The Logistic Network:
Design and Planning
©Copyright 1999 D. Simchi-Levi, P. Kaminsky & E. Simchi-Levi
Lecture Outline
1) The Logistics Network
2) Warehouse Location Models
3) Solution Techniques
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
The Logistics Network
The Logistics Network consists of:
• Facilities:
Vendors, Manufacturing Centers, Warehouse/
Distribution Centers, and Customers
• Raw materials and finished products that flow
between the facilities.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Sources:
plants
vendors
ports
Regional
Warehouses:
stocking
points
Field
Warehouses:
stocking
points
Customers,
demand
centers
sinks
Supply
Production/
purchase
costs
Inventory &
warehousing
costs
Transportation
costs
Inventory &
warehousing
costs
Transportation
costs
Network Design
The Key Issues:
1. Number of warehouses
2. Location of each warehouse
3. Size of each warehouse
4. Allocation of products to the different warehouses
5. Allocation of customers to each warehouse
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Network Design
The objective is to balance service level against
• Production/ purchasing costs
• Inventory carrying costs
• Facility costs (storage, handling and fixed costs)
• Transportation costs
That is, we would like to find a minimal-annual-cost
configuration of the distribution network that satisfies
product demands at specified customer service
levels.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Data for Network Design
1. A listing of all products
2. Location of customers, stocking points and sources
3. Demand for each product by customer location
4. Transportation rates
5. Warehousing costs
6. Shipment sizes by product
7. Order patterns by frequency, size, season, content
8. Order processing costs
9. Customer service goals
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Too Much Information
Customers and Geocoding
• Sales data is typically collected on a by-customer
basis
• Network planning is facilitated if sales data is in a
geographic database rather than accounting
database
1. Distances
2. Transportation costs
• New technology exists for Geocoding the data based
on Geographic Information System (GIS)
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Aggregating Customers
• Customers located in close proximity are
aggregated using a grid network or clustering
techniques. All customers within a single cell or a
single cluster are replaced by a single customer
located at the centroid of the cell or cluster.
We refer to a cell or a cluster as a customer zone.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Impact of Aggregating Customers
• The customer zone balances
1. Loss of accuracy due to over aggregation
2. Needless complexity
• What effects the efficiency of the aggregation?
1. The number of aggregated points, that is the
number of different zones
2. The distribution of customers in each zone.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Why Aggregate?
• The cost of obtaining and processing data
• The form in which data is available
• The size of the resulting location model
• The accuracy of forecast demand
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Demand Forecast
• The three principles of all forecasting
techniques:
– Forecasting is always wrong
– The longer the forecast horizon the worst is the
forecast
– Aggregate forecasts are more accurate
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Recommended Approach
• Use at least 200-300 aggregated points
• Make sure each zone has an equal amount of total
demand
• Place the aggregated point at the center of the zone
In this case, the error is typically no more
than 1%
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Product Grouping
• Companies may have hundreds to thousands of
individual items in their production line
1. Variations in product models and style
2. Same products are packaged in many sizes
• Collecting all data and analyzing it is impractical for
so many product groups
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Product Grouping
• In practice, items are aggregated into a reasonable
number of product groups, based on
1. Distribution pattern
2. Product type
3. Shipment size
4. Transport class of merchandise
It is common to use no more than 20 product
groups.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Transport Rate Estimation
• Huge number of rates representing all combinations
of product flow
• An important characteristic of a class of rates for
truck, rail, UPS and other trucking companies is that
the rates are quite linear with the distance.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
UPS 2 Day Rates for 150 lb.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
LTL Freight Rates
• Each shipment is given a class ranging from 500 to
50
• The higher the class the greater the relative charge
for transporting the commodity.
• A number of factors are involved in determining a
product’s specific class. These include
1. Density
2. Ease or difficulty of handling
3. Liability for damage
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Basic Freight Rates
• With the commodity class and the source and
destination Zip codes, the specific rate per hundred
pound can be located.
• This can be done with the help of CZAR, Complete
Zip Auditing and Rating, which is a rating engine
produced by Southern Motor Carriers.
• Finally to determine the cost of moving commodity
A from City B to City C, use the equation
weight in cwt  rate
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Yellow Freight (LTL) Rates for Shipping
4000 lb.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Other Issues
• Mileage Estimation
1. Street Network
2. Straight line distances
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Mileage Estimations
Straight line distances:
Example: Suppose we want to estimate the
distance between two points a and b where Lona and
Lata are the longitude and latitude of the point a and
similarly for b.
Then
Dab  69 (lon a  lon b ) 2  (lat a  lat b ) 2
where Dab is the straight line distance (miles) from a
to b.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Mileage Estimations
Straight line distances:
The previous equation is accurate only for short
distances; otherwise we use
2
D ab  2(69) sin 1
 lat - lat b 
 lon - lon b 
sin  a
  cos(lat a )  cos(lat b )  sin  a

2
2




2
This is of course an underestimate of the road distance.
To estimate the road distance we multiply Dab by a
scale factor, .
Typically =1.3.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Other Issues
• Future demand
• Facility costs
1. Fixed costs; not proportional to the amount of
material the flows through the warehouse
2. Handling costs; labor costs, utility costs
3. Storage costs; proportional to the inventory level
• Facilities capacities
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Other Issues
• How to measure storage costs?
Define
Inventory turnover ratio =
annual sales
=
average inventory level
In our case it is the ratio of the total flow through the
warehouse to the average inventory level. If the ratio
is  than the average inventory level is total flow over

