Problems Network Flow Programming Models
 Network Flow Programming Models - Distribution and Worker Assignment

A company has three plants: P1, P2 and P3, and two customers: C1 and C2. You are to construct and solve a network flow model to make several decisions for the company. Details of the situation are listed below for a one month period.
• C1 has a firm demand for 1000 units of product, while C2 has a demand for 600 units. These demands must be satisfied.
• The cost of transferring a unit of product from plant i to customer j is c(i, j) These costs are shown in the table.

 c(i,j) 1 2 1 10 15 2 14 20 3 25 22

• Each plant can manufacture no more that 500 units of product during regular time. Not including labor cost, the cost of manufacture at P1 is \$100 per unit, at P2 the cost is \$110 per unit, and at P3 the cost is \$120 per unit.
• At each plant an additional 100 units can be manufactured on overtime. The overtime cost, again not including labor, is 1.5 times the regular time cost.
• The company has two sources of labor: skilled labor indicated by W1 and semi-skilled by W2. There are 100 skilled laborers available and 200 semi-skilled laborers. Skilled laborers are paid \$2000 per month and semiskilled laborers are paid \$1700 per month. Not all workers available need be hired.
• Each skilled laborer will produce 12 units of product per month, while each semi-skilled laborer will produce 10 units per month.
• The company must transport workers to the plants. The cost of transporting a worker to P1 is \$300 per month, to P2 the cost is \$250, and to P3 the cost is \$275.
• The network model is to minimize total cost.

Operations Research Models and Methods
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by Paul A. Jensen