the logistic network: design and planning ©copyright 1999 d. simchi-levi, p. kaminsky & e....

The Logistic Network:Design and Planning

©Copyright 1999 D. Simchi-Levi, P. Kaminsky & E. Simchi-Levi

©Copyright 1999 D. Simchi-Levi, P. Kaminsky and E. Simchi-Levi

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 of customers to each warehouse


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.


Data for Network Design

1. A listing of all products2. Location of customers, stocking points and sources3. Demand for each product by customer location4. Transportation rates5. Warehousing costs6. Shipment sizes by product7. Order patterns by frequency, size, season, content8. Order processing costs9. 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 database1. Distances2. 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.


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


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%


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.


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.


UPS 2 Day Rates for 150 lb.


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.


Other Issues

• Mileage Estimation

1. Street Network

2. Straight line distances


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.

2

baba

2

ba1ab 2

lon-lonsin)cos(lat)cos(lat

2

lat-latsinsin)69(2D


Other Issues

• Future demand

• Facility costs

1. Fixed costs; not proportional to the amount of material the flows through the warehouse2. Handling costs; labor costs, utility costs3. Storage costs; proportional to the inventory level

• Facilities capacities


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

Supply

Sources:plantsvendorsports

RegionalWarehouses:stocking points

Field Warehouses:stockingpoints

Customers,demandcenterssinks

Production/purchase costs

Inventory &warehousing 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


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 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.


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


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.


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.


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.


Heuristics andthe Need for Exact Algorithms

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 components1. Aggregate customers located in close proximity2. Estimate total distance traveled by radial distance to the market area3. Estimate inventory costs using the eoq model

• Use a simulation model to evaluate optimal solutions generated in the first phase.

the logistic network: design and planning ©copyright 1999 d. simchi-levi, p. kaminsky & e....

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