1. 13-1 Facility Location Decisions Chapter 13 CR (2004) Prentice Hall, Inc. Experience teaches that men are so much governed by what they are accustomed to see and practice, that the simplest and most obvious improvements in the most ordinary occupations are adopted with hesitation, reluctance, and by slow graduations. Alexander Hamilton, 1791

2. 13-2 CR (2004) Prentice Hall, Inc. Facility Location in Location Strategy PLANNING ORGANIZING CONTROLLING Transport Strategy Transport fundamentals Transport decisions Customer service goals The product Logistics service Ord. proc. & info. sys. Inventory Strategy Forecasting Inventory decisions Purchasing and supply scheduling decisions Storage fundamentals Storage decisions Location Strategy Location decisions The network planning process PLANNING ORGANIZING CONTROLLING Transport Strategy Transport fundamentals Transport decisions Customer service goals The product Logistics service Ord. proc. & info. sys. Inventory Strategy Forecasting Inventory decisions Purchasing and supply scheduling decisions Storage fundamentals Storage decisions Location Strategy Location decisions The network planning process

3. 13-3 CR (2004) Prentice Hall, Inc. Location Overview What's located?  Sourcing points  Plants  Vendors  Ports  Intermediate points  Warehouses  Terminals  Public facilities (fire, police, and ambulance stations)  Service centers  Sink points  Retail outlets  Customers/Users

4. 13-4 CR (2004) Prentice Hall, Inc. Location Overview (Cont’d) Key Questions  How many facilities should there be?  Where should they be located?  What size should they be? Why Location is Important  Gives structure to the network  Significantly affects inventory and transportation costs  Impacts on the level of customer service to be achieved

5. 13-5 CR (2004) Prentice Hall, Inc. Methods of Solution  Single warehouse location – Graphic – Grid, or center-of-gravity, approach  Multiple warehouse location – Simulation – Optimization – Heuristics Location Overview (Cont’d)

6. 13-6 CR (2004) Prentice Hall, Inc. Nature of Location Analysis Manufacturing (plants & warehouses) Decisions are driven by economics. Relevant costs such as transportation, inventory carrying, labor, and taxes are traded off against each other to find good locations. Retail Decisions are driven by revenue. Traffic flow and resulting revenue are primary location factors, cost is considered after revenue. Service Decisions are driven by service factors. Response time, accessibility, and availability are key dimensions for locating in the service industry.

7. 13-7 Weber’s Classification of Industries CR (2004) Prentice Hall, Inc.

8. 13-8 CR (2004) Prentice Hall, Inc. Agglomeration Based on the observation that the output of one industry is the input of another. Customers for an industry’s products are the workers of those industries. Hence, suppliers, manufacturers, and customers group together, especially where transportation costs are high. Historically, the growth of the auto industry showed this pattern. Today, the electronics industry (silicon valley) has a similar pattern although it is less obvious since the product value is high and transportation costs are a small portion of total product price.

9. 13-9 CR (2004) Prentice Hall, Inc. Method appraisal  A continuous location method  Locates on the basis of transportation costs alone The COG method involves  Determining the volumes by source and destination point  Determining the transportation costs based on $/unit/mi.  Overlaying a grid to determine the coordinates of source and/or destination points  Finding the weighted center of gravity for the graph COG Method

10. 13-10 CR (2004) Prentice Hall, Inc. COG Method (Cont’d) where V i = volume flowing from (to) point I R i = transportation rate to ship V i from (to) point i X i,Y i = coordinate points for point i = coordinate points for facility to be located

11. 13-11 CR (2004) Prentice Hall, Inc. COG Method (Cont’d) Example Suppose a regional medical warehouse is to be established to serve several Veterans Administration hospitals throughout the country. The supplies originate at S 1 and S 2 and are destined for hospitals at H 1 through H 4. The relative locations are shown on the map grid. Other data are: Note rate is a per mile cost Point i Prod- uctsLocation Annual volume, cwt. Rate, $/cwt/ mi.X i Y i 1 S 1 ASeattle8,0000.020.67.3 2 S 2 BAtlanta10,0000.028.63.0 3 H 1 A & BLos Angeles 5,0000.052.03.0 4 H 2 A & BDallas3,0000.055.52.4 5 H 3 A & BChicago4,0000.057.95.5 6 H 4 A & BNew York6,0000.0510.65.2

12. 13-12 CR (2004) Prentice Hall, Inc. COG Method (Cont’d) Map scaling factor, K

13. 13-13 CR (2004) Prentice Hall, Inc. COG Method (Cont’d) Solve the COG equations in table form iX i Y i V i R i V i R i V i R i X i V i R i Y i 10.67.38,0000.02160961,168 28.63.010,0000.022001,720600 32.03.05,0000.05250500750 45.52.43,0000.05150825360 57.95.54,0000.052001,5801,100 610.65.26,0000.05 300 3,180 1,560 1,2607,9015,538

14. 13-14 COG Method (Cont’d) Now, X = 7,901/1,260 = 6.27 Y = 5,538/1,260 = 4.40 This is approximately Columbia, MO. The total cost for this location is found by: whereK is the map scaling factor to convert coordinates into miles. CR (2004) Prentice Hall, Inc.

