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Chapter 8

Chapter 8. Location. Dr. Ardavan Asef-Vziri Operations and Supply Chain Management March 2001. Nature of Location Decisions. Location decisions are strategic decisions. The reasons for location decisions Growth Expand existing facilities Add new facilities Production Cost

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Chapter 8

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  1. Chapter 8 Location Dr. Ardavan Asef-Vziri Operations and Supply Chain Management March 2001

  2. Nature of Location Decisions Location decisions are strategic decisions. • The reasons for location decisions • Growth • Expand existing facilities • Add new facilities • Production Cost • Depletion of Resources

  3. Factors Affecting Plant location Regional Factors Community Factors Site Factors Multiple Plant Strategies

  4. Regional; Raw Material 1-Location of raw material Raw material oriented factories; weight of input >>> weight of output

  5. Regional; Raw Material • These types of plants tends to be closer to • the raw material resources. • Indeed row material or any other important • input.

  6. Regional; Market 2-Location of market Market oriented plants; Space required for output >>> space required for input. Car manufacturing, Appliances

  7. Regional; Labor, Water, Electricity 3-Labor, water, Electricity Availability of skilled labor, productivity and wages, union practices Availability of water; Blast furnace requires a high flow of water Availability of electricity;Aluminum plant strongly depends on availability and cost of electricity, it dominates all other inputs.

  8. Community 1-Quality of Life; Cost of living, housing, schools, health care, entertainment, church 2- Financial support; Tax regulations, low rate loans for new industrial and service plants

  9. Site 1-Land; Cost of land, development of infrastructure. 2-Transportation; Availability and cost of rail road, highways, and air transportation. 3-Environment; Environmental and legal regulations and restrictions

  10. Decentralization Small is beautiful; Instead of a single huge plant in one location, several smaller plants in different locations Decentralization based on product Decentralization based on geographical area Decentralization based on process

  11. Decentralization based on Product Each product or sub-set of products is made in one plant Each plant is specialized in a narrow sub-set of products. Lower operating costs due to specialization.

  12. Decentralization Based on Geographical Area Each plant is responsible for a geographical region, Specially for heavy or large products. Lower transportation costs.

  13. Decentralization Based on Process Car industry is an example. Different plants for engine, transmission, body stamping, radiator. Specialization in a process results in lower costs and higher quality. Since volume is also high, they also take advantage of economy of scale. However, coordination of production of all plants becomes an important issue and requires central planning and control

  14. Trends in Global Locations • Foreign producers locating in U.S. • “Made in USA” • Currency fluctuations • Just-in-time manufacturing techniques • Focused factories • Information highway

  15. BEP in Location Analysis • Cost-volume Analysis • Determine fixed and variable costs • Plot total costs • Determine lowest total costs

  16. Example Fixed and variable costs for four potential locations

  17. Solution

  18. Graphical Solution $(000) 800 700 600 500 400 300 200 100 0 D B C A A Superior C Superior B Superior 0 2 4 6 8 10 12 14 16 Annual Output (000)

  19. Center of Gravity ; Single Facility Location Center of gravity is a method to find the optimal location of a single facility The single facility is serving a set of demand centers or It is being served by a set of supply centers The objective is to minimize the total transportation Transportation is Flow ×Distance

  20. Examples of Single Facility Location Problem There are a set of demand centers in different locations and we want to find the optimal location for a Manufacturing Plant or a Distribution Center (DC) or a Warehouse to satisfy the demand of the demand centers or There are a set of suppliers for our manufacturing plant in different locations and we want to find the optimal location forour Plant to get its required inputs The objective is to minimize total Flow × Distance

  21. Center of Gravity ; Single Facility Location Suppose we have a set of demand points. Suppose demand of all demand points are equal. Suppose they are located at locations Xi, Yi Where is the best position for a DC to satisfy demand of these points Distances are calculated as straight line not rectilinear. There is another optimal solution for the case when distances are rectilinear.

  22. Optimal Single Facility Location The coordinates of the optimal location of the DC is

  23. Example We have 4 demand points. Demand of all demand points are equal. Demand points are located at the following locations

  24. Example Where is the optimal location for the center serving theses demand points (3,5) (8,5) (5,4) (2,2)

  25. Solution Where is the optimal location for the center serving theses demand points (2,2) (3,5) (5,4) (8,5)

  26. Solution The optimal location for the center serving theses demand points (3,5) (8,5) (5,4) (2,2)

  27. Center of Gravity ; Single Facility Location Suppose we have a set of demand points. Suppose they are located at locations Xi, Yi Demand of demand point i is Qi. Now where is the best position for a DC to satisfy demand of these points Again; the objective is to minimize transportation.

