Operations Research Team 2.

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Presentation transcript:

Operations Research Team 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:

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

Distribution Centers Annual Demand Boston 30000 Atlanta 20000 Houston

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

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 +175000y1+300000y2+375000y3+500000y4 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

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

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