15. 13-15 CR (2004) Prentice Hall, Inc. COG COG Method (Cont’d)

16. 13-16 CR (2004) Prentice Hall, Inc. COG Method (Cont’d) 2,360,882 Total 660,4920.056,0005.210.66 196,6440.054,0005.57.95 160,7330.053,0002.45.54 561,7060.055,0003.02.03 271,8250.0210,0003.08.62 509,4820.028,0007.30.61 TCRiRi ViVi YiYi XiXi i Calculate total cost at COG

17. 13-17 CR (2004) Prentice Hall, Inc. Note The center-of-gravity method does not necessarily give optimal answers, but will give good answers if there are a large numbers of points in the problem (>30) and the volume for any one point is not a high proportion of the total volume. However, optimal locations can be found by the exact center of gravity method.      i iii i iiii n i iii i iiii n /dRV YRV Y, RV XRV X where 22 )Y(Y)X(Xd n i n ii  andn is the iteration number. COG Method (Cont’d)

18. 13-18 CR (2004) Prentice Hall, Inc. Solution procedure for exact COG COG Method (Cont’d) 1)Solve for COG 2)Using find d i 3)Re-solve for using exact formulation 4)Use revised to find revised d i 5)Repeat steps 3 through 5 until there is no change in 6)Calculate total costs using final coordinates

19. 13-19 CR (2004) Prentice Hall, Inc.  A more complex problem that most firms have.  It involves trading off the following costs:  Transportation inbound to and outbound from the facilities  Storage and handling costs  Inventory carrying costs  Production/purchase costs  Facility fixed costs  Subject to:  Customer service constraints  Facility capacity restrictions  Mathematical methods are popular for this type of problem that:  Search for the best combination of facilities to minimize costs  Do so within a reasonable computational time  Do not require enormous amounts of data for the analysis Multiple Location Methods

20. 13-20 Location Cost Trade-Offs Number of warehouses Cost Production/purchase and order processing Inventory carrying and warehousing Warehouse fixed Inbound and outbound transportation Total cost 0 0 CR (2004) Prentice Hall, Inc.

21. 13-21 Multiple COG  Formulated as basic COG model  Can search for the best locations for a selected number of sites.  Fixed costs and inventory consolidation effects are handled outside of the model. A multiple COG procedure  Rank demand points from highest to lowest volume  Use the M largest as initial facility locations and assign remaining demand centers to these locations  Compute the COG of the M locations  Reassign all demand centers to the M COGs on the basis of proximity  Recompute the COGs and repeat the demand center assignments, stopping this iterative process when there is no further change in the assignments or COGs CR (2004) Prentice Hall, Inc.

22. 13-22 CR (2004) Prentice Hall, Inc.  Location of truck maintenance terminals  Location of public facilities such as offices, and police and fire stations  Location of medical facilities  Location of most any facility where transportation cost (rather than inventory carrying cost and facility fixed cost) is the driving factor in location  As a suggestor of sites for further evaluation Examples of Practical COG Model Use

23. 13-23 CR (2004) Prentice Hall, Inc.  A method used commercially -Has good problem scope -Can be implemented on a PC - Running times may be long and memory requirements substantial - Handles fixed costs well - Nonlinear inventory costs are not well handled  A linear programming-like solution procedure can be used (MIPROG in LOGWARE) Mixed Integer Programming

24. 13-24 CR (2004) Prentice Hall, Inc. Example The database for the illustrated problem is prepared as file ILP02.DAT inMIPROG. The form is dictated by the problem formulation in the technical supplement of the location chapter. The solution is to open only one warehouse (W 2 ) with resulting costs of: CategoryCost Production$1,020,000 Transportation1,220,000 Warehouse handling310,000 Warehouse fixed 500,000 Total$3,050,000 MIP (Cont’d)

25. 13-25 MIP (Cont’d) A Multiple Product Network Design Problem The situation

26. 13-26 Mixed Integer programming

27. 13-27

28. 13-28 CR (2004) Prentice Hall, Inc. Guided Linear Programming Searches for the best locations. A typical problem is shown in the next figure and can be configured as a transportation problem of linear programming in terms of its variable costs.  The inventory and warehouse fixed costs are computed as per-unit costs, but this depends on the warehouse throughput. They are placed along with the variable costs in the linear programming problem.  The linear programming problem is solved. This gives revised demand assignments to warehouses. Some may have no throughput and are closed.  Fixed costs and inventory carrying costs are recomputed based on revised warehouse throughputs.  When there is no change in the solution from one iteration to the next, STOP.

