Plan production for a four-month period: February through May. For February and
ID: 327108 • 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, 80,256; March, 70,400; April, 100,360; May, 40,360. Productivity is four units per worker hour, eight hours per day, 22 days per month. Assume zero inventory on February 1. Costs are hiring, $45 per new worker; layoff, $65 per worker laid off; inventory holding, $10 per unit-month; straight-time labor, $10 per hour; overtime, $15 per hour; backorder, $20 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 no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Round your answers to the nearest whole number.)
Explanation / Answer
ANSWER
FOR PLAN PRODUCTION FOR A FOUR MONTH PERIOD
February March April May Forecast (a) 80256 70400 100360 40360 Beginning inventory (b) 0 0 0 0 Production required (c = a-b) 80256 70400 100360 40360 Production hours required (d = c/4) 20064 17600 25090 10090 Regular workforce (e ) 100 100 100 100 Regular production (f = e*22*8*4) 70400 70400 70400 70400 Overtime hours (g) 0 0 5000 0 Overtime production (h = g* 4) 0 0 20000 0 Total production (i=f+h) 70400 70400 90400 70400 Ending inventory (j = b+i-a (if b+i-a>0,else 0) 0 0 0 10224 Ending backorders (k = a-b-i (if a-b-i>0,else 0) 9856 9856 19816 0 Workers hired (l) 0 0 0 0 Workers laid off (m) 0 0 0 0 February March April May Straight time (n = $10 * f/4) $176,000 $176,000 $176,000 $176,000 Overtime (o = $15 * g) $0 $0 $75,000 $0 Inventory (p = $10 * j) $0 $0 $0 $102,240 Backorder (q = $20 * k) $197,120 $197,120 $396,320 $0 Hiring (r = $45 * l) $0 $0 $0 $0 Layoff (s = $65 * m) $0 $0 $0 $0 Total $373,120 $373,120 $647,320 $278,240 Total cost $1,671,800 Overtime Calculation February March April May Total Demand 80256 70400 100360 40360 291376 Regular Production 70400 70400 70400 70400 281600 Overtime Required 9856 0 29960 -30040 9776 Hence, no overtime in the month of May, due to spare capacity