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During the next six months the Surester Company must meet (on time) the following demands for pairs of shoes: 3000 in month 1; 5000 in month 2; 2000 in month 3; 2000 in month 4, 3500 in month 5, and 2500 in month 6. At the beginning of month 1, 500 pairs of shoes are on hand, and Suresten has 100 workers. A worker is paid $1500 per month. Each worker can work up to 160 hours per month before he or she receives overtime. A worker can work up to 20 hours of overtime per month and is paid $15 per hour for overtime labor. It takes five hours of labor and $15 of raw material to produce a pair of shoes. At the beginning of each month, workers can be hired or fired. Each hired worker costs $1600, and each fired worker costs $2000. At the end of each month, a holding cost of $3 per pair of shoes left in inventory is incurred. If a customer demand is backordered, the company must pay a backorder cost $30 per pair of shoes. The company has 1000 pair of shoes and 100 workers initially. Production in a given month can be used to meet that month's demand and the backordered demand from previous months. Suresten wants to use LP to determine its optimal production schedule and labor policy. Please notice that the number of shoes produced, the number of workers hired and fired must be integer. a E22 f B D E H 1 K L 1 SureStep aggregate planning model 2 3 Input data 4 Initial inventory of shoes 5 Initial number of workers 6 Regular hours/worker/month 7 Maximum overtime hours/worker/month 8 Hiring cost/worker 9 Firing cost/worker 10 Regular wages/worker/month 11 Overtime wage rate/hour 12 Labor hours/pair of shoes 13 Raw material cost/pair of shoes 14 Holding cost/pair of shoes in inventory/month 15 Unit backordering cost 16 1000 100 160 20 $1,600 $2,000 $1,500 $15 5 $15 $3 $30 $30 Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 15 Unit backordering cost 16 17 Worker plan 18 Workers from previous month 19 Workers hired 20 Workers fired 21 Workers available after hiring and firing 22 23 Regular-time hours available 24 Overtime labor hours used 25 26 Maximum overtime labor hours available 27 28 Total hours for production 29 30 Production plan 31 Shoes produced 32 33 Production capacity 34 35 Inventory after production 36 Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 3000 5000 2000 2000 3500 2500 34 35 Inventory after production 36 37 Forecasted demand 38 Ending inventory 39 40 On-hand inventory 41 Backordering 42 On-hand inventory - Backordering 43 44 Monetary outputs 45 Hiring cost 46 Firing cost 47 Regular-time wages 48 Overtime wages 49 Raw material cost 50 Backordering cost 51 Holding cost 52 Totals 53 Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Totals During the next six months the Surester Company must meet (on time) the following demands for pairs of shoes: 3000 in month 1; 5000 in month 2; 2000 in month 3; 2000 in month 4, 3500 in month 5, and 2500 in month 6. At the beginning of month 1, 500 pairs of shoes are on hand, and Suresten has 100 workers. A worker is paid $1500 per month. Each worker can work up to 160 hours per month before he or she receives overtime. A worker can work up to 20 hours of overtime per month and is paid $15 per hour for overtime labor. It takes five hours of labor and $15 of raw material to produce a pair of shoes. At the beginning of each month, workers can be hired or fired. Each hired worker costs $1600, and each fired worker costs $2000. At the end of each month, a holding cost of $3 per pair of shoes left in inventory is incurred. If a customer demand is backordered, the company must pay a backorder cost $30 per pair of shoes. The company has 1000 pair of shoes and 100 workers initially. Production in a given month can be used to meet that month's demand and the backordered demand from previous months. Suresten wants to use LP to determine its optimal production schedule and labor policy. Please notice that the number of shoes produced, the number of workers hired and fired must be integer. a E22 f B D E H 1 K L 1 SureStep aggregate planning model 2 3 Input data 4 Initial inventory of shoes 5 Initial number of workers 6 Regular hours/worker/month 7 Maximum overtime hours/worker/month 8 Hiring cost/worker 9 Firing cost/worker 10 Regular wages/worker/month 11 Overtime wage rate/hour 12 Labor hours/pair of shoes 13 Raw material cost/pair of shoes 14 Holding cost/pair of shoes in inventory/month 15 Unit backordering cost 16 1000 100 160 20 $1,600 $2,000 $1,500 $15 5 $15 $3 $30 $30 Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 15 Unit backordering cost 16 17 Worker plan 18 Workers from previous month 19 Workers hired 20 Workers fired 21 Workers available after hiring and firing 22 23 Regular-time hours available 24 Overtime labor hours used 25 26 Maximum overtime labor hours available 27 28 Total hours for production 29 30 Production plan 31 Shoes produced 32 33 Production capacity 34 35 Inventory after production 36 Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 3000 5000 2000 2000 3500 2500 34 35 Inventory after production 36 37 Forecasted demand 38 Ending inventory 39 40 On-hand inventory 41 Backordering 42 On-hand inventory - Backordering 43 44 Monetary outputs 45 Hiring cost 46 Firing cost 47 Regular-time wages 48 Overtime wages 49 Raw material cost 50 Backordering cost 51 Holding cost 52 Totals 53 Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Totals