  28. Optimal Single Facility Location The coordinates of the optimal location of the DC is

  29. Example Where is the optimal location for the center serving theses demand points 900 100 (3,5) (8,5) 200 (5,4) 800 (2,2)

  30. Solution Where is the optimal location for the center serving theses demand points 800 : (2,2) 900 : (3,5) 200 : (5,4) 100 : (8,5)

  31. Solution Where is the optimal Y location for the center serving theses demand points 800 : (2,2) 900 : (3,5) 200 : (5,4) 100 : (8,5)

  32. Solution The optimal location for the center serving theses demand points (900) (100) (200) (800)

  33. Example 900 100 (1,3) (6,3) 200 (3,2) 800 (0,0) Where is the optimal location for the center serving theses demand points

  34. Solution Where is the optimal location for the center serving theses demand points 800 : (0,0) 900 : (1,3) 200 : (3,2) 100 : (6,3)

  35. Solution Where is the optimal location for the center serving theses demand points 800 : (0,0) 900 : (1,3) 200 : (3,2) 100 : (6,3)

  36. Solution The optimal location for the center serving theses demand points is at the same location (900) (100) (200) (800)

  37. The Transportation Problem Dr. Ardavan Asef-Vaziri Industrial Engineering Mar 2003

  38. The Transportation Problem D (demand) S (supply) S (supply) D (demand) D (demand) S (supply)

  39. Transportation problem : Narrative representation There are 3 plants, 3 warehouses. Production of Plants 1, 2, and 3 are 300, 200, 200 respectively. Demand of warehouses 1, 2 and 3 are 250, 250, and 200 units respectively. Transportation costs for each unit of product is given below Warehouse 1 2 3 1 16 18 11 Plant 2 14 12 13 3 13 15 17 Formulate this problem as an LP to satisfy demand at minimum transportation costs.

  40. Transportation problem I : decision variables x11 300 1 x12 1 250 x13 x21 200 2 x22 2 250 x23 x31 x32 3 200 3 x33 200

  41. Transportation problem I : decision variables x11 = Volume of product sent from P1 to W1 x12 = Volume of product sent from P1 to W2 x13 = Volume of product sent from P1 to W3 x21 = Volume of product sent from P2 to W1 x22 = Volume of product sent from P2 to W2 x23 = Volume of product sent from P2 to W3 x31 = Volume of product sent from P3 to W1 x32 = Volume of product sent from P3 to W2 x33 = Volume of product sent from P3 to W3 We want to minimize Z = 16 x11 + 18 x12 +11 x13 + 14 x21 + 12 x22 +13 x23 + 13 x31 + 15 x32 +17 x33

  42. Transportation problem I : supply and demand constraints x11 + x12 + x13 = 300 x21 + x22 + x23 =200 x31 + x32 + x33 = 200 x11 + x21 + x31 = 250 x12 + x22 + x32 = 250 x13 + x23 + x33 = 200 x11, x12, x13, x21, x22, x23, x31, x32, x33 0

  43. 1 2 i m Origins s1 s2 si sm • We have a set of ORIGINs • Origin Definition: A source of material • - A set of ManufacturingPlants • - A set of Suppliers • - A set of Warehouses • - A set of Distribution Centers (DC) • In general we refer to them as Origins There are m origins i=1,2, ………., m Each origin i has a supply of si

  44. 1 2 j n Destinations d1 d2 di dn We have a set of DESTINATIONs Destination Definition: A location with a demand for material - A set of Markets - A set of Retailers - A set of Warehouses - A set of Manufacturing plants In general we refer to them as Destinations There are n destinations j=1,2, ………., n Each origin j has a supply of dj

  45. Transportation Model Assumptions • Total supply is equal to total demand. • There is only one route between each pair of origin and destination • Items to be shipped are all the same • for each and all units sent from origin i to destination j there is a shipping cost of Cij per unit

  46. Cij: cost of sending one unit of product from origin i to destination j C11 1 1 C21 C12 2 C22 2 C2n C1n i j n m

  47. Xij : Units of product sent from origin i to destination j X11 1 1 X12 X21 2 2 X22 X2n X1n i j n m

  48. The Problem The problem is to determine how much material is sent from each origin to each destination, such that all demand is satisfied at the minimum transportation cost 1 1 2 2 i j n m

  49. The Objective Function 1 1 If we send Xij units from origin i to destination j, its cost is Cij Xij We want to minimize 2 2 i j n m

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