The Warehouse Location Problem

Huntco Produces tomato sauce at five different plants. The capacity (in tons) of each plant is given in the table below:

Plant 1 2 3 4 5 Tons 300 200 300 200 400

The tomato sauce is stored at one of three warehouses. The per ton cost of producing tomato sauce at each plant and shipping it to each warehouse is given in the following table:

TO Warehouse 1 Warehouse 2 Warehouse 3

M Plant 1 $800 $1000 $1200 O Plant 2 $700 $500 $700 R

F Plant 3 $800 $600 $500 Plant 4 $500 $600 $700 Plant 5 $700 $600 $500

Huntco has four customers. The cost of shipping a ton of sauce from each warehouse to each customer as well as each customer’s requirements (in tons) are given in the following table:

M Customer 1 Customer 2 Customer 3 Customer 4 O Warehouse 1 $40 $80 $90 $50 R

F Warehouse 2 $70 $40 $60 $80 Warehouse 3 $80 $30 $50 $60 Requirements 200 300 150 250

Finally, each plant and warehouse has the following fixed operating cost:

COST ($000) Plant 1 Plant 2 Plant 3 Plant 4 Plant 5 Whse. 1 Whse. 2 Whse. 3 35 45 40 42 40 40 20 60

Huntco would has a goal of meeting customer demands at minimum cost. Determine which plants and warehouses that will remain open as well as the optimal distribution plan.