Problem $8-13($Algo$)$

Shoney Video Concepts produces a line of video streaming servers that are linked to 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 prompt any adverse feelings from 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 $810$

Manufacturing cost is $$210$ per server, equally divided between materials and labor. Inventory storage cost is $$5$ per month. A shortage of servers results in lost sales and is estimated to cost an overall $$21$ per unit short.

The inventory on$-$hand at the beginning of the planning period is $210$ units. Ten labor hours are required per DVD player. The workday is eight hours.

Develop an aggregate production schedule for the year using a constant workforce. For simplicity, assume $23$ working days each month except July, when the plant closes down for three weeks' vacation $($leaving eight working days$).$ Assume that total production capacity is greater than or equal to total demand $($i$.$e$.,$ compute workforce level based on annual demand and annual capacity$).$

Note: Leave the cells blank, whenever zero $(0)$ is required. Indicate monthly shortages using a negative ending inventory level. Round up the "number of workers" to the next whole number and round down your "monthly production rates" to the next lower whole number.