a series of dependent choices from a
homogeneous population, assumed to be a Bernoulli random variable.
Each customer has identical valuations of the utilities for the variants, and this
uniform set of utilities is determined by a single sample of the MNL model.  each
customer same choice.
Supply process: costs of stockout and not sold, (assumption: no salvage value).
Expected profit: 𝐸[ 𝑝 𝑚𝑖𝑛 { 𝑥𝑗 , 𝑌𝑗 } − 𝑐𝑥𝑗 ].
Independent Population Model: the maximum expected profit depends on 𝑆 and 𝑣
through their effect on the choice probabilities, which in turn determine 𝑌𝑗 . Given a
normal distribution the maximum formula becomes:
Trend-Following Population Model:
a  high margins create an incentive to stock higher levels of variety.
b  considers the effect of no-purchase utility on variety. as the no-purchase utility
declines, the prospect of losing a purchase to an external option decreases while the
threat of within-assortment cannibalization increases. Therefore, it is in the retailer’s
interest to decrease the breadth of the assortment. (More competitive environment,
more variety)
c  in the independent demand case, as the volume of business increases, high
variety becomes increasingly more profitable, and a store will carry all variants for a
sufficiently high volume. =scale economies. due to the risk pooling (overstocking,
understocking, fragmented purchase decision) inherent in a large number of
independent purchase decisions. In trend-following case, profit is direct proportional
to 𝜆.
Defining Fashion Using Majorization Ordering
This paragraph considers comparisons among different merchandise categories. We show
below that the “evenness” of the preference vector 𝑣 provides a natural measure of
“fashion” and this notion can be made precise using the theory of majorization.
Assortment Optimization
The Assortment optimization problem (AP) is a knapsack problem with a nonlinear and
nonseparable objective function. For this, a iterative heuristic is given:
Numerical study
This section assesses the performance of the iterative heuristic.
than inventory holding costs. Performance can be still improved by optimizing amount of
order advancement.
Future research:
 Interaction effects between regression coefficients (so between explanatory
variables).
 Only looked at periodic demand patterns, but you can also take stock outs into
account
 Focused on common logistics variables rather than the store wise fixed effects in the
regression model. Include bias and competence.
 Apply to other retailers
[18] GAUR, FISHER (2004)
Title: A Periodic Inventory Routing Problem at a Supermarket Chain
How the scale of the business, gross profit margins and the attractiveness of outside
alternatives affect the optimal level of variety offered:
Estimation of Stockout-Based Substitution with Inventory-Transactions Data
If the service levels are not high enough to ignore stockouts and stockout-based
substitution but inventory-transactions data are available, one can estimate the original
demand for each product and substitution probabilities (for both stockout- and
assortment-based substitution) simultaneously by using a generalization of the earlier
mentioned demand estimation approach.
Demand estimation
Data available for estimating parameters of a demand model:
#customers that made transactions on a given day
Sales for exact product-store-day
Additional demand influencing variables (such as weather, holidays, price,
promotion)
The Optimal Assortment Problem
The problem admits a two level hierarchy:
At the lower level the retailer selects the optimal stocking levels given 𝑆 and 𝑣.
At a higher level, the retailer chooses the best set of variants S by solving
𝑚𝑎𝑥 𝑝𝑖(𝑆, 𝑣).
1: A nonnegative vector 𝑦 that majorizes 𝑥 tends to have more of its “mass”
concentrated in a few components. In our problem, majorization provides an
appropriate measure for the degree of fragmentation in consumer preference within
a given category of merchandise.
2: assumptions are that they have same number of variants and sum of parts is
equal.
Definition 2 says that, for fashion categories, preferences are more evenly spread out
across variants. Alternatively, in the trend-following demand case, the degree of
fragmentation of the retailer’s prior information of consumer preferences for
variants is higher for the fashion category than for the basic category.
Fashion corresponds to fragmentation in preference (or prior information on
preference), while trendy corresponds to correlated purchase behaviour among
consumers.
The profits of two categories are affected, in general, by a combination of volume,
gross margin and fashion effects.
If one merchandise category is more fashionable than another, then, all other things
being equal, the optimal profit of the fashion category will be lower than that of the
more basic category. The intuitive reason for this is that the risk of inventory overage
and underage is higher due to the higher fragmentation of consumer purchase
decisions in the fashion category. Thus, even under optimal variety and stocking
decisions, the fashion category is less profitable at a given price.
