1. Business Location Decisions Dr. Everette S. Gardner, Jr.

2. Business Location2 Complexity of the location problem If there are N potential facility sites, there are (2^N) – 1 different geographical configurations. Example: 4 potential sites (A,B,C,D) (2^4) – 1 = 15Number of facilities used AlternativesAlternatives 1 A,B,C,D 4 2 AB, AC, AD, BC, 6 BC, CD 3 BC, ABD, ACD, 4 BCD 4 ABCD 1 15

3. Business Location3 Complexity of the location problem (cont.) ● Number of Number of alternative potential sitesgeographical configurations 5 31 10 1,023 201,048,575 50> 10^5 100> 10^30

4. Business Location4 100% Customer service level (%) Total distribution costs Transportation costs 0 0 Number of warehouses  Cost-service tradeoffs in logistics planning Inventory costs Fixed facility costs Customer service axis: % of demand filled within given time frame Dollar cost axis

5. Business Location5 Analog model for facility location Center.xls

6. Business Location6 Dimensional analysis in location decisions Location decisions are based on two types of information: Tangibles (objective or quantitative) Intangibles (subjective) Dimensional analysis helps: Measure and evaluate intangibles Combine tangible and intangible measurements into an overall value index for each location

7. Business Location7 Building a dimensional analysis model 1.List the decision factors 2.Score the decision factors: Natural units for tangible factors (usually financial) Subjective scores for intangibles, scale of 1 to 10 1 represents the ideal 10 represents a disaster 3.Weight each decision factor (scale of 1 to 5) 4.Compute weighted ratios (Score for option A / Score for option B)^Weight 5.Compute preference number Product of weighted ratios Dimensional.xls

8. Business Location8 Basic calculations in dimensional analysis: U.S. Air vs. Alaska airlines

9. Business Location9 Break-even analysis Break-even Total fixed costs point= Unit Variable cost in units price per unit Example: FC = $25,000, P = $20, VC = $10 BE = $25,000 = 2,500 units 20 – 10

10. Business Location10 Break-even analysis (cont.) $ Sales revenue Profit 1000 2000 3000 4000 5000 Units of output Total costs Variable costs Fixed costs Losses Break- even point

11. Business Location11 Determining market areas “Laid down costs” are the delivered costs of a product. LDC = P + RX Where P = Production cost/unit R = Transportation rate X = Distance

12. Business Location12 Determining market areas (cont.) Market boundaries are at points where lines of equal LDC intersect: A $2 $4 $6 $8 x y z $4 $2 $6 B C $2 $4 $6 $8 N

13. Business Location13 LP models for location decisions Simple transportation model Sources  Destinations

14. Business Location14 LP models for location decisions (cont.) Transshipment model Sources  Transshipment  Destinations points Both models can be used to plan shipments over multiple time periods

15. Business Location15 Preliminary steps in locating service outlets 1.Group population into geographic areas (usually use census blocks) 2.Use demographic data to determine probable facility usage for each potential location 3.Choose objective function: A. Maximize utilization B. Minimize distance per capita C. Minimize distance per visit D. Minimize average reduction in number of visits made due to location decision E. Weighted measures

16. Business Location16 Figure 7. A hypothetical medical service area with 32 census blocks and three cities. City populations are (approximately) A = 17,000, B = 9,000, and C = 13,000. Distances on x-y axes are in miles. 6 7 11 10 20 Y X -10 21 22 23 -10 10 26 20 2 3 5 1 4 9 13 City A 10 8 15 12 18 14 25 30 17 19 20 29 3231 16 24 26 27 City C City B

17. Business Location17 TABLE 12 Location coordinates in miles for three criteria and different numbers of centers* Criterion Center number (1) Maximize (2) Minimize distance (4) Minimize distance utilization per capita per encounter x y x y x y I With 1 center 1 21.00 -3.00 0.64 1.20 -8.70 10.10 II With 2 centers 1 21.4 -3.7 17.6 -3.30 18.50 -3.30 2 -9.89 10.4 9.89 10.4 -9.90 10.40 III With 3 centers 1 22.40 -3.1 21.52 -2.78 22.30 -3.20 2 -10.16 10.40 -10.20 10.40 -10.20 10.40 3 3.63 -2.75 3.60 -2.80 3.60 -2.80 * See figures 7 and 8 for locations of coordinates. ** Determined only for the first criterion.

18. Business Location18 TABLE 12 Location coordinates in miles for three criteria and different numbers of centers* (cont.) Criterion Center number (1) Maximize (2) Minimize distance (4) Minimize distance utilization per capita per encounter x y x y x y IV With 4 centers 1 22.40 -3.14 22.00 -3.50 21.23 -3.08 2 -10.20 10.40 -10.10 10.30 -9.80 10.40 3 3.59 -2.78 2.69 -4.80 3.61 - 2.70 4 11.32 -2.25 3.76 3.04 -11.35 3.00 V With 5 centers** 1 22.40 -3.10 2 -9.72 10.61 3 3.24 -3.19 4 -11.62 3.24 5 11.04 -2.00 * See figures 7 and 8 for locations of coordinates. ** Determined only for the first criterion.

19. Business Location19 City A Center Criterion governing center locations Figure 8. Location of one center based on three different criteria. 3 2 1 15 -5 -10 City B City C 10 5 -15-10 -5 5 10152025