Develop a production plan and calculate the annual cost for a firm whose demand forecast is fall, 10,000, winter, 8,000, spring, 7,000 and summer 12,0000. Inventory at the beginning of fall is 500 units. At the beginning of fall you currently have 30 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 if overtime is necessary to prevent stockouts at the end of those quarters. Overtime is not available during the fall. Relevant costs are: hiring , $100 for each temp; layoff, $200 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.
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To develop a production plan and calculate the annual cost for the firm, we need to follow a few steps:
Step 1: Determine the production requirements for each season based on the demand forecast and beginning inventory.
- Fall demand: 10,000 units
- Winter demand: 8,000 units
- Spring demand: 7,000 units
- Summer demand: 12,000 units
- Beginning inventory at the start of fall: 500 units
Therefore, the total production requirements for each season are as follows:
- Fall production requirement: 10,000 units - 500 units = 9,500 units
- Winter production requirement: 8,000 units
- Spring production requirement: 7,000 units
- Summer production requirement: 12,000 units
Step 2: Determine the workforce needed for each season.
- Beginning workforce at the start of fall: 30 workers
- Workforce required per unit produced: 0.5 units per worker hour
Given that there are 8 hours per day and 60 days per season, we can calculate the required workforce per season as follows:
- Fall workforce requirement: (9,500 units / (0.5 units per worker hour x 8 hours per day x 60 days per season)) ≈ 3.96 workers (round up to 4 workers)
- Winter workforce requirement: (8,000 units / (0.5 units per worker hour x 8 hours per day x 60 days per season)) ≈ 3.33 workers (round up to 4 workers)
- Spring workforce requirement: (7,000 units / (0.5 units per worker hour x 8 hours per day x 60 days per season)) ≈ 2.92 workers (round up to 3 workers)
- Summer workforce requirement: (12,000 units / (0.5 units per worker hour x 8 hours per day x 60 days per season)) ≈ 5 workers
Step 3: Determine the hiring and layoff requirements.
- Hiring cost per temporary worker: $100
- Layoff cost per worker: $200
Since we need to hire temporary workers at the beginning of summer and lay them off at the end of summer, the hiring and layoff requirements are as follows:
- Hiring requirements: 5 workers (beginning of summer)
- Layoff requirements: 0 workers (end of summer)
Step 4: Calculate the annual cost.
- Inventory holding cost per unit-quarter: $5
- Backorder cost per unit: $10
- Straight time wage rate per hour: $5
- Overtime wage rate per hour: $8
We need to consider the costs for each season and the associated production. The annual cost is calculated as follows:
- Fall cost: (9,500 units x $5) + (max(0, 9,500 units - beginning inventory) x $10)
- Winter cost: (8,000 units x $5) + (max(0, 8,000 units - regular production) x $10) + (overtime requirement x $8)
- Spring cost: (7,000 units x $5) + (max(0, 7,000 units - regular production) x $10) + (overtime requirement x $8)
- Summer cost: (12,000 units x $5) + (max(0, 12,000 units - regular production) x $10)
To calculate the overtime requirement, we need to determine the production shortfall compared to regular production for winter and spring:
- Winter shortfall: max(0, 8,000 units - regular production)
- Spring shortfall: max(0, 7,000 units - regular production)
Finally, we can sum up the costs for each season to get the annual cost for the firm.