Skycell, a major European cell phone manufacturer, is making production plans for the coming year. Skycell has worked with its customers (the service providers) to come up with forecasts of monthly requirements (in thousands of phones) as shown in the table below:

| Month | January | February | March | April | May | June |
|------------|---------|----------|-------|-------|------|------|
| Demand (k) | 1,000 | 1,100 | 1,000 | 1,200 | 1,500| 1,600|

| Month | July | August | September | October | November | December |
|------------|---------|---------|-----------|---------|----------|----------|
| Demand (k) | 1,600 | 900 | 1,100 | 800 | 1,400 | 1,700 |

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, eight hours each day. One person can assemble a phone every 10 minutes. Workers are paid 20 euros per hour and a 50 percent premium for overtime. The plant currently employs 1,250 workers. Component cost for each cell phone totals 20 euros. Given the rapid decline in component and finished-product prices, carrying inventory from one month to the next incurs a cost of 3 euros per phone per month. Skycell currently has a no-layoff policy in place. Overtime is limited to a maximum of 20 hours per month per employee. Assume that Skycell has a starting inventory of 50,000 units and wants to end the year with the same level of inventory.

(a) Assuming no backlogs, no subcontracting, and no new hires, what is the optimum production schedule? What is the annual cost of this schedule?

(b) Is there any value for management to negotiate an increase of allowed overtime per employee per month from 20 hours to 40?

(c) A third party has offered to produce cell phones as needed at a cost of $26 per unit (this includes component costs of $20 per unit). How should Skycell use the third party? How does your answer change if the third party offers a price of $25 per unit?

(d) Is it profitable (and why) for Skycell to use the third party even when the per-unit cost of the third party is higher than the average per-unit cost (including inventory holding and overtime for in-house production)?

(e) Assume now the initial situation without subcontracting option. Skycell has a team of 50 people who are willing to work as seasonal employees. The cost of bringing them on is 800 euros per employee, and the layoff cost is 1,200 euros per employee. What is the optimal production, hiring, and layoff schedule?

(f) Relative to having 1,250 permanent employees and 50 seasonal, will Skycell gain significantly if it carries only 1,100 permanent employees but has 200 seasonal employees?

a) The optimum production schedule would involve adjusting production levels to meet monthly demand without carrying excess inventory. Skycell should produce the exact number of phones required each month. The annual cost of this schedule would include labor costs (regular and overtime), component costs, and inventory holding costs. The annual cost can be calculated by summing these costs for each month.

b) Increasing allowed overtime from 20 to 40 hours per employee per month may be valuable if it helps meet increased demand without the need for hiring more workers or subcontracting. It would reduce the need for seasonal employees and potentially lower hiring and layoff costs.

c) Skycell should use the third party to produce cell phones as needed if the third party's cost of $26 per unit is lower than Skycell's total in-house production cost. If the third party offers a price of $25 per unit, the decision remains the same, as it is still lower than Skycell's in-house production cost.

d) It can be profitable for Skycell to use the third party even when the per-unit cost is higher because it allows Skycell to avoid costs associated with hiring, layoff, overtime, and holding excess inventory. The third party's flexibility and cost structure may still make it a cost-effective option.

e) To determine the optimal production, hiring, and layoff schedule, Skycell should consider the costs of hiring and laying off seasonal employees along with production costs. The goal is to minimize costs while meeting demand.

f) Having 1,100 permanent employees and 200 seasonal employees instead of 1,250 permanent employees can be advantageous if it reduces overall labor costs while meeting production needs. The cost savings from hiring and laying off seasonal employees may outweigh the additional costs of recruitment and layoff, leading to a more cost-effective workforce strategy.

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