Solution skycell amajor european cell phone manufacturer making PDF

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ProblemSkycell, 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 Table 8-9.Manufacturing is primarily an assem...

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Problem 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 Table 8-9. 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 cell phone 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, 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. Reconsider parts (a) and (b) if Skycell starts with only 1,200 employees. Reconsider parts (a) and (b) if Skycell starts with 1,300 employees. What happens to the value of additional overtime as the workforce size decreases?

d. Consider part (a) for the case in which Skycell aims for a level production schedule such that the quantity produced each month does not exceed the average demand over the next 12 months (1,241,667) by 50,000 units. Thus, monthly production including overtime should be no more than 1,291,667. What would be the cost of this level production schedule? What is the value of overtime flexibility?

Step-by-step solution 1. Step 1 of 12 The forecast of monthly demand for cell phones is given below:

2. Step 2 of 12 a. The plant operates for 20 days a month, for 8 hours each day. The capacity of the production operation is determined primarily by the number of people on production line. Further, no employee can work for more than 20 hours of overtime per month. The various costs are shown in the table below:

The total cost incurred during the planning horizon is determined as

…… (1) Here,

is the workforce size in a particular month,

is the number of

overtime labor hours, is the inventory at the end of the month, and is the number of units produced in each month. SC’s objective is to minimize its total cost. These costs are evaluated as follows: • With regular-time wage of €3,200 and size of the workforce, the regular-time labour cost over 12 month planning horizon is

• With overtime wage of €30 per units per month and hours of overtime, the overtime cost over 12 month planning horizon is

• With inventory holding cost of €3 per unit and size of inventory (thousands of units) at the end of each month, the cost of inventory over 12 month planning horizon is

• With component cost of €20 per unit and number of units ( in thousands) produced in a month, the cost of components over 12 month planning horizon is

Constraints: • The workforce constraint is given as

…… (2) The current size of the workforce at SC is 1,250 workers. Thus, the workforce constraint is

• The capacity is determined by the number of people on production line current. As each worker produces 960 units per month on regular time (6 units per hour) and one unit for every 0.167 hour of overtime, the capacity constraint is …… (3) • The inventory balance constraint is given as

…… (4) The starting inventory at SC is 50,000 units. It wants to maintain the same level at the end of the year. Thus, the inventory balance constraint is

• Since no employee can work for more than 20 hours of overtime per month, the overtime limit constraint is …… (5) The decision variables and the constraints for the 12 months planning horizon are listed in the excel sheet below.

The sheet formulated is as follows:

3. Step 3 of 12

To find optimum production level and cost, select the “Data” tab and click “Solver” in the “Analysis” grouping. Enter the following details:

The final production plan is as follows:

4. Step 4 of 12

The optimal solution is shown above. Thus, the annual total cost of the schedule is

5. Step 5 of 12 b. An increase of allowed overtime In the previous sheet, change the formula in cell O5 to and copy it through cell O16. Now, run the solver. The results obtained are

.

Worksheet-2

The optimal solution is shown above. Thus, the annual total cost of the schedule is

.

6. Step 6 of 12 Increasing the allowed overtime per employee per month from 20 to 40 hours reduces the total cost. Thus, the company would gain by doing so.

7. Step 7 of 12 c. A decrease in workforce from 1,250 to 1,200 In Worksheet-1, change the workforce in cell D4 to 1,200. Now, run the solver. The results obtained are Worksheet-3

The optimal solution is shown above. Thus, the annual total cost of the schedule is Increased overtime with reduced workforce In Worksheet-3, change the formula in the cell O5 to and copy it through cell O16. Now, run the solver. The results obtained are Worksheet-4

8. Step 8 of 12

.

The optimal solution is shown above. Thus, the annual total cost of the schedule is

.

Increasing the allowed overtime per employee per month from 20 to 40 hours with reduced workforce reduces the total cost. Thus, the company would gain by doing so. An increase in workforce from 1,250 to 1,300 In Worksheet-1, change the workforce in cell D4 to 1,300. Now, run the solver. The results obtained are Worksheet-5

9. Step 9 of 12

The optimal solution is shown above. Thus, the annual total cost of the schedule is Increased overtime with increased workforce In Worksheet-5, change the formula in the cell O5 to and copy it through cell O16. Now, run the solver. The results obtained are Worksheet-6

.

10.

Step 10 of 12

The optimal solution is shown above. Thus, the annual total cost of the schedule is

.

Increasing the allowed overtime per employee per month from 20 to 40 hours with increased workforce reduces the total cost. Thus, the company would gain by doing so. (d) Production constraint Production in any month should not exceed the average demand by 50,000. The average demand is 1,241,667. Thus, the production should not exceed 1,291,667 units

. That is,

In worksheet-1, add the following production constraint

Now, run the solver. The results obtained are Worksheet-7

11.

Step 11 of 12

The optimal solution is shown above. Thus, the annual total cost of the schedule is Increased overtime with production constraint In Worksheet-7, change the formula in the cell O5 to and copy it through cell O16. Now, run the solver. The results obtained are Worksheet-8

.

12.

Step 12 of 12

The optimal solution is shown above. Thus, the annual total cost of the schedule is

.

Increasing the allowed overtime per employee per month from 20 to 40 hours with production constraint increases the cost. Thus, the value of additional overtime declines....