Plan production for a four-month period: February through May. For February and
ID: 443485 • Letter: P
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, 81,984; March, 67,200; April, 100,320; May, 40,320. Productivity is four units per worker hour, eight hours per day, 21 days per month. Assume zero inventory on February 1. Costs are hiring, $50 per new worker; layoff, $70 per worker laid off; inventory holding, $11 per unit-month; straight-time labor, $12 per hour; overtime, $18 per hour; backorder, $22 per unit.
Find the total cost of this plan. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your answers to the nearest whole number.)
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, 81,984; March, 67,200; April, 100,320; May, 40,320. Productivity is four units per worker hour, eight hours per day, 21 days per month. Assume zero inventory on February 1. Costs are hiring, $50 per new worker; layoff, $70 per worker laid off; inventory holding, $11 per unit-month; straight-time labor, $12 per hour; overtime, $18 per hour; backorder, $22 per unit.
Explanation / Answer
solution as per the tables required as follows:
In order to produce exact quantity as per forecast demand for Feb. and March, we are required to hire 22 workers in Feb. and lay-off same number in March. Further we are required to have constant number of workers from March to May, so no hiring and lay-off in April & May.
Total cost as per above calculations is $1,290,112/-
February March April May Forecast 81,984 67,200 100,320 40,320 Beginning inventory 0 0 0 0 Production required 81984 67200 100320 53440 Production hours required 20496 16800 25080 13360 Regular workforce 122 100 100 100 Regular production 81984 67200 67200 53440 Overtime hours 0 0 5000 0 Overtime production 0 0 20000 0 Total production 81984 67200 87200 53440 Ending inventory 0 0 0 0 Ending backorders 0 0 13120 0 Workers hired 22 0 0 0 Workers laid off 0 22 0 0 February March April May Straight time 245952 201600 300960 160320 Overtime 0 0 90000 0 Inventory 0 0 0 0 Backorder 0 0 288640 0 Hiring 1100 0 0 0 Layoff 0 1540 0 0 Total 247052 203140 679600 160320 Total cost 1290112