Question

Plan production for a four-month period: February through May. For February and March, you should produce to exact demand forecast. For April and May, you should use overtime and inventory with a stable workforce; stable means that the number of workers needed for March will be held constant through May. However, government constraints put a maximum of 5,000 hours of overtime labor per month in April and May (zero overtime in February and March). If demand exceeds supply, then backorders occur. There are 100 workers on January 31. You are given the following demand forecast: February, 80,640; March, 64,000; April, 100,120; May, 40,120. Productivity is four units per worker hour, eight hours per day, 20 days per month. Assume zero inventory on February 1. Costs are: hiring, $52 per new worker; layoff, $72 per worker laid off; inventory holding, $12 per unit-month; regular time labor, $8 per hour; overtime, $12 per hour; backorder, $16 per unit. Develop a production plan and calculate the total cost of this plan. Note: Assume any layoffs occur at beginning of next month. (Leave the cells blank, whenever zero (0) is required. Negative values should be indicated by a minus sign. Round your answers to the nearest whole number.)

Answer 1

The optimal production plan gives a total costs of $417,672 for the periods Feb to May

In Feb we will have to hire 26 workers to close the gap between demand and production from our 100 existing workers

In March however, we will have to lay them off (26 workers) to keep our production in line with demand.

In April, we are constrained to 100 workers, thus requiring that we run overtime. The overtime requirement is between 3,060 hours to max of 5,000 hours. Note that inspire of the hours chosen, demand for April still won't be fulfilled.

The best option will be the one that gives us last backlog because of the costs of backorder being extremely costly.

5,000 overtime hours in April is the best option .

In May, we are constrained to our 100 workers, meaning we will fulfill our back orders and also retain inventory in hand of 7,760 units.

The 3 pages attached show how the cost is worked out and the presentation as well.