Facility Location

1. Facility Location Operations Management

2. Location Decisions • Long-term decisions • Difficult to reverse • Affect fixed & variable costs • Transportation costs (25% of price) • Other costs: taxes, wages, rent • Objective: maximize benefit of location to firm

3. What factors should we consider? • Skilled workforce • Environmental laws / cost of compliance • Cost of utilities, labor, taxes • Suppliers close by – fast & cheap access • Customers close by • Competitors close by? Skilled labor pool • International - control issues?

4. Service Facilities – Traffic focus • Revenue changes a huge amount, depending on the location. • Old Navy in Stead because of cheap land? • Location, location, location: you need traffic • Make it convenient! • vitamins: need enough, but it has to be the right kind • people who would want to buy your products when they are there. • Cost probably doesn’t change nearly as much, by location • All malls have high rent

5. Cost Focus • Revenue does not vary much, depending on the location. • Customers don’t care if your warehouse is in Sparks or Sacramento • Location is a major cost driver • Impacts shipping, labor, production costs • Varies greatly by location

6. Cost Minimization Identify the costs that will vary most with the location you choose. • Transportation, taxes, labor, • Facility construction cost, utilities Other considerations • Proximity of services, suppliers • Quality of life • Government incentives

7. Cost Focus Process Overview • Identify general region to locate in • Usually based on mostly on transp. costs • Identify a list of candidate cities • Choose cities with good transp. Access • Estimate labor cost & availability, facilities costs • Select metro area, identify candidate properties. • Find cost of building or leasing individual properties

8. Distribution Center Location • Minimize demand-weighted distance: distance to each customer times the volume of shipments to the customer • How many to build? • Where to build?

9. Location Methods • Minimize demand-weighted distance • Center of Gravity – minimizing demand-weighted distances of one facility • Ardalan – minimize transportation of multiple facilities, but must locate by customers • Factor Weighting – consider qualitative factors • Break-even – Consider fixed & variable costs

10. Center of Gravity • Compute X and Y coordinates separately • dix is the X coordinate of location i. • diy is the Y coordinate of i. • Wi is the X demand at i. • CX and CY are the coordinates of the DC.

11. Center of Gravity Example 1 • You need to decide where to build a new DC for Motorola. • It needs to serve wholesalers in Reno, Dallas, and Chicago. • Locate these cities on an unscientific, rectangular grid. • Grid must maintain relative distances, but X and Y grids could be different.

12. 100 80 60 40 20 0 0 20 40 60 80 100 120 140 160

13. Center of Gravity Method City Demand • Reno is at 17, 55 100 • Fort Worth is at 78, 20 90 • Chicago is at 110, 65. 120 • Demand is TL/month

14. Center of Gravity

15. 100 80 60 40 20 0 0 20 40 60 80 100 120 140 160

16. Center of Gravity Example 2 • You need to decide where to locate a DC in South Dakota X Y Demand • Pierre 78 47 50 • Watertown 150 65 8 • Sioux Falls 160 25 90 • Rapid 12 42 60

17. 100 80 60 40 20 0 0 20 40 60 80 100 120 140 160

18. Center of Gravity

19. 100 80 60 40 20 0 0 20 40 60 80 100 120 140 160

20. Ardalan Heuristic • Need a matrix of distances or costs from each customer location to every other location • Demand at each location • Weight – give higher weight to more important customers – their pain of traveling a longer distance is worth more. • Only consider locating where customers are • Identify the one best place to locate at, then the second one to add, then the third, etc.

