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Operations Research

Operations Research. Team 2. Distribution Systems Design

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Operations Research

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  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. 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

  4. Subject to: x11+x12+x13<=10y1 x21+x22+x23<=20y2 x31+x32+x33<=30y3 x41+x42+x43<=40y4 x51+x52+x53<=30 x11+x21+x31+x41+x51=30 x12+x22+x32+x42+x52=20 x13+x23+x33+x43+x53=20

  5. 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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