29. 13-29 Guided Linear Programming (Cont’d) The situation CR (2004) Prentice Hall, Inc.

30. Guided Linear Programming (Cont’d) Example  Use data from the network figure.  Allocate the fixed costs. Assume initially that each warehouse handles the entire volume. Hence, Warehouse 1 100,000/200,000 = $0.50/cwt. Warehouse 2 400,000/200,000 = $2.00/cwt.  Allocateinventory carrying costs. Assume that throughput for each product is equally divided between warehouses. Each warehouse 100{[200,000/2) 0.7 ]/(200,000/2)} = $3.2  Build the cost matrix for the transportation problem of LP. Note its special structure. Total customer demand No.ofwhses 13-38

31. Matrix of Cell Costs and Solution Values for the First Iteration in the Example Problem Warehouses Customers W 1 W 2 C 1 C 2 C 3 Plant & warehouse capacities P 1 4 a 60,000 999 b 60,000 P 2 86 140,000 99 999,999 c W 1 0999.7 d 8.7 60,000 10.7 60,000 W 2 99 b 08.2 e 50,000 7.2 40,000 8.2 50,000 999,999 c Warehouse capacity & customer demand60,000999,999 c 50,000100,00050,000 Plants Warehouses 13-39

32. CR (2004) Prentice Hall, Inc. Guided Linear Programming (Cont’d)  Solve as an LP problem, transportation type. Note the results in the solution matrix.  Recompute the per-unit fixed and inventory costs from the first solution results as follows. 1 + 2 + 3.57 + 2.86 = 9.43 Ware- house Per-unit Fixed Cost, $/cwt. Per-Unit Inventory Carrying Cost, $/cwt. W 1 $100,000/60,000 cwt. = 1.67 $100(60,000 cwt.) 0.7 /60,000 cwt. = 3.69 W 2 $400,000/140,000 cwt. = 2.86 $100(140,000 cwt.) 0.7 /140,000 cwt. = 2.86  Place these per-unit costs along with transportation costs in the transportation matrix. The portion of the matrix that is revised is: C 1 C 2 C 3 W 1 11.36 a 10.3612.36 W 2 8.72 b 7.728.72 a 2 + 4 + 1.67 + 3.69 = 11.36 b 13-40

33. 13-33 Guided Linear Programming (Cont’d) Cost type Warehouse 1 0 cwt. Warehouse 2 200,000 cwt. Production$0 200,000  4 = $800,000 Inbound transportation 0 200,000  2 = 400,000 Outbound transportation 0 50,000  2 = 100,000 100,000  1 = 100,000 50,000  2 = 100,000 Fixed0 400,000 Inventory carrying0100(200,000) 0.7 = 513,714 Handling0 200,000  1 = 200,000 Subtotal$0$2,613,714 Total $2,613,714

34. 13-34 Location by Simulation CR (2004) Prentice Hall, Inc. Can include more variables than typical algorithmic methods Cost representations can be precise so problem can be more accurately described than with most algorithmic methods Mathematical optimization usually is not guaranteed, although heuristics can be included to guide solution process toward satisfactory solutions Data requirements can be extensive Has limited use in practice

35. 13-35 Shycon/Maffei Simulation CR (2004) Prentice Hall, Inc.

36. 13-36 Commercial Models for Location Features Includes most relevant location costs Constrains to specified capacity and customer service levels Replicates the cost of specified designs Handles multiple locations over multiple echelons Handles multiple product categories Searches for the best network design CR (2004) Prentice Hall, Inc.

37. Commercial Models (Cont’d) 13-45

38. CR (2004) Prentice Hall, Inc. Commercial Models (Cont’d) 13-46

39. 13-39 CR (2004) Prentice Hall, Inc. Dynamic Location Retail Location Methods  The general long-range nature of the location problem -Network configurations are not implemented immediately -There are fixed charges associated with moving to a new configuration  We seek to find a set of network configurations that minimizes the present value over the planning horizon  Contrasts with plant and warehouse location. -Revenue rather than cost driven -Factors other than costs such as parking, nearness to competitive outlets, and nearness to customers are dominant  Weighted checklist - Good where many subjective factors are involved - Quantifies the comparison among alternate locations

40. CR (2004) Prentice Hall, Inc. A Hypothetical Weighted Factor Checklist for a Retail Location Example (1)(1) Factor Weight (1 to 10) a Location Factors (2)(2) Factor Score (1 to 10) b (3)=(1)  (2)(2) Weighted Score 8Proximity to competing stores 5 40 5Space rent/lease considerations 3 15 8Parking space 10 80 7Proximity to complementary stores 8 56 6Modernity of store space 9 54 9Customer accessibility8 72 3Local taxes 2 6 3Community service 4 12 8Proximity to major transportation arteries 7 56 Total index 391 13-48