Question

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 the forecasts of monthly requirements (in thousands of phones) as shown in the table.

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 costs for each cellphone total 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, formulate the aggregate planning problem to minimize the total cost. (6 pts)

b. Assume Skycell aims for a level production schedule, what changes you need to make in your formulation? (6 pts)

c. Now Skecell has a team of 50 people who are willing to work as seasonal works. The cost of bringing them is 800 euros per employee and the layoff cost is 1,200 euros per employee. How do you change your formulation in part a? (6 pts)

Month

Demand

Jan.

1000

Feb.

1100

March

1000

April

1200

May

1500

June

1600

July

1600

Aug.

900

Sep.

1100

Oct.

800

Nov.

1400

Dec.

1700

d. Solve part a in excel. Is there any value for management to negotiate an increase of allowed overtime per employee per month from 20 hours to 40 hours? (6 pts)

e. Solve part b in excel. (3 pts)

f. Solve part c in excel. (3 pts)

Answer 1

Aggregate Production Plan
Month	Demand	Regular Time Production	Over-   time	Sub-conract	Inventory	No. of Workers	No. Hired	No. Fired
					50000	1250
January	1000000	1200000	0	0	250000	1250	0	0
February	1100000	1200000	0	0	350000	1250	0	0
March	1000000	1200000	0	0	550000	1250	0	0
April	1200000	1200000	0	0	550000	1250	0	0
May	1500000	1200000	0	0	250000	1250	0	0
June	1600000	1200000	150000	0	0	1250	0	0
July	1600000	1200000	150000	0	0	1250	0	0
August	900000	1185600	0	0	285600	1235	0	15
September	1100000	1185600	0	0	371200	1235	0	0
October	800000	1185600	0	0	756800	1235	0	0
November	1400000	1185600	0	0	542400	1235	0	0
December	1700000	1185600	22000	0	50000	1235	0	0
Total	14900000	14328000	322000	0			0	15
Costs
Month	Material	Regular Time	Over-     time	Sub-contracting	Inventory Holding		Hiring	Firing
January	20000000	4000000	0	0	750000
February	22000000	4000000	0	0	1050000
March	20000000	4000000	0	0	1650000
April	24000000	4000000	0	0	1650000
May	30000000	4000000	0	0	750000
June	32000000	4000000	750000	0	0
July	32000000	4000000	750000	0	0
August	18000000	4000000	0	0	856800
September	22000000	4000000	0	0	1113600
October	16000000	4000000	0	0	2270400
November	28000000	4000000	0	0	1627200
December	34000000	4000000	110000	0	150000
Total Cost	298000000	48000000	1610000	0	11868000	0	0	0

b) For level production planning the fixed average demand of all months needs to be calculated and no of employees kept as close to that as possible to ensure overall production equals demand without any major modifications on a continuous basis.

c) We would hire them for March to July to avoid the loss of sales in July due to excessive seasonal demand remaining unmet in the final month. each extra worker makes 960 units a month giving 48,000 units for five months a total of 240,000 units which is close to overall loss from the shortage in July of 250,000.

d) Yes, There is definitely a value as overtime units would double to 300000 and be sufficient to cover shortages in any month allowing the exceptional facility in chase production plan by varying production to meet demand so minimizing cost from overheads due to excess inventory.