Operations ResearchTeam 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 20000

Plant size Boston Atlanta Houston

Detroit 5 2 3

Toledo 4 3 2

Denver 9 7 5

Kansas city 10 4 2

St.Louis 8 4 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

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

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