Linear Programming Model for Aggregate Planning

Linear Programming models can be used to determine an optimal strategy between the chase and level strategies. We shall present the LP model using an Example problem. 

A parts supplier has a contract with an OEM to supply 1550 units of some component C for the next 6 months. Table 2.10 gives the OEM s monthly requirements during the contract period. 

The supplier has 20 workers and 50 units of C on hand now. Each worker can produce 10 units of C per month. The company can recruit from the local labor market, but the recruits have to be trained for 1 month by a worker before they can be used in production. Each worker can train at most five recruits during a month. A worker is paid 3000 per month, when used in production or training. A worker can be laid off at a cost of 2000 per month. Firing a worker costs 5000. Each recruit is paid 1500 during training. 

Production ahead of schedule incurs an inventory holding cost of 50 per unit per month. Each unit of C not delivered on schedule involves a penalty cost of 75 per month until delivery is completed. However, all deliveries must be completed in 6 months. The supplier requires a final labor force of 30 workers and 50 units of C at the end of the 6th month. 

Decision variables The decision variables of the LP model for month f (f = 1, 2,..6) are defined as follows  

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