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Magazine Chapter 4: Q8OQ. (page 507)
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, and 20 days per month. Assume zero inventory on February 1. Costs are hiring, \(50 per new worker; layoff, \)70 per worker laid off; inventory holding, \(10 per unit-month; straight-time labor, \)10 per hour; over time, \(15 per hour; backorder, \)20 per unit. Find the total cost of this plan.
Short Answer
The total cost of this plan is $1,318,000.
Step by step solution
Please refer to the following calculation
Employed = Maximum of (Number of laborers of this current month - Number of laborers for the earlier month, 0)
Terminated = Maximum of (Number of laborers of the earlier month - Number of laborers during the current month, 0)
Normal Production = Number of laborers x 8 (hours/day) x 20 (days/month) x 4 (units/hour)
Since Regular Production < Demand in April,
Extra time creation in April = 5000 hours x 4 (hours/unit) = 20000 units
Complete Production = Regular Production + Overtime Production
Inventory for February = Total Production - Demand for February
Inventory for February = 0
Inventory for March = Inventory for February + Total Production for March - Demand for March
Inventory for March = 0
Since for April, Total Production < Demand, Inventory = 0
Delay purchase = Demand for April - Total Production for April
Inventory for May = Total Production for May - Demand for May
Complete Cost = Total Hired x 50 + Total Fired x 70 + Total Regular Production x 10 ($/hour)/4 (units/hour) + Total Overtime Production x 10 ($/hour)/4 (units/hour) + Total Inventory x 10 + Total Backorder x 20
Calculations
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