Problem 1

Formulation

– Index

Customer location: Cj, j=stl1, stl2, stl3, stl4, ks1, ks2, col, spr

Product:

Plants: Pi, i=stl, kc, co, sp, in

Production lines:

Demand for each type from each customer location: Dij for i in P for j in C

Transportation distance from each plant to each customer location: TCij

Variable cost for shoes and boots from each plant: VCi

Fixed cost: FC1i for one production line for each plant; FC2i for two production lines for each plant

– Decision Variables

i = plant, except St. Louis, l=1 or 2

8 binary variables to decide whether set plant in these 4 plants with 1/2 production lines or not.

i=plant, j=customer location

32 variables representing the quantity of shoes sent from each plant to each customer location

i=plant, j=customer location

32 variables representing the quantity of boots sent from each plant to each customer location

– Objective Function

– Constraints

Demand for shoes should be satisfied:

Demand for boots should be satisfied:

Capacity for St. Louis:

Capacity for other plants:

Kansas City has either 1 production line or 2 production lines:

Number of production lines in Columbia, Springfield and Independence (i=co, sp, in)

Optimal Solution:

Total cost is $ 5990884

The distribution quantity is shown as below:

For shoes:

For boots:

There’s no need for expansion in Kansas City and we should open a new plant located in Independence with two production lines.

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