But: higher gross margins may serve to compensate retailers for the increased
inventory risks induced by the highly fragmented purchase choices of the fashion
category.  equilibrium price: equilibrium margins tend to be higher for fashion
categories.
Implications:
High margins may justify using fast and expensive logistic processes  replenish is
season. (strategy to manage a fashion category with dependent (trend-following)
purchase behaviour)
Theorem 2 suggests that there are scale economies to offering variety in the
independent (non-trend-following) population case. As a result, fast replenishment
may not be a viable logistics strategy for this type of category because competing
retailers can mitigate fashion risks using large-scale store formats (or centralized
warehouses) without resorting to expensive logistics options.
[13]
DONSEL AAR
GAUR
WOENSEL
BR OEKMEUL EN
FRANSOO – 2010
Title: Ordering behavior in retail stores and implications for automated replenishment
Abstract:
Retail store managers may not follow order advices generated by an automated inventory
replenishment system if their incentives differ from the cost-minimization objective of
the system or if they perceive the system to be suboptimal. We study the ordering
behavior of retail store managers in a supermarket chain to characterize such deviations
in ordering behavior, investigate their potential drivers, and thereby devise a method to
improve automated replenishment systems. Using orders, shipments, and point-of-sale
data for 19,417 item–store combinations over five stores, we show that (i) store
managers consistently modify automated order advices by advancing orders from peak
to nonpeak days, and (ii) this behavior is explained significantly by product
characteristics such as case pack size relative to average demand per item, net shelf
space, product variety, demand uncertainty, and seasonality error. Our regression
results suggest that store managers improve upon the automated replenishment system
by incorporating two ignored factors: in-store handling costs and sales improvement
potential through better in-stock. Based on these results, we construct a method to
modify automated order advices by learning from the behavior of store managers.
Motivated by the management coefficients theory, our method is efficient to implement
and outperforms store managers by achieving a more balanced handling
workload with similar average days of inventory.
Introduction:
A store manager may choose to sometimes bypass the ordering system and instead
decide orders manually. The system is about inventory holding costs, while managers care
more about product availability and labor capacity requirements because they are
rewarded based on revenues and labor costs. So, the system is overruled when system
inadequacy or incentive misalignment. Managers effectively advance orders from peak
days to preceding nonpeak days. Their analysis follows the approach of Bowman, who
formulated a management coefficients theory stating that “managerial decisions might
be improved more by making them more consistent from one time to another than by
approaches purporting to give optimal solutions to explicit cost models … especially for
problems where intangibles must otherwise be estimated or assumed.” Our paper
presents a new test of this theory and develops a methodology for applying it to
inventory replenishment in retail stores. The retail store inventory management problem
described in our paper is similar to the capacitated lot-sizing problem (CLSP) in
production planning as well as the periodic inventory control problem with batch
ordering in inventory theory. The paper differs from literature by examining the ideas not
in a normative model, but through the behavior of managers, and showing that managers
apply these ideas independently to improve upon an automated decision support system.
Context:
Large supermarket chain in Europe. Demand for products follows a weekly seasonality
pattern. Excess demand is lost. The demand forecast is based on an exponential
smoothing model taking into account the weekly seasonality pattern. Stores receive three
to six replenishments each week. The policy implemented in the automated ordering
system at our subject retailer is an (R,nQ) policy where R denotes the reorder level and Q
the case pack size, in which the value of R is set taking into account not only inventory
costs but also marketing considerations. The length of the review period is the time
between two deliveries. The lead time is one sales day. ASO System: determines the
order quantity for each item i in store s given the delivery schedule, demand forecast and
case pack size. R is based on, for example, service level and after determining this level,
the ASO checks current inventory position and eventually orders minimum number of
case packs required. Deviations from the ASO system: We identify system inadequacy and
incentive misalignment as the main reasons for store managers to deviate from the ASO
system. The store manager is not penalized for inventory holding costs, whereas the ASO
system explicitly considers them in its objective function. Thus, the store manager may
prefer to carry extra inventory in the store to reduce stock outs and improve sales.
Further, ASO system does not include workload balancing. It is not that retailers do not
care about inventory costs, but rather, they treat them as a corporate-level responsibility,
creating incentive misalignment at the store level.
Hypotheses:
Order advancement index AI: we measure the extent of order advancement for each SKU
by computing the average number of days that order quantities are moved forward in
time compared to the benchmark ASO system. This is the dependent variable. The
method is suitable for periodic demand patterns. The index allows them to utilize
transactional data even though both inventory and transactional data are not 100%
accurate. Because they use actual sales to simulate the ASO system, they test the
robustness of this approach by also simulating the ASO system on random draws of
demand from its forecast distribution.