21. Ardalan Heuristic • Minimize weighted distance traveled To FromA B C DDem. Weight A 0 11 8 12 10 1.1 B 11 0 10 7 8 1.4 C 8 10 0 9 20 0.7 D 9.5 7 9 0 12 1.0

22. Ardalan Method • Expected demand at each location. • Weight represents importance of serving location (bigger = more important) • Step 1: Multiply distances * weights * demand • A to B: 11 * 1.1 * 10 = 121

23. Ardalan Method Step 2. Add up values in columns FromA B C D A 0 121 88 132 B 123.2 0 112 78.4 C 112 140 0 126 D 114 84 108 0 349.2 345 308 336.4

24. Ardalan Method Choose smallest value as first site. FromA B C D A 0 121 88 132 B 123.2 0 112 78.4 C 112 140 0 126 D 114 84 108 0 349.2 345 308 336.4

25. Ardalan Method 3. If larger, set each cost equal to cost in same row in the chosen column FromA B C D A 0 88 88 88 B 112 0 112 78.4 C 0 0 0 0 D 108 84 108 0 220 172 308 166.4

26. Ardalan Method Get rid of previously chosen column. Sum, choose smallest sum. FromABD A 0 88 88 B 112 0 78.4 C 0 0 0 D 108 84 0 220 172 166.4

27. Ardalan Method Repeat 3 & 4 until enough sites chosen. FromA B D A 0 88 88 B 78.4 0 78.4 C 0 0 0 D 0 0 0 78.4 88 166.4

28. Ardalan Method Repeat 3 & 4 until enough sites chosen. FromA B A 0 88 B 78.4 0 C 0 0 D 0 0 78.4 88

29. Ardalan Summary • What we decided is that if we only want to build one location, it should be in C. • If we want to build two, they should be in C and D. If we add a third one, it should be in A.

30. Ardalan Summary • Assumes that we have to locate in the same city as one of our customers, which is not always the case. • However, it can be used to find more than one location. • Center of Gravity does not try to locate in the same city as one of the customers, but can only set one site. • If we choose the same sites as customers A and X, we obviously don’t really have to put the warehouses in those exact cities.

31. Factor Rating Example • We need to decide where to build a new coffee roasting plant. There are two possible locations: Dallas, and Denver. • We consider the following factors • Transp: annual trucking costs in $k • Lease: annual costs in $k • Labor availability: scale 1-10, unemployment, related industries • Quality of life: scale 1-10: outdoor activities, cultural, sports, education

32. Factor Rating Example • Using a scoring system we developed, we have the following. Factor Weight TX CO Transportation 0.5 900 1,023 Plant Lease Cost 0.3 45 39 Labor availability 0.2 10 8 Quality of Life 0.1 7 9.5

33. Normalizing Scores • All factors must be scored on the same scale, like 1-10, or 0-1.0, etc. • Costs need to be re-scaled • Lowest cost site gets a 10. • More expensive site gets less than 10

34. Factor Rating Example TX CO Factor Wt Raw Wtd Raw Wtd Tr 0.4 10 4.00 8.80 3.52 Plant 0.3 8.7 2.61 10 3.00 Labor 0.2 10 2.00 8 1.60 Q Life 0.1 7 0.70 9.5 0.95 TOTAL 9.31 9.07 TX is best

35. Possible Approach • Use Ardalan to find out which general regions to locate in (state / county). • Use factor weighting to choose city. • Ardalan has disadvantage of choosing weights -- difficult to set levels.

36. Break-Even Analysis • Determine fixed and variable costs for each location • Fixed cost: how much it would cost to open a facility there • Variable cost: how much total costs would increase as production increases: • Transportation costs • Labor costs • Taxes • Increased construction costs

37. Locating Service Facilities Using Linear Regression • Collect data about your current facilities • Use regression to determine which variables have a significant impact on profits • Choose new facilities which have these characteristics

38. Method Comparison • Center of gravity minimizes average distance for one facility only. • Ardalan Minimizes weighted distances for more than one facility. • Breakeven: fixed & variable costs. • Factor weighting considers many other important aspects of location, but does not minimize distance.

39. Transportation Method You have 3 DCs, and need to deliver product to 4 customers. Find cheapest way to satisfy all demand D 2 A 10 E 4 B 10 F 12 C 10 G 11

40. Solving Transportation Problems • Trial and Error • Linear Programming – ooh, what’s that?! • Tell me more!