Month	Demand					Materials cost/unit	$ 20.0
May	1,500,000					Inventory holding cost/unit/month	$ 3.0
June	1,600,000					Marginal cost of stockout/unit/month
July	1,600,000					Hiring and training cost/worker	$ 1,000.0
August	900,000					Layoff cost/worker	$ 2,000.0
September	1,100,000					Labor hours required/unit
October	800,000					Regular time cost/hour	$ 20.0
November	1,400,000					Over time cost/hour
December	1,700,000					Subcontracting cost/unit	$ 25.0
Initial number of workers	1,250
Initial inventory	50,000
Minimum ending inventory	50,000

Question 1 (25 pts.): Skycell, a major European cell phone manufacturer, is making production plans for the last 8 months of the year. Skycell has worked with its customers (the service providers) to come up with forecasts of monthly requirements as shown in the spreadsheet named Question1. Assume that the demand during a stockout is backlogged and the cost of stocking out is $4 per phone per month.

Manufacturing is primarily an assembly operation, and capacity is governed by the number of people on the production line. The plant operates for 20 days a month, 8 hours each day. One person can assemble a phone every 10 minutes. Workers are paid $20 per hour and a 50% premium for overtime. The plant currently employs 1,250 workers. Material costs for each cell phone total $20. Carrying inventory from one month to the next incurs a cost of $3 per phone per month.

Assume that Skycell has a starting inventory of 50,000 units and wants to end the year with at least the same level of inventory, 50,000 units.

a) (6 pts.) Assuming no subcontracting, no new hires, no layoffs, and no maximum overtime limit (overtime is allowed), what is the optimum aggregate plan that minimizes the total annual cost? What is the total annual cost of this plan?

b) (7 pts.) Assume that a third party has offered to produce cell phones as needed at a cost of $25 per unit (this includes component costs of $20 per unit). Also, Skycell can now hire and lay off employees. The cost of hiring them is $1,000 per employee and the layoff cost is $2,000 per employee. Overtime is limited to at most 20 hours per employee per month. Assume that all the demand during a stockout is backlogged and the firm plans to meet all of the demand. For this case, what is the optimum aggregate plan that minimizes the total annual cost? What is the total annual cost of this plan? Also report the average amount of time that a product spends in the system, from production to sales (in months).

c) (5 pts.) For the case provided in part (b), consider the scenario in which Skycell aims for a chase production schedule. For this case, what is the optimum aggregate plan that minimizes the total annual cost? What is the total annual cost of this plan?

d) (7 pts.) For the case provided in part (b), consider the scenario in which all the demand during a stockout is lost and the cost of stocking out is $24.5 per phone. For this case, what is the optimum aggregate plan that minimizes the total annual cost? What is the total annual cost of this plan? Also report the average amount of time that a product spends in the system, from production to sales (in months).

Notes:

1. Check the Answers spreadsheet to determine what to report for each part.

2. Make sure to create copies of the spreadsheet Question1 and show your work for each part.

3. It might take some time for Solver to return a solution for parts (b) to (d). If Solver does not return a solution in a few minutes, then try to solve those parts after removing the integer constraints on number of hires and layoffs.

4. Parts (c) and (d) are independent, i.e., assumptions made in part (c) do not carry over to part (d)