'. RMIT Supply Chain Analysis and Design Page 1 of3 UNIVERSITY Assignment 1 Case Analysis Case: AGGREGATE PLANNING Denition In these models, the workforce level is allowed to change each period through the hiring and ring of workers. Such models, where we determine workforce levels and production schedules for a multiperiod time horizon, are called aggregate planning models. Case Renova company is a manufacturer of fancy bags in Melbourne. The demand for the next four months is forecasted as below: Month 1 Month 2 Month 3 Month 4 3000 5000 2000 1000 500 bags are on hand at the beginning of month 1, and the company has 20 workers. The wage of a worker is $1500 per month. The standard working time for a worker is up to 160 hours per month before he or she receives overtime. The maximum overtime for a worker is 20 hours per month and is paid $13 per hour for overtime labour. It takes four hours of labour and $15 of raw material to make a bag. At the beginning of each month, workers can be hired or red. Each hired worker costs $1600. and each red worker costs $2000. At the end of each month, a holding cost of $3 per bag left in inventory is incurred. Production in a given month can be used to meet that month's demand. Renova wants to use LP to determine its optimal production schedule and labour policy. Additional info: I The data on the current number of workers, the regular hours per worker per month, the regular hourly wage rates, and the overtime hourly rate, should be well known. The maximum number of overtime hours per worker per month is probably the result of a policy decision by management or a clause in the workers' contracts. . The costs for hiring and ring a worker are not trivial. The hiring cost includes training costs and the cost of decreased productivity due to the fact that a new worker must learn the job. The ring cost includes severance costs and costs due to loss of morale. Neither the hiring nor the ring cost would be simple to estimate accurately, but the human resources department should be able to estimate their values. a The unit production cost is a combination of two inputs: the raw material cost per bag and the labour hours per bag. The raw material cost is the going rate from the supplier(s). The labour per bag represents the \"production function"the average labour required to produce a unit of the product. The operations managers should be able to supply this number. . The big picture for aggregate demand planning model is presented as below: RMIT Supply Chain Analysis and Design Page 2 of 3 UNIVERSITY Initial number of workers Workers from Hiring cost per Total hiring Workers previous month worker cost hired Total regular- Regular wages per time wages worker per month Workers available after Workers Firing cost per Total firing Workers hiring and firing Maximum overtime Maximum overtime hours per worker cost fired labour hours available worker per month Regular hours per Regular-time hours Overtime labour Total overtime Overtime wage worker per month available hours used wages rate per hour Labour hours per Workers to bag production Total hours for Minimise total cost (sum production bag of costs in gray) Raw material cost per Total raw Bags Production bag material cost produced capacity Initial inventory of Inventory after Forecasted bag production bags production demand Holding cost per bags per Total holding Ending month cost inventory1. Developing Mathematical Model Develop a LP model that relates workforce and production decisions to monthly costs, and to nd the minimum-cost solution that meets forecasted demands on time and stays within limits on overtime hours and production capacity. (6 marks Word Document) RMIT Classification: Trusted Production Scheduling Mathematical Model 9) 0.10X41 + 0.08x21 $ 400 (Machine capacity, April) 10) 0.10X12 + 0.08X22 $ 500 (Machine capacity, May) 11) 0.10X13 + 0.08X23 $ 600 (Machine capacity, June) 12) 0.05X11 + 0.07X21 S 300 (Labour capacity, April) 13) 0.05X12 + 0.07X22 $ 300 (Labour capacity, May) 14) 0.05X13 + 0.07X23 - 300 (Labour capacity, June) 15) 2S11 + 3521 $ 10,000 (Storage capacity, April) 16) 2S12 + 3S22 $ 10,000 (Storage capacity, May) 17) 2513 + 3S23 $ 10,000 (Storage capacity, June) 18) X11 + X21 - 1, + D, = 2500 (increase or decrease in the total production level for month April) 19) X12 + X22 - X11 - X21 - 12 + D2 =0 (increase or decrease in the total production level for month May) 20) X13 + X23 - X12 - X22 - I3 + D3= 0 (increase or decrease in the total production level for month June) X11, X12, X13, X21, X22, X23, |1, 12, 13, D1, D2, Da, $11, $12, $13, $21, $22, S23 2 0 (Non-negativity)Production Scheduling - Solution Summary of Production Schedule Activity April May June Production Component 322A 500 3200 5200 Component 8023 2500 2000 0 Totals 3000 5200 5200 Ending inventory Component 322A 0 200 400 Component 802B 1700 3200 200 Machine usage Scheduled hours 250 480 520 Slack capacity hours 150 20 80 Labor usage Scheduled hours 200 300 260 Slack capacity hours 100 0 40 Storage usage Scheduled storage 5100 10,000 1400 Slack capacity 4900 0 8600 Total production, inventory, and production-smoothing cost = $225,295 Supply Chain Analysis and Design 25