Location analysis

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  • 1. Location Planning and Analysis
  • 2. DefinitionDefinition of Facility Planningof Facility Planning Facility Planning determines how an activity’s tangible fixed assets best support achieving the activity’s objectives. Examples: a. In manufacturing, the objective is to support production. b. In an airport, the objective is to support the passenger airplane interface. c. In a hospital, the objective is to provide medical care to patients.
  • 3. Hierarchy of Facility PlanningHierarchy of Facility Planning Location: is the placement of a facility with respect to customers, suppliers, and other facilities with which it interfaces. Structure: consists of the building and services (e.g., gas, water, power, heat, light, air, sewage). Layout: consists of all equipment, machinery, and furnishings within the structure. Handling System: consists of the mechanism by which all interactions required by the layout are satisfied (e.g., materials, personnel, information, and equipment handling systems). Facility Planning Structural Design Facility Location Facility Design Layout Design Handling System Design
  • 4. Need for Location DecisionsNeed for Location Decisions • Marketing Strategy • Cost of Doing Business • Growth • Depletion of Resources
  • 5. Making Location DecisionsMaking Location Decisions • Decide on the criteria • Identify the important factors • Develop location alternatives • Evaluate the alternatives • Make selection
  • 6. Location Decision FactorsLocation Decision Factors Regional Factors Site-related Factors Multiple Plant Strategies Community Considerations
  • 7. Evaluating LocationsEvaluating Locations • Transportation Model • Decision based on movement costs of raw materials or finished goods • Factor Rating • Decision based on quantitative and qualitative inputs • Center of Gravity Method • Decision based on minimum distribution costs
  • 8. Factor RatingFactor Rating General approach to evaluating locations that includes quantitative and qualitative inputs.
  • 9. ExampleExample 11 A photo-processing company intends to open a new branch store. The following table contains information on two potential locations. Which is the better alternative? Alternative 2 is better because it has the higher composite score.
  • 10. Example 2Example 2 Using the following factor ratings, determine which location alternative should be chosen on the basis of maximum composite score, A, B, or C.
  • 11. Example 2Example 2 Solution: Therefore, Location A is better.
  • 12. The Center of Gravity MethodThe Center of Gravity Method The method use to determine the location of a facility that will minimize shipping costs or travel time to various destinations.
  • 13. If the quantities to be shipped in everyIf the quantities to be shipped in every location are equallocation are equal where: n = Number of destinations. xi = x coordinate of destination i. yi = y coordinate of destination i. n x x i∑ = n y y i∑ =
  • 14. When the number of units to be shippedWhen the number of units to be shipped is not the same for all destinationsis not the same for all destinations ∑ ∑ = i ii Q Qx x ∑ ∑ = i ii Q Qy y where Qi = Quantity to be shipped to destination i xi = x coordinate of destination i yi = y coordinate of destination i
  • 15. ExampleExample 11 Destination x, y D1 2, 2 D2 3, 5 D3 5, 4 D4 8, 5 18 16 5.4 4 18 === ∑ n x x i 4 4 16 === ∑ n y y i Hence, the center of gravity is at (4.5,4).
  • 16. Example 2Example 2 Destination x, y Weekly Quantity D1 2, 2 800 D2 3, 5 900 D3 5, 4 200 D4 8, 5 100 2000 3)to(round05.3 2000 6100 2000 )100(8)200(5)900(3)800(2 == +++ == ∑ ∑ i ii Q Qx x 70.3 2000 7400 2000 )100(5)200(4)900(5)800(2 == +++ == ∑ ∑ i ii Q Qy y Hence, the center of gravity are approximately (3,3.7). This would place it south of destination D2, which has coordinates of (3,5).
