Problem:

Shoney Video Concepts produces a line of video streaming servers that are linked to personal computers for storing movies. These devices have very fast access and large storage capacity.

Shoney is trying to determine a production plan for the next 12 months. The main criterion for this plan is that the employment level is to be held constant over the period. Shoney is continuing in its R&D efforts to develop new applications and prefers not to cause any adverse feelings with the local workforce. For the same reason, all employees should put in full workweeks, even if that is not the lowest-cost alternative.

The forecast for the next 12 months is:

Month          Forecast Demand

January               600

February              800

March                  900

April                    600

May                    400

June                    300

July                     200

August                 200

September           300

October               700

November            800

December            900

Manufacturing cost is $200 per set, equally divided between materials and labor. Inventory storage cost is $5 per month. A shortage of sets results in lost sales and is estimated to cost an overall $20 per unit short.

The inventory on hand at the beginiing of the planning period is 200 units. Ten labor hours are required per DVD player. The workday is eight hours.

Required:

Develop an Aggregate production schedule for the year using a constant workforce. For simplicity, assume 22 working days each month except July, when the plant closes down for three weeks' vacation (leaving seven working days). Assume that total production capacity is greater than or equal to total demand.

Solve the numerical problem and show step by step calculation.