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Contributions to Location Theory Transportation Location Factors

Facility Location. Contributions to Location Theory Transportation Location Factors Non-transportation Location Factors Types of Location Problems Measures of Spatial Analysis Methods of Analysis Site Selection. Contributions to Location Theory. Von Thunen - Isolated State

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Contributions to Location Theory Transportation Location Factors

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  1. Facility Location Contributions to Location Theory Transportation Location Factors Non-transportation Location Factors Types of Location Problems Measures of Spatial Analysis Methods of Analysis Site Selection

  2. Contributions to Location Theory Von Thunen - Isolated State Weber - Locational Triangle Losch - Profit Maximization/Spatial Equilibrium Hotelling - Maximize Market Territory/Monopoly/Duopoly Hoover - Tapering Rates Greenhut - Cost, Revenue, and Personal Factors Isard - Spatial Competition and Game Theory

  3. Von Thunen Isolated State - Uniform Plane Purely Competitive Market Distance is the Only Advantage Thus, Minimize Transportation Cost Concentric Circles (Von Thunen's Belts) Low Value, high Weight - Near the Market Perishables - Near the Market High Value, Low Weight, Away from the Market

  4. Alfred Weber German Geographer Weber's Locational Triangle Differentiated Between Raw Material and Finished Goods Weight Gain in Production Weight Loss in Production Pure Materials (No Weight Gain or Loss) Localized Materials Ubiquitous Materials Effects of Labor and Agglomeration The Generalized Weber Problem

  5. MKT RM2 RM1 Alfred Weber Weber's Locational Triangle

  6. Alfred Weber German Geographer Weber's Locational Triangle Differentiated Between Raw Material and Finished Goods Weight Gain in Production Weight Loss in Production Pure Materials (No Weight Gain or Loss) Localized Materials Ubiquitous Materials Effects of Labor and Agglomeration The Generalized Weber Problem

  7. Alfred Weber German Geographer Weber's Locational Triangle Differentiated Between Raw Material and Finished Goods Weight Gain in Production Weight Loss in Production Pure Materials (No Weight Gain or Loss) Localized Materials Ubiquitous Materials Effects of Labor and Agglomeration The Generalized Weber Problem

  8. Transportation Location Factors Location of Market Location of Raw Materials Demand at the Market (Volume to be Moved) Supply of Raw Materials (Volume to be Moved) Weight Gain in Production Weight Loss in Production Rate Structure Ratio of Inbound to Outbound Rates Quality of Transportation Services Quantity of Transportation Services

  9. Non-transportation Location Factors Resources (Quality, Cost, Availability) Labor Management Raw Materials Financial Energy Environment Natural Climate Political Climate Government Regulation Competition Market Size Cultural (Quality of Life, etc.) Taxes Corporate Income Individual Income Real Estate Inventory Incentives

  10. Types of Location Problems The Allocation Problem The Single Source Problem The Multiple Source Problem The Dynamic Problem

  11. Types of Location Problems The Allocation Problem Also known as the Assignment Problem Not really a location problem Facilities already exist Allocate supply to demand Northwest Corner, Simplex Method, etc.

  12. = Facility = Customer Types of Location Problems The Allocation Problem 25 40 60 80 25 50

  13. Customer 1 Customer 2 Customer 3 Customer 4 50 0 60 10 0 Source 1 Source 2 80 40 0 15 25 40 50 25 25 Types of Location Problems The Allocation Problem Resources are allocated to customers or Demands are assigned to supplies Use Linear Programming to Solve

  14. Measures of Spatial Analysis Single Space Two Space Manhattan Metric Euclidian Metric Graph Metric

  15. Methods of Analysis Mean vs Median Optimization Heuristics Simulation

  16. Σ Ci wi Mean = Σ wi Types of Location Problems The Single Source Problem Measures of Central Tendency Median = The One in the Middle Σ Aggregate Distance Ci- L wi =

  17. wi 3 5 2 1 2 6 Ci 0 1 2 3 4 5 6 7 8 9 10 Types of Location Problems The Single Source Problem Single Space Upper level numeric values (wi) denote customer demands at those locations. Lower level numeric values (Ci) denote mile posts where customers are located; viz., i = 3, 4, 5, 7, 9, and 10.

  18. wi wi 3 5 2 1 2 6 = 19 Ci 0 1 2 3 4 5 6 7 8 9 10 Median Mean Σ Ci wi Mean = 3x3 +5x4 + 2x5 + 1x7 + 2x9 +6x10 = 124 = Σ wi 124/19 = 6.5 Types of Location Problems The Single Source Problem Mean vs Median Median = The one in the middle, (19/2) = 9.5 or 10. There are 9 on either side, and the 10th unit is delivered to C5. Thus, the median (M) = C5 (or mile post 5).

  19. Σ Aggregate Distance Ci- L wi (Note absolute values) = Σ Aggregate Distance Ci- X wi (Mean) = 3|3-6.5 | + 5|4-6.5| + 2|5-6.5| + 1|7-6.5| + 2|9-6.5| + 6|10-6.5| = 52.5 Σ Aggregate Distance Ci- M wi = (Median) 3|3-5| + 5|4-5| + 2|5-5| + 1|7-5| + 2|9-5| + 6|10-5| = 51 Types of Location Problems The Single Source Problem Mean vs Median

  20. wi wi 3 5 2 1 2 16 = 29 Ci 0 1 2 3 4 5 6 7 8 9 10 Median Types of Location Problems The Single Source Problem Majority Theorem Anytime a majority of the demand is a one location, you will locate there.