We identify seven (explanatory) variables that are related to the AI:
1. Case pack cover: AI is positively correlated with case pack cover, because the store
manager can transfer the handling workload for such SKUs completely from peak to
non-peak days –and- larger cover increases AI (larger cover means less frequently
ordering)
2. Net shelf space: AI is positively correlated with the amount of net shelf space
available, because SKUs with larger net shelf space are more suitable candidates to
be ordered earlier since backroom inventory is undesirable.
3. Physical volume: AI is positively correlated with the physical volume of the item,
because they require greater handling effort.
4. Profit margin: AI is positively correlated with absolute profit margin, because the
increased service level obtained from advancing orders translates into a larger profit
increase for higher-absolute margin items.
5. Variety: AI is positively correlated with variety in a product subgroup, because 1) it is
well known that the optimal assortment size in a product category is inversely
related to the degree of substitution among products, and 2) variety can stimulate
demand as modeled in many papers.
6. Seasonality error: AI is positively correlated with seasonality error (root mean
squared error of the difference between the seasonality pattern of demand input
into the ASO system and the actual seasonality pattern of demand estimated from
the sales realization in the subgroup), to avoid taking the risk of stock outs due to
poor seasonality estimates.
7. Forecast dispersion: AI is positively correlated with forecast dispersion (standard
deviation of the daily forecast error of sales divided by average sales) to protect itself
against potential forecast errors and resulting stock outs by advancing orders for
those items that have higher forecast dispersion.
Data:
Five stores that represent a diverse set of values of selling space and turnover, and are
considered by the retail chain’s management to be well operated and representative of
the chain. Delivery through the central warehouse ensures that we have invoice data for
all SKUs in the data set. Ordering via the ASO system ensures that we have the inventory
control parameters (by the way, no frozen or perishable goods are taken into account).
Daily sales data for each SKU are obtained from the cash register systems of the stores.
Sales promotions are identical across all stores and typically last a week. The data is not
corrected for promotions, because it is not possible to make a unique link between the
sales in the promotion week and the deliveries in the weeks before the promotion and in
the promotion week. Data is also not filtered for phasing-in and phasing-out effects. A
conservative trading period is used to filter out SKUs with very few sales (outflow) and
order (inflow) transaction data points, which would lead to estimation errors.
Analysis:
1. Present a way to measure order advancement using detailed point-of-sale (POS) and
order transaction data.
2. Build a regression model to describe the decision rule that the store manager would
(hypothetically) use to decide the amount of order advancement for each item.
3. The method learns from the managers’ behavior and feeds it back into decision rules.
Models with results:
Model 1: base case
Model 2: tests role of explanatory variables (not number 5 and 6, see above)
Model 3: same as Model 2, but variable 5 and 6 included and also removed subgrouplevel fixed effects and store-subgroup interaction effects
Model 4: same as Model 3, but also exclude store-level fixed effects
Results:
The hypotheses tests show that most of the explanatory variables are statistically
significant and explain a large proportion of the variance of order advancement. We
implement the management coefficients model of inventory replenishment in our
simulations and evaluate its performance in terms of the seasonality range of the
workload pattern and the average days of extra inventory as measured by the order
advancement metric. The management coefficients model performs better than the
human process in balancing handling workload. The store manager may modify orders
too much or too little for different SKUs. Our model by consistently advancing the orders
for all items, reduces this error. Our model does however not correct for bias.
The results can be used in two ways:
1. We show how Bowman’s method can be extended for modifying the automated
store ordering (ASO) system by constructing a decision rule based on the store
managers’ behavior that works even in the absence of clean inventory data.
2. The results of the empirical analysis can be useful in improving the design and
implementation of ASO systems.
Conclusion
Order advancement led to more balanced workload. It also leads to an increase of 0,5 day
of inventory, which is 9..6% increase over the automated replenishment system.