  • 17. Example 3Example 3 Destination x,y Coordinates Weekly Quantity D1 3,5 20 D2 6,8 10 D3 2,7 15 D4 4,5 15 60 5.3 60 210 60 )15(4)15(2)10(6)20(3 =≡ +++ ≡= ∑ ∑ i ii Q Qx x 0.6 60 360 60 )15(5)15(7)10(8)20(5 =≡ +++ ≡= ∑ ∑ i ii Q Qy y Hence, the center of gravity has the coordinates x = 3.5 and y = 6.0
  • 18. The Transportation Model
  • 19. Requirements for Transportation ModelRequirements for Transportation Model • List of origins and each one’s capacity • List of destinations and each one’s demand • Unit cost of shipping
  • 20. Transportation Model AssumptionsTransportation Model Assumptions 1. Items to be shipped are homogeneous 2. Shipping cost per unit is the same 3. Only one route between origin and destination
  • 21. The Transportation ProblemThe Transportation Problem D (demand) D (demand) D (demand) D (demand) S (supply) S (supply) S (supply)
  • 22. • m- number of sources • n- number of destinations • ai- supply at source I • bj–demand at destination j cij–cost of transportation per unit from source i to destination j Xij–number of units to be transported from the source i to destination j
  • 23. DESTINATION j cc1111 cc1212 cc1j1j cc1n1n cci1i1 cci2i2 ccijij ccinin ccm1m1 ccm2m2 ccmnmn S O U R C E i 1 2 i m 1 2 j n Demand b1 b2 bj bn Supply a1 a2 ai am
  • 24. Transportation problem:Transportation problem: represented as an LP modelrepresented as an LP model njandmiforX njbX miaXtosubject XcZMinimize ij j m i ij i n j ij ij m i n j ij ,..1,...10 ,.....,2,1 ,....,2,1 : 1 1 1 1 ==≥ =≥ =≤ = ∑ ∑ ∑∑ = = = =
  • 25. Summary of ProcedureSummary of Procedure • Make certain that supply and demand are equal • Develop an initial solution using intuitive, low-cost approach • Check that completed cells = m+n-1 • Evaluate each empty cell • Repeat until all cells are zero or positive
  • 26. Determination of Starting Basic Feasible SolutionDetermination of Starting Basic Feasible Solution •NORTH-WEST Corner MethodNORTH-WEST Corner Method -- is a method for computing a basic feasible solution of a transportation problem, where the basic variables are selected from the North – West corner. •LEAST COST Method -LEAST COST Method - This method takes consideration the lowest cost and therefore takes the less time to solve the problem. •Vogel’s Approximation Method (VAM) -Vogel’s Approximation Method (VAM) - This method also takes costs into account in allocation. VAM usually produces an optimal or near- optimal starting solution. One study found that VAM yields an optimum solution in 80 percent of the sample problems tested.
  • 27. The Amulya Milk Company has three plants located throughout a state with production capacity 5000, 2000 and 3000 gallons. Each day the firm must furnish its four retail shops with at least 3000, 3000 , 2000, and 2000 gallons respectively. Example 1Example 1
  • 28. 33 77 66 44 55 22 44 33 22 22 44 33 88 55 33 33 33 22 22 Destination 1 2 3 4 Supply Row Penalties S o u r c e 1 2 3 Demand Total shipping cost = 32 Column Penalties 1 0 1 1 1 3 2 2 0 1 - 1 1 4 - 1 3 0 3 0 0 2
  • 29. TO FROM A B C SUPPLY W 9 8 5 25 X 6 8 4 35 Y 7 6 9 40 DEMAND 30 25 45 100 100 ROW/COLUMN SEC-LOWEST COST ━ LOWEST COST = OPPORT-CST ROW W 8 5 3 LARGEST ROW X 6 4 2 ROW Y 7 6 1 COLUMN A 7 6 1 COLUMN B 8 6 2 COLUMN C 5 4 1 25 20 Example 2Example 2
  • 30. VAM: VOGEL APPROXIMATION METHOD TO FROM A B C SUPPLY W 9 8 5 25 X 6 8 4 35 Y 7 6 9 40 DEMAND 30 25 45 100 100 ROW/COLUMN SEC-LOWEST COST ━ LOWEST COST = OPPORT-CST ROW X 6 4 2 ROW Y 7 6 1 COLUMN A 7 6 1 COLUMN B 8 6 2 COLUMN C 9 4 5 LARGEST 25 20 20 15
  • 31. VAM: VOGEL APPROXIMATION METHOD TO FROM A B C SUPPLY W 9 8 5 25 X 6 8 4 35 Y 7 6 9 40 DEMAND 30 25 45 100 100 ROW/COLUMN SEC-LOWEST COST ━ LOWEST COST = OPPORT-CST ROW X 8 6 2 LARGEST ROW Y 7 6 1 COLUMN A 7 6 1 COLUMN B 8 6 2 LARGEST 25 20 25 15 15 20
  • 32. TO FROM A B C SUPPLY W WA 9 WB 8 WC 5 25 X XA 6 XB 8 XC 4 35 Y YA 7 YB 6 YC 9 40 DEMAND 30 25 45 100 100 25 20 2515 15 Q X COST / UNIT = TC ($) WC 25 5 125 XA 15 6 90 XC 20 4 80 YA 15 7 105 YB 25 6 150 TOTAL TRANSPORTATION COST 540 15 15 20