Question

Develop a production plan and calculate the annual cost for a firm whose demand forecast is fall, 10,500; winter, 8,400; spring, 6,800; summer, 12,000. Inventory at the beginning of fall is 525 units. At the beginning of fall you currently have 35 workers, but you plan to hire temporary workers at the beginning of summer and lay them off at the end of summer. In addition, you have negotiated with the union an option to use the regular workforce on overtime during winter or spring only if overtime is necessary to prevent stockouts at the end of those quarters. Overtime is not available during the fall. Relevant costs are hiring, $90 for each temp; layoff, $180 for each worker laid off; inventory holding, $5 per unit-quarter; backorder, $10 per unit; straight time, $5 per hour; overtime, $8 per hour. Assume that the productivity is 0.5 unit per worker hour, with eight hours per day and 60 days per season. (Round up number of workers to the next whole number and the rest of your values to the nearest whole number. Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required.)

Fall Winter Spring Summer
Forecast 10,500 8,400 6,800 12,000
Beginning inventory
Production required
Production hours required
Production hours available1
Overtime hours
Temp workers2
Temp worker hours available
Total hours available
Actual production
Ending inventory
Workers hired
Workers laid off
Fall Winter Spring Summer
Straight time $ $ $ $
Overtime
Inventory
Backorder
Hiring
Layoff
Total $ $ $ $
Annual cost $

Answer 1

The best production method when labor costs $100/unit is Method 1, with a cost of $9,000. If the cost of labor rises to $200/unit, Method 1 remains the best option, with increased total cost to $14,000.

Step-by-step explanation:

The production method that should be selected is the one that minimizes total costs given the costs of labor and capital. We compare the total cost of each method at two different labor rates.

Method 1: 50 units of labor, 10 units of capital

Method 2: 20 units of labor, 40 units of capital

Method 3: 10 units of labor, 70 units of capital

When labor costs $100/unit and capital costs $400/unit:

Method 1 Cost = (50 * $100) + (10 * $400) = $5,000 + $4,000 = $9,000

Method 2 Cost = (20 * $100) + (40 * $400) = $2,000 + $16,000 = $18,000

Method 3 Cost = (10 * $100) + (70 * $400) = $1,000 + $28,000 = $29,000

The best production method at this labor rate is Method 1, with the lowest total cost of $9,000.

When labor costs rise to $200/unit and capital costs remain at $400/unit:

Method 1 Cost = (50 * $200) + (10 * $400) = $10,000 + $4,000 = $14,000

Method 2 Cost = (20 * $200) + (40 * $400) = $4,000 + $16,000 = $20,000

Method 3 Cost = (10 * $200) + (70 * $400) = $2,000 + $28,000 = $30,000

Even with the increased labor cost, Method 1 remains the best production method, now with a total cost of $14,000.

Answer 2

Fall Winter Spring Summer

Forecast 10,500 8,400 6,800 12,000

Beginning inventory 525 -1575 0 1600

Production required 9975 9975 6800 10400

Production hours required 19950 19950 13600 20800

Production hours available 16800 16800 16800 16800

Overtime hours 3150 0

Temp workers 0 0 0 9

Temp worker hours available 0 0 0 4321

Total hours available 16800 19950 16800 21120

Actual production 8400 9975 8400 10560

Ending inventory -1575 0 1600 160

Workers hired 0 9

Workers laid off 0 0

Costs

Straight time $ 5 84000 84000 84000 105600

Overtime $ 8 0 25200 0 0

Inventory $ 5 0 0 8000 800

Backorder $ 10 15750 0 0 0

Hiring $ 90 0 0 0 810

Layoff $ 180 0 0 0 0

Total 99750 109200 92000 107210

Therefore total cost = 99750 + 109200 + 92000 + 107210

= $ 408,160