Mrs. Z, vice president for operations of XY, Inc., a manufacturer of imaginary product T, is constrained from meeting her 5-year forecast by limited capacity at the company’s two existing facilities, which are in San Diego, California (F1) and Grenville, South Carolina (F2). As her able assistant, you have been told that because of existing capacity constraints and the expanding market for the company’s product, a third plant is to be added. The real estate department has advised Mrs. Z that two potential sites seem particularly good, located in Waco, Texas (F3), and Norfolk, Nebraska (F4). The company ships the products to three demand markets in East (M1), Mid-West (M2), and West (M3), via its two cross-docking distribution centers in Colorado (D1) and Kentucky (D2). You are asked to find the optimal distribution strategy that will determine where the third facility be located (F3 or F4), and the best distribution pattern across the supply chain. The company consider the transportation cost as the performance measure. Consider the following data in solving this problem. Given are transportation Cost ($ per unit), capacity, and demand figures. From Facilities to Distribution Centers Distribution From Distribution Centers to Market F1 F2 F3 F4 Centers M1 M2 M3 4 6 5 3 DC1 6 4 5 7 3 6 8 DC2 3 5 8 Capacity Available   Demand 140,000 60,000 80,000 80,000   80,000 130,000 70,000   Display the supply chain network for this problem Formulate the problem into linear programming. Define Variables Write the objective function Define the constraints and formulate them Find the optimum solution using Excel Solver

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter9: Decision Making Under Uncertainty
Section: Chapter Questions
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Mrs. Z, vice president for operations of XY, Inc., a manufacturer of imaginary product T, is constrained from meeting her 5-year forecast by limited capacity at the company’s two existing facilities, which are in San Diego, California (F1) and Grenville, South Carolina (F2). As her able assistant, you have been told that because of existing capacity constraints and the expanding market for the company’s product, a third plant is to be added. The real estate department has advised Mrs. Z that two potential sites seem particularly good, located in Waco, Texas (F3), and Norfolk, Nebraska (F4). The company ships the products to three demand markets in East (M1), Mid-West (M2), and West (M3), via its two cross-docking distribution centers in Colorado (D1) and Kentucky (D2). You are asked to find the optimal distribution strategy that will determine where the third facility be located (F3 or F4), and the best distribution pattern across the supply chain. The company consider the transportation cost as the performance measure. Consider the following data in solving this problem. Given are transportation Cost ($ per unit), capacity, and demand figures.

From Facilities to Distribution Centers

Distribution

From Distribution Centers to Market

F1

F2

F3

F4

Centers

M1

M2

M3

4

6

5

3

DC1

6

4

5

7

3

6

8

DC2

3

5

8

Capacity Available

 

Demand

140,000

60,000

80,000

80,000

 

80,000

130,000

70,000

 

  1. Display the supply chain network for this problem
  2. Formulate the problem into linear programming.
    1. Define Variables
    2. Write the objective function
    3. Define the constraints and formulate them
  3. Find the optimum solution using Excel Solver

 

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