Consider the aggregate planning problem discussed in Example 2.13 (Section 2.15). Discuss how the LP formulation will change if the following constraints are added.

(a) Union regulation requires that no more than 10% of the workforce can be laid off in any month.

(b) The personnel department estimates that no more than 50 trainees can be hired in any month.

(c) The company wants to limit the change in workforce from 1 month to the next to 10 workers.

(d) Company's warehouse limits the monthly inventory to 120 units.

Example 2.13

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. The aggregate planning problem is to decide what hiring, firing, producing, storing, and shortage policy the supplier should follow in order to minimize the total costs during the contract period. Formulate this problem as an LP model and solve. Discuss the production plan.