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Operations Research Team 2.

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Presentation on theme: "Operations Research Team 2."— Presentation transcript:

1 Operations Research Team 2

2 Distribution Systems Design
The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional centers located in Boston, Atlanta, Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase the capacity by constructing a new plant in one or more of the following cities Detroit, Toledo, Denver or Kansas City. The estimated annual fixed cost and the annual capacity for the 4 proposed plants is as follows:

3 Proposed plant Annual fixed cost Annual Capacity Detroit 175000 10000 Toledo 300000 20000 Denver 375000 30000 Kansas city 500000 40000

4 Distribution Centers Annual Demand Boston 30000 Atlanta 20000 Houston

5 Plant size Boston Atlanta Houston Detroit 5 2 3 Toledo 4 Denver 9 7 Kansas city 10 St.Louis 8

6 y1=1 if a plant is constructed in Detroit, 0 if not
Min Z= 5x11+2x12+3x13+4x21+3x22+4x23+9x31+7x32+5x33+10x41+4x42+2x43+8x51+4x52+3x53 y y y y4 y1=1 if a plant is constructed in Detroit, 0 if not y2=1 if a plant is constructed in Toledo, 0 if not y3=1 if a plant is constructed in Denver, 0 if not y4=1 if a plant is constructed in Kansas city, 0 if not

7 Subject to: x11+x12+x13<=10y1 x21+x22+x23<=20y2
x11+x21+x31+x41+x51=30 x12+x22+x32+x42+x52=20 x13+x23+x33+x43+x53=20

8 Solution: The optimal solution is that a plant should be constructed at Kansas City (y4=1); 20,000 units will be shipped from Kansas City to Atlanta, 20,000 units would be shipped from Kansas City to Houston and 30,000 units would be shipped from St. Louis


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