  21. N 10 10 15 25 5 5 15 5 10 15 15 20 20 5 S E W Types of Location Problems The Single Source Problem The Generalized Weber Problem Numeric values denote customer demands at those locations

  22. Σ  wi dij = (Y2-Y1)2 + (X2-X1)2 Minimize Types of Location Problems The Single Source Problem The Generalized Weber Problem Pythagorean Theorem: The square of the hypotenuse is equal to the sum of the two sides squared.

  23. 7 10 10 15 25 6 5 5 15 5 5 4 10 3 15 15 2 20 20 5 1 0 0 1 2 3 4 5 6 7 8 9 10 Types of Location Problems The Single Source Problem The Generalized Weber Problem

  24. 7 6 5 4 (d) (1) 3 (2) 2 1 0 Types of Location Problems The Single Source Problem The Generalized Weber Problem 10 10 15 25 5 15 5 5 10 15 15 20 20 5 0 1 2 3 4 5 6 7 8 9 10

  25.    d = d = d = d = (Y2-Y1)2 + (X2-X1)2 (4 - 3)2 + (8 - 6)2 5 (1)2 + (2)2 d = 2.24 Types of Location Problems The Single Source Problem The Generalized Weber Problem

  26. Σ  wi dij = (Y2-Y1)2 + (X2-X1)2 Minimize Types of Location Problems The Single Source Problem The Generalized Weber Problem Problem – You cannot isolate either X or Y. That is, anytime you solve for X in terms of Y, X is still on the right hand side. Ditto, Y. Thus, a solution is not trivial. This problem has generated enormous attempts to find a solution.

  27. 7 10 10 15 25 6 5 5 5 5 15 4 10 3 15 15 2 20 20 5 1 0 Types of Location Problems The Single Source Problem Manhattan Matrix 0 1 2 3 4 5 6 7 8 9 10

  28. 7 10 10 15 25 60 6 5 5 5 5 5 15 25 4 10 3 10 15 15 2 30 20 20 5 1 45 0 10 25 20 20 20 20 15 45 Types of Location Problems The Single Source Problem Manhattan Matrix 0 1 2 3 4 5 6 7 8 9 10

  29. 7 10 10 15 25 6 5 60 5 5 5 15 5 4 25 10 3 15 15 10 2 20 20 5 30 1 45 0 175 M = 88 10 25 20 20 20 20 15 45 Types of Location Problems The Single Source Problem Manhattan Matrix 0 1 2 3 4 5 6 7 8 9 10

  30. Types of Location Problems The Allocation Problem The Single Source Problem The Multiple Source Problem The Dynamic Problem

  31. Types of Location Problems The Multiple Source Problem Locate – Allocate, Locate – Allocate, Locate – Allocate

  32. 10 10 15 25 5 5 15 5 10 15 15 20 20 5 Types of Location Problems The Multiple Source Problem Locate – Allocate

  33. 10 10 15 25 5 5 15 5 10 15 15 20 20 5 Types of Location Problems The Multiple Source Problem Locate

  34. 10 10 15 25 5 5 15 5 10 15 15 20 20 5 Types of Location Problems The Multiple Source Problem Allocate

  35. 10 15 5 10 15 5 Types of Location Problems The Multiple Source Problem Locate

  36. 10 15 5 10 15 5 Types of Location Problems The Multiple Source Problem Locate

  37. 10 25 5 5 Types of Location Problems The Multiple Source Problem Locate

  38. 10 25 5 5 Types of Location Problems The Multiple Source Problem Locate

  39. 15 15 20 20 Types of Location Problems The Multiple Source Problem Locate

  40. 15 15 20 20 Types of Location Problems The Multiple Source Problem Locate

  41. 10 10 15 25 5 5 15 5 10 15 15 20 20 5 Types of Location Problems The Multiple Source Problem Locate

  42. 10 10 15 25 5 5 15 5 10 15 15 20 20 5 Types of Location Problems The Multiple Source Problem Allocate

  43. 10 15 5 5 5 10 15 15 5 Types of Location Problems The Multiple Source Problem Locate

  44. 10 15 5 5 5 10 15 15 5 Types of Location Problems The Multiple Source Problem Locate

  45. 10 25 15 Types of Location Problems The Multiple Source Problem Locate

  46. 10 25 15 Types of Location Problems The Multiple Source Problem Locate

  47. 20 20 Types of Location Problems The Multiple Source Problem Locate

  48. 20 20 Types of Location Problems The Multiple Source Problem Locate

  49. 10 10 15 25 5 5 15 5 10 15 15 20 20 5 Types of Location Problems The Multiple Source Problem Locate

  50. 10 10 15 25 5 5 15 5 10 15 15 20 20 5 Types of Location Problems The Multiple Source Problem Allocate Solution is stable when no customers are reassigned

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