Question

1 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

Given :

Number of workers: 1250

Work time: 20 days * 8 hrs = 160 hrs

Salary = 20 Euros and Premium = 50% of the Salary

Component cost = 20 Euros

Inventory cost for 1 month = 3 Euros / phone

Overtime conditions for 1 employee  = 20 hrs / month

Solution A: & D
Overtime Producti Overtime Inventory Total PRODUCTION (in Overtime on(in100 cost (in Componentcost (in Salary (in Producti MONTH units) DEMAND (in 1000s) Inventory (in hrs) Os) 1000s) cost (in 1000s) 1000s) 1000s) on cost Jan Feb Mar 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 1200 24 24 24 24 24 24 24 24 24 24 24 24 1000 1100 1000 1200 4774 5074 65 34 6894 6354 5514 4674 5074 5374 6574 5974 4474 67438 350 500 500 500 500 500 1050 2010 2370 1830 990 Ma Jun Jul 790 610 330 1600 1600 900 1100 800 1400 1700 350 1050 1350 2550 1950 450 Se 850 Nov TOTAL COST

SOLUTION B: & E :

TO create Production level schedule

Overtime Total Producti Overtime Inventory Overtime on(in100 cost (in Componentcost (in Salary (in Producti PRODUCTION (in 1000s) on cost 1000s) cost (in 1000s) 1000s) MONTH units) DEMAND (in 1000s) Inventory Workers (in hrs) 0s) 24 24 24 24 24 24 24 24 24 24 24 24 4774 5074 65 34 6894 6354 5514 4674 4764 5224 5964 5524 4024 65468 Jan Feb Mar 1000 1100 1000 1050 2010 2370 1830 990 350 790 610 330 120 120 120 120 120 500 500 500 500 Ma Jun Jul 1600 1600 900 1100 800 1400 1700 900 3840 1150 300 Se 2100 3840 1100 500 Nov TOTAL COST