However, this increase can benefit in case of stock outs and handling costs are higher
The vehicle routing and delivery scheduling (VRDS) of Albert Heijn (AH) has the
following features:
1. 1 national DC, 4 regional DC’s to which stores are assigned
2. Intervals between successive deliveries should not exceed a specified limit (for
example because of perishable goods, small backroom capacity)
3. Delivery times for a store remain the same every week (this periodic delivery
schedule is called VVM heartbeat (vandaag voor morgen))
4. Demand is random and varies with time; hourly demand varies much during the
week, but every week same pattern, except from holidays and promotions
5. Shipments based on orders; if exceeds available truck capacity, an extra shipment is
scheduled
6. Routes are assigned to a heterogeneous fleet of trucks with different fixed and
variable cost parameters and different loading-unloading times
7. Departure time of trucks from the DCs is such that there is a balanced workload
throughout the day
8. Delivery scheduling problem must not only incorporate variable transportation costs,
but also randomness of demand, fixed truck rental costs, fleet-size constraints, and
workload capacity at the DC
Advantages of periodic schedule:
Simplifies workforce scheduling at the DCs and stores
Synchronization of periodic schedules, goods can often be cross-docked from
suppliers’ trucks to stores’ trucks
Able to have cheaper long-term contracts with truck-leasing companies
This paper: describe the development and implementation of a system to solve the VRDS
problem at AH, given the features above (and other constraints later on)
The system has three modules:
Inventory routing problem (IRP): determines delivery times of stores and the vehicle
routes (ignoring variability in demand and fleet-size constraints)
Truck assignment module: minimize cost of transportation and incorporates fleetsize and time restrictions
Workload balancing module: readjust departure time to match target workload of
the DCs as closely as possible
Now: hierarchical approach: first assign delivery times based on geography and demand
patterns, then plan routes based on software package > worse than if (as done in this
article) delivery times and routes are determined jointly > cost savings by optimize
replenishment schedule and also strategic and tactical benefits to firm
From literature: IRPs can be classified in three types:
Strategic IRP: estimate minimum cost of vehicle fleet to supply inventory, based on
probability distributions of demand, to purchase or lease vehicles for long time
periods
Tactical/finite horizon IRP: considers set of customers over finite horizon and fixed
truck fleet and each period there is a trade-off between current costs and future
costs
Infinite horizon IRP: replenishments from a central DC to a set of customers with
objective to minimize sum of long-run average transportation, ordering and
inventory holding costs
IRP seems a bit as vehicle routing problem (VRP), whereby each customer is visited
several times during planning horizon
In this article: the supermarkets are owning the distribution network
Assumptions:
Fleet-size restrictions are ignored
Fixed partition policy: customers partitioned in regions/clusters which are served
separately and independently  first considered: at most two stores per cluster
because of big volumes
A single homogeneous product with deterministic but time-varying demand 
because of this time variation: two types of routes, namely, shared routes (visit every
store in cluster) and direct shipments (individual stores) dependent on for example a
high- or low-volume day
Model:
Objective function: transportation costs of all direct and shared shipments (inventory
holding costs are ignored)
Constraints:
Delivered quantity at time t is equal to the total demand between this delivery at
time t and delivery at time t+1 for store i
Number of direct and shared shipments are sufficient to deliver required quantities
to cluster k at time t
The numbers of shipments are integers
This is a simplified VRP in cluster k with only two types of routes  extension: larger
clusters and a heterogeneous vehicle fleet (instead of single truck type as in the previous
model): first least-cost scheduling, then single- and two-route improvement steps to
replace shared shipments by cost-improving direct shipments
Model:
Objective function: minimize costs of optimal delivery schedule; with constraint that each
store must be included in exactly one cluster (en zit wel of niet in bepaald cluster)
Special case: at most two stores per cluster
Periodic IRP as set-partitioning problem P can be solved by algorithms: shortest path
problem and weighted matching  Generalized weighted matching problem (GWMP):
problem of finding a matching such that the sum of the costs of the edges in the matching
and the penalties of the unmatched nodes is minimum  in this article: use algorithm
wherefore converting the problem into a maximum weight matching problem
General case for clustering
Solve P for any cluster size: heuristic of randomized sequential matching algorithm
(RSMA) with two main ideas: repeated application of GWMP and randomized splitting of
clusters
Computational Analysis
Characteristics of store demand: higher on Friday+Saturday, much variation between
stores, maximum daily demand on each day is larger than vehicle capacity (so more than
1 delivery a day)
Five solutions per problem (three problems based on one week data of three different
DCs):
A is AHs current system
B and C is using identical delivery times as AH and solve VRP (B: max. 2 deliveries per
route: GWMP; C: no restriction number of deliveries per route: RSMA)
D and E optimize both delivery times and vehicle routes (D: 2 stores per cluster; E: no
restriction on cluster size).
