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.

Supply

Sources:plantsvendorsports

RegionalWarehouses:stocking points

Field Warehouses:stockingpoints

Customers,demandcenterssinks

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 geogra

phic 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

where Dab is the straight line distance (miles) from a to b.

2ba

2baab )lat(lat)lon(lon69D

Mileage Estimations

Straight line distances:

The previous equation is accurate only for short distances;

otherwise we use

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

2

baba

2

ba1ab 2

lon-lonsin)cos(lat)cos(lat

2

lat-latsinsin)69(2D

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

levelInventory 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 1Distribution costs per unit

FacilityWarehouse

P1 P2 C1 C2 C3

W1W2

05

42

32

41

52

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:

250000 + 1100000 + 2*50000

+ 260000 + 5140000 = 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 p1w1c1, p1w2c1, p2 w1c1, p2w2c1. Of these the cheapest is p1w1c1 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 Heuristics Approach

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 2Distribution strategy

FacilityWarehouse

P1 P2 C1 C2 C3

W1W2

1400000

060000

500000

4000060000

500000

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.