Plan production for a four-month period: February through May. For February and
ID: 326231 • 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, 80,000; March, 64,000; April, 100,000; May, 40,000. Productivity is four units per worker hour, eight hours per day, 20 days per month. Assume zero inventory on February 1. Costs are hiring, S50 per new worker; layoff, $70 per worker laid off; inventory holding, S10 per unit-month; straight-time labor, $10 per hour; overtime, $15 per hour; backorder, $20 per unit. Find the total cost of this plan. February March April May Forecast Beginning Inventory Production hours Regular workforce Regular production Overtime hours Overtime roduction Total Production Ending invento Workers hired Workers laid ofif Straight time Overtime Inventor Backorder Hirin Layoff Total Total Cost:Explanation / Answer
feb and march exact demand forecast with 0 overtime Productivity 4 unit / worker / hour 8 hr / day 20 hr / month one worker in one day = 4*8=32 one worker in one month = 32*20= 640 100 regular workers = 64000 = demand for march in Feb extra units required 16000 ( 80000-64000) number of workers required = 16000/640 = 25 So workers hired in Feb = 25 Workers laid off in Feb end = 25 For Apr and May we have 100 workers max that can be produced = 128000 Required Demand = 140000 Inventory to be produced through OT = 12000 Number OF OT hours = 12000/4 = 3000 Cost Feb Mar Apr May Forecast 80000 64000 100000 40000 Beginning inventory 0 0 0 0 Production hours 16000 16000 19000 16000 Regular production hr 16000 16000 16000 16000 Overtime hours 0 0 3000 0 Overtime Production 0 0 12000 0 Total Production 80000 64000 76000 64000 Ending inventory 0 0 -24000 0 Workers hired 25 0 0 0 Workers laid off 25 0 0 0 straight time 10 160000 160000 160000 160000 Overtime 15 0 0 45000 0 inventory 10 0 0 0 0 Backorder 20 0 0 480000 0 hiring 50 1250 0 0 0 layoff 70 1750 0 0 0 total cost 163000 160000 685000 160000