Comparing B-C with D-E, respectively, gives incremental gain from inventory routing
Findings:
Cost savings (most D-E relative to A but also savings of D-E relative to B-C)
Total number of routes in B-C-D-E decline by 20.3%-28.4% relative to A
Average number of deliveries per route decreases when going from B-C to D-E
Number of deliveries per route is just marginally larger in C-E than B-D (because
relatively few clusters with more than two stores)  advantage large cluster:
increase capacity utilization of trucks because pools volume across several stores;
disadvantage: increase distance per unit shipment and transportation costs  is a
trade-off: large clusters mainly in cities where stores close together

Cost savings to AH, based on inventory routing module
>
Additional savings were obtained from other two modules
Important aspects of three modules:
Inventory routing module: extra constraints are added such as store-specific loadingand unloading time, truck-store feasibility, pre-emption (because of taking into
account traffic delays) and a trade-off between expected costs of spillovers (if order
exceeds buffer space) against cost of added buffer space (based on standard
deviations in demand)
Truck assignment module: assigns routes to trucks such that sum of leasing-, waitingand driver costs is minimized; there is a heuristic to iterate the IRP module and this
module
Workload balancing module: each DC has a target workload profile specified for each
15-minute interval of the day and therefore (un)loading is balanced; the heuristic is
complicated by the fact that reassigning a route to a different time can change
duration (traffic delays) and costs of routes
Implementation of VRS system (vehicle route scheduling): approval of implementation
did depend on the distribution logistics division; route planners were involved and before
the implementation; the system was tested on a large number of simulated and real-life
test problems, and run in parallel with the existing system of AH for six months. The
implementation was done in three steps.
VRS system realizes savings of 4% of transportation costs in the first year, and expects
total savings of 12%-20% in the future
Functionality has enhanced since implementation include both deliveries and pick ups (so,
also schedule shipments from central DC to regional DCs)
It is also implemented in other companies of Ahold Corporation
Benefits of implementation:
Sensitivity analysis of operational factors is possible
Performance analysis through enhance ordering decisions from stores (through point
them for example to the cost impact of high order variability that they have)
Strategic benefits: improve logistics increase replenishment frequency and reduce
lead time and therefore more fresh products, what can differentiate from
competitors
[1] AGATZ CAMPBELL FL EISHMANN SAVELSBERGH
Title: Time Slot Management in Attended Home Delivery
1.
Motivation
What real-life problem motivated the writing of the research paper?
The success of many e-commerce business hinges upon their ability to offer efficient and
effective “last-mile” delivery. This paper uses the attended home delivery service of
Albert Heijn (albert.nl) as example throughout the paper. This service provides customers
to order their groceries and get them delivered in a certain two-hour delivery time slot.
While ordering, a customer can make a choice between a number of offered time slots.
Each time slot has a corresponding delivery fee.
The problem that is addressed in this paper is Time Slot Management Problem (TSMP). In
other words: selecting the set of timeslots to offer in each of the zip codes in a service
region (i.e., given service requirements and average weekly demands for each zip code in
the delivery region, determine the set of time slots to offer in each zip code so as to
minimize expected delivery costs while meeting the service requirements). At this
moment, this time slot determination is done manually by Albert Heijn.
This problem has two sides:

Operational: facilitating a cost-effective delivery schedule.

Marketing: ensuring an acceptable level of service to the customer, i.e. time
slots for a certain zip code evenly distributed over mornings and afternoons
and over the week and narrow timeslots.
How relevant is this problem?
The online grocery market has an an
If the distance or cost required to reach the hub is greater than the distance or cost
required for a direct shipment, then indirect shipment is not interesting from a cost
perspective, regardless of the volume. The model uses a graphical shape parameter 𝑟,
varying continuously (=not discrete) between 0 ≤ 𝑟 ≤ 1. A parameter value of 0 mean
the transportation costs are linear with the volume 𝑣𝑖𝑗 , where a value for 𝑟 = 1 displays
single stop routes.
Results:
Based on a cost function that depends on shape parameter 𝑟, we conclude that a mixed
consolidation strategy that uses direct and indirect shipments through a hub,
outperforms pure direct shipment strategies and pure indirect shipment strategies. A
major retailer in general will have more than one distribution center. Such retailers can
improve the possibilities for consolidation by not centralizing all product flows in one
RCC, but by decentralizing the consolidation function of an RCC over their distribution
centers.
Conclusion:
In this paper, V&B(06) described a basic model to analyze a mixed consolidation strategy
with direct and indirect shipments through stockless consolidation centers. This model
can help to approximate the potential savings in a retail distribution network. Based on
our transport consolidation model, we show that Supply Chain Synchronization
considerably increases the use of direct shipments and lowers the costs of handling and
transport.