Business Location Decisions

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

2. 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 = 15 Number of Number of facilities used Alternatives Alternatives 1 A,B,C,D 4 2 AB, AC, AD, BC, 6 BC, CD 3 BC, ABD, ACD, 4 BCD 4 ABCD 1 15 Business Location

3. Complexity of the location problem (cont.) ● Number of Number of alternative potential sites geographical configurations 5 31 10 1,023 20 1,048,575 50 > 10^5 100 > 10^30 Business Location

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

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

6. 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 Business Location

7. Building a dimensional analysis model • List the decision factors • 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 • Weight each decision factor (scale of 1 to 5) • Compute weighted ratios (Score for option A / Score for option B)^Weight • Compute preference number Product of weighted ratios Business Location Dimensional.xls

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

9. 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 Business Location

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

11. 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 Business Location

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

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

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

15. Preliminary steps in locating service outlets • Group population into geographic areas (usually use census blocks) 2.Use demographic data to determine probable facility usage for each potential location • 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 Business Location

16. Y 20 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. 7 6 11 21 2 10 3 1 8 5 10 City A 22 15 4 9 23 13 12 10 26 20 -10 18 X 14 17 25 30 19 29 32 31 20 16 24 27 26 City B -10 City C Business Location

17. TABLE 12Location coordinates in miles for three criteriaand 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. Business Location

18. TABLE 12Location coordinates in miles for three criteriaand 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. Business Location

19. 3 15 City A Center Criterion governing center locations Figure 8. Location of one center based on three different criteria. 10 5 2 10 15 20 25 5 -5 -15 -10 -5 1 -10 City B City C Business Location