# solution

An automobile manufacturer needs to plan its production for the next 12 months. Demands for the next 12 months are forecasted in the table below:

 1 2 3 4 5 6 7 8 9 10 11 12 940 790 360 720 270 130 160 300 990 290 280 790

Other relevant information is as follows:

• Workers are paid \$5,000 per month;
• It costs \$500 to hold a car in inventory for a month. The holding cost is based on each monthâ€™s ending inventory;
• It costs \$4,000 to hire a worker; while it costs \$6,000 to fire a worker. Workers are hired and fired at the beginning of each month;
• Each worker can make up to eight cars per month;
• At the beginning of month 1, there are 500 cars in inventory and 60 workers.

The manufacturer wants to minimize the total inventory and staffing cost of meeting demands for cars in the next 12 months.

1. Define the decision variables and write down the detailed mathematical formulation of the automobile manufacturerâ€™s optimization problem.
2. Solve the optimization problem by Excel Solver. Write down the manufacturerâ€™s detailed optimal production and staffing plan for the next 12 months.

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