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Sources:
plants
vendors
ports
Regional
Warehouses:
stocking
points
Field
Warehouses:
stocking
points
Customers,
demand
centers
sinks
Supply
Inventory &
warehousing
costs
Production/
purchase
costs
Transportation
costs
Inventory &
warehousing
costs
Transportation
costs
The Impact of Increasing the
Number of Warehouses
• Improve service level due to reduction of average
service time to customers
• Increase inventory costs due to a larger safety stock
• Increase overhead and set-up costs
• Reduce transportation costs in a certain range
– Reduce outbound transportation costs
– Increase inbound transportation costs
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Warehouse Location Models
When locating new facilities such as
warehouses, a number of requirements have
to be satisfied:
1. Geographical and infrastructure conditions
2. Natural resources and labor availability
3. Local industry and tax regulations
4. Public interest
As a result, there is only a limited number of
locations that would meet all the requirements.
These are the potential location sites for the new
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
facilities.
A Typical Network Design Model
• Several products are produced at several plants.
• Each plant has a known production capacity.
• There is a known demand for each product at each
customer zone.
• The demand is satisfied by shipping the products via
regional distribution centers.
• There may be an upper bound on total throughput at
each distribution center.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
A Typical Location Model
• There may be an upper bound on the distance
between a distribution center and a market area
served by it
• A set of potential location sites for the new facilities
was identified
• Costs:
– Set-up costs
– Transportation cost is proportional to the distance
– Storage and handling costs
– Production/supply costs
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Complexity of Network Design Problems
• Location problems are, in general, very difficult
problems.
• The complexity increases with
– the number of customers,
– the number of products,
– the number of potential locations for warehouses, and
– the number of warehouses located.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Solution Techniques
• Mathematical optimization techniques:
1. Exact algorithms: find optimal solutions
2. Heuristics: find “good” solutions, not necessarily
optimal
• Simulation models: provide a mechanism to evaluate
specified design alternatives created by the designer.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Heuristics and
the Need for Exact Algorithms
• Single product
• Two plants p1 and p2
• Plant p2 has an annual capacity of 60,000 units.
• The two plants have the same production costs.
• There are two warehouses w1 and w2 with identical
warehouse handling costs.
• There are three markets areas c1,c2 and c3 with demands
of 50,000, 100,000 and 50,000, respectively.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Heuristics and
the Need for Exact Algorithms
Table 1
Distribution costs per unit
Facility
Warehouse
W1
W2
P1
P2
C1
C2
C3
0
5
4
2
3
2
4
1
5
2
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
The Heuristics Approach
Heuristic 1: For each market we choose the
cheapest warehouse to source demand. Thus, c1, c2
and c3 would be supplied by w2.
Now for every warehouse choose the cheapest plant,
i.e., get 60,000 units from p2 and the remaining
140,000 from p1. The total cost is:
250000 + 1100000 + 2*50000
+ 260000 + 5140000 = 1,120,000.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
The Heuristics Approach
Heuristic 2: For each market area, choose the
warehouse such that the total costs to get delivery
from the warehouse is the cheapest, that is, consider
the source and the distribution.
Thus, for market area c1, consider the paths
p1w1c1, p1w2c1, p2 w1c1,
p2w2c1. Of these the cheapest is p1w1c1
and so choose w1 for c1.
Similarly, choose w2 for c2 and w2 for c3.
The total cost for this strategy is 920,000.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
The Optimization Model
The problem described earlier can be framed as the
following linear programming problem.
Let
• x(p1,w1), x(p1,w2), x(p2,w1) and x(p2,w2) be the
flows from the plants to the warehouses.
• x(w1,c1), x(w1,c2), x(w1,c3) be the flows from the
warehouse w1 to customer zones c1, c2 and c3.
• x(w2,c1), x(w2,c2), x(w2,c3) be the flows from
warehouse w2 to customer zones c1, c2 and c3
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
The problem we want to solve is:
min 0x(p1,w1) + 5x(p1,w2) + 4x(p2,w1)
+ 2x(p2,w2) + 3x(w1,c1) + 4x(w1,c2)
+ 5x(w1,c3) + 2x(w2,c1) + 2x(w2,c3)
subject to the following constraints:
x(p2,w1) + x(p2,w2)  60000
x(p1,w1) + x(p2,w1) = x(w1,c1) + x(w1,c2) + x(w1,c3)
x(p1,w2) + x(p2,w2) = x(w2,c1) + x(w2,c2) + x(w2,c3)
x(w1,c1) + x(w2,c1) = 50000
x(w1,c2) + x(w2,c2) = 100000
x(w1,c3) + x(w2,c3) = 50000
all flows greater than or equal to zero.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
The Optimal Strategy
Table 2
Distribution strategy
Facility
Warehouse
W1
W2
P1
P2
C1
C2
C3
140000
0
0
60000
50000
0
40000
60000
50000
0
The total cost for the optimal strategy is 740,000.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Simulation Models and Optimization
Techniques
• Optimization techniques deal with static models:
1. Deal with averages.
2. Does not take into account changes over time
• Simulation takes into account the dynamics of the
system
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Optimization Techniques and
Simulation
• Simulation models allow for a micro-level analysis:
1. Individual ordering pattern analysis
2. Transportation rates structure
3. Specific inventory policies
4. Inter-warehouse movement of inventory
5. Unlimited number of products, plants, warehouses
and customers
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Optimization Techniques vs.
Simulation
• The main disadvantage of a simulation model is that
it fails to support warehouse location decisions; only
a limited number of alternatives are considered
• The nature of location decisions is that they are
taken when only limited information is available on
customers, demands, inventory policies, etc, thus
preventing the use of micro level analysis.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi
Recommended approach
• Use an optimization model first to solve the problem
at the macro level, taking into account the most
important cost components
1. Aggregate customers located in close proximity
2. Estimate total distance traveled by radial distance
to the market area
3. Estimate inventory costs using the eoq model
• Use a simulation model to evaluate optimal solutions
generated in the first phase.
©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi