Problem:
Plan production for the next year. The demand forecast is spring, 20,000; summer, 10,000; fall, $200 per worker 15,000; winter, 18,000. At the beginning of spring you have 70 workers and 1,000 units in inventory. The union contract specifies that you may lay off workers only once a year, at the beginning of summer. Also, you may hire new workers only at the end of summer to begin regular work in the fall. The number of workers laid off at the beginning of summer and the number hired at the end of summer should result in planned production levels for summer and fall that equal the demand forecasts for summer and fall, respectively. If demand exceeds supply, use overtime in spring only, which means that back-orders could occur in winter. You are given these costs: hiring, $100 per worker; layoff, $200 per worker laid off; holding, $20 per unit-quarter; back-order cost, $8 per unit; straight time labor, $10 per hour; overtime, $15 per hour. Productivity is 0.5 unit per worker hour, eight hours per day. 50 days per quarter. Find the total cost.