Plan production for the next year. The demand forecast is spring, 20,000; summer
ID: 2720883 • Letter: P
Question
Plan production for the next year. The demand forecast is spring, 20,000; summer, 10,000; fall, 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 backorders could occur in winter. You are given these costs: hiring, $100 per new worker; layoff, $200 per worker laid off; holding, $20 per unit-quarter; backorder cost, $8 per unit; straight-time labor, $10 per hour; overtime, $15 per hour. Productivity is 0.5 units per worker hour, eight hours per day, 50 days per quarter. Find the total cost.
Explanation / Answer
Spring Summer Fall Winter Forecast A 20,000 10,000 15,000 18,000 Beginning inventory B 1000 0 0 0 Production required C = A-B 19,000 10,000 15,000 18,000 Production hours required D = C/0.5 38,000 20,000 30,000 36,000 Regular workforce E 28,000 20,000 30,000 30,000 Regular production F = E*0.5 14,000 10,000 15,000 15,000 Overtime hours G = D-E 10,000 0 0 0 Overtime production H = G*0.5 5,000 0 0 0 Total production I = F + H 19,000 10,000 15,000 15,000 Ending inventory J = I - C 0 0 0 0 Ending backorders K = A-B-I 0 0 0 3,000 Workers hired L 0 0 25 0 Workers laid off M 0 20 0 0 Spring Summer Fall Winter $ $ $ $ Straight time @ $10 per hour $ 10 * E $252,000.00 $180,000.00 $270,000.00 $270,000.00 Overtime @ $15 per hour $ 15 * G $140,000.00 $0.00 $0.00 $0.00 Inventory @ $20 per unit $ 20 * J $0.00 $0.00 $0.00 $0.00 Backorder @ $8 per unit $ 8 * K $0.00 $0.00 $0.00 $24,000.00 Hiring @ $100 per labor $ 100 * L $0.00 $0.00 $2,500.00 $0.00 Layoff @ $200 per labor $ 200 * M $0.00 $4,000.00 $0.00 $0.00 Total $392,000.00 $184,000.00 $272,500.00 $294,000.00 $1,142,500.00 Labor productivity per quarter Std Hours 8 Days 50 Productivity 0.5 Units/labor quarter 200 Regular Workhour Calulation Spring = 70*8*50 = 28000 hours Calculation of workers laid off in the beginning of Summer Production Hours Required 20000 No of labor required (2000/400) 50 Labor force in system 70 Laid off 20 Calculation of workers hired at the end of Summer Production Hours Required 30000 No of labor required (30000/400) 75 Labor force in system 50 Hired 25 Further, hiring in Summer can happen only for Fall requirements. Also, there cannot be overtime in winter, resulting in backorder with 3000 units