The Logistic Network:
Design and Planning
Chap 02
王仁宏 助理教授
國立中正大學企業管理學系
©Copyright 2001 製商整合科技中心
Case: The Big Corporation (1/3)
• A soft drinks company
• 2 plants in Atlanta and Denver
• 3 warehouses in Chicago, Dallas, and
Sacramento
• 120,000 accounts (retailers or stores)
• Value of each SKU is $1,000 for all
products
Case: The Big Corporation (2/3)
• Redesign the logistics network:
– about 10,000 accounts should received
deliveries directly from the plants
– group the accounts into 250 zones
– group the different products into 5 families
– delivery time should be no more than 48
hours, i.e., the distance within 900 miles
– expand old plants instead of building a new
one
Case: The Big Corporation (3/3)
• Questions:
– How many distribution centers should be
established?
– Where should they be located?
– How should the plants’ output of each product
be allocated between warehouse?
– Should production capacity be expand?
When and where?
Lecture Outline
1) The Logistics Network
2) Warehouse Location Models
3) Solution Techniques
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.
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 space for products in each warehouses
6. Allocation of customers to each warehouse
Network Design
The objective is to balance service level subject to:
• Production/ purchasing costs
• Inventory holding costs
• Facility costs (storage, handling and fixed costs)
• Transportation costs (different transportation mode)
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.
The More Warehouse, the
more ...
• Improvement in service level
• inventory costs due to increased safety
stock
• overhead and setup costs
• reduction in outbound transportation costs
(from warehouses to customers)
• inbound transportation costs (from plants
to warehouses)
Data Collection 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
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)
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.
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.
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
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.
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
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
• The variability faced by the aggregated customer is
smaller than the combined variabilities faced by the two
existing customers
Recommended Approach
• Aggregate demand points for 150 to 200 zones.
• Make sure each zone has an equal amount of total
demand
• Place the aggregated point at the center of the zone
• Aggregate the product into 20 to 50 product groups
In this case, the error is typically no more than
1%
Transport Rate Estimation
• 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.
• Huge number of rates representing all combinations
of product flow
UPS 2 Day Rates for 150 lb.
Mileage Estimation
• Street Network
• Straight line distances
• Geographic Information Systems (GIS)
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.
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 for metropolitan areas, =1.14 for
continental Unite States
Warehouse Costs
• Fixed costs: proportional to the warehouse capacity in
a nonlinear way
• Handling costs: labor costs, utility costs, proportional
to annual flow through the warehouse
• Storage costs: proportional to the average inventory
level
Inventory turnover ratio
=
annual sales (flow)
average inventory level
Warehouse Capacity
• The requires storage space is
approximately twice of the average
inventory level.
• Also require empty space for access and
handling: aisles, picking, sorting, AGV,…
• Multiply requires storage space by a factor
(>1), a practical one is “3”.
Potential Warehouse Location
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 facilities.
Service Level Requirement
• Two types:
– delivery time
– specifying a maximum distance between
customers and warehouse
A Typical Network Design
Model (1/2)
• 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.
A Typical Network Design
Model (2/2)
• 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
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 warehouses located
– the number of potential locations for warehouses,
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.
Example 2.4.1
• 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.
Example 2.4.1
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
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.
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.
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
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.
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.
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
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
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.
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.
Key Features of a Network
Configuration DSS
•
•
•
•
•
•
•
•
Customer-specific service level requirements
existing warehouses
expansion of existing warehouses
specific flow patterns
warehouse-to-warehouse flow
Bill-of-Material
effectiveness (robustness)
reasonable running time
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
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
Yellow Freight (LTL) Rates for
Shipping 4000 lb.