Linear Programming

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Noble Amazon sells books online. Management is trying to determine the best sites for the company’s warehouses. Five potential sites are under consideration. Most of the sales come from customers in the United States. The average weekly demand from each region of the country, the average shipping cost from each warehouse site to each region of the country, the fixed cost per week of each warehouse if it is operated, and the maximum capacity of each warehouse (if it is operated) are shown in the table below. Formulate and solve a mixed BIP model in a spreadsheet to determine which warehouse sites Noble Amazon should operate and how books should be distributed from each warehouse to each region of the country to minimize total cost. (Hint: there are two decision variable types – # of shipments from each potential warehouse to each location, and the binary variables on should you or should you not build the warehouse. The capacity of a warehouse depends on whether or not it is built).

**See attachment for actual chart

Warehouse Site Northwest Southwest Midwest Southeast Northeast Fixed (cost per week) Capacity (books per week)
Spokane $2.40 $3.50 $4.80 $6.80 $5.75 $40,000 20,000
Reno $3.25 $2.30 $3.40 $5.25 $6.00 $30,000 20,000
Omaha $4.05 $3.25 $2.85 $4.30 $4.75 $25,000 15,000
Harrisburg $5.25 $6.05 $4.30 $3.25 $2.75 $40,000 25,000
Jacksonville $6.95 $5.85 $4.80 $2.10 $3.50 $30,000 15,000

Customer demand per week 8,000 12,000 9,000 14,000 17,000

a) Formulate and solve this linear programming problem using solver.

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