Plan production for a four-month period: February through May. For February and
ID: 363506 • 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 90 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 inventories 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. $12 per hour overtime. $18 per hour: backorder. $24 per unit. Find the total cost of this plan.
Explanation / Answer
Total Cost of Plan January February March April May Forecast 80,000 64,000 100,000 40,000 Beginning Inventory 0 0 0 -16,000 Production Required (forecast -Inventory) 80,000 64,000 100,000 56,000 Production Hours Required (Production required/4 units per hour) 20,000 16,000 25,000 14,000 Regular workforce required (Production Hours Required /(8 *20) 90 125 100 100 100 Regular Production (Workforce *8*20*4) 80,000 64,000 64,000 64,000 Workers hired 35 0 0 0 Workers laid-off 0 25 0 0 Overtime hours 0 0 5,000 0 Overtime Production (Overtime Hours *4 Units/hour) 0 0 20,000 0 Total Production (Regular Production + Overtime Production) 80,000 64,000 84,000 64,000 Ending Inventory 0 0 0 -16,000 8,000 Ending Backorders 0 0 16,000 0 Cost: straight-time labor cost of production ($12/hour) $240,000 $192,000 $192,000 $192,000 Overtime cost of production ($18/hour) $0 $0 $360,000 $0 Inventory holding cost ($10/unit per month) $0 $0 $0 $80,000 Backorder cost ($24/ unit) $0 $0 $384,000 $0 Hiring cost ($45) $1,575 $0 $0 $0 Layoff cost ($65) $0 $1,625 $0 $0 Total Cost (Per Month) $241,575 $193,625 $936,000 $272,000 Total Cost for four months $1,643,200