The Barberton Municipal division of Road Maintenance is charged with road repair in the city of Barberton and the surrounding area. Vijay​ Gupta, road maintenance​ director, must submit a staffing plan for the next year based on a set schedule for repairs and on the city budget. Gupta estimates that the labor hours required for the next four quarters are 6,500 ​, 12,500 ​, 19,500 ​, and 10,000 ​, respectively. Each of the 11   workers on the workforce can contribute 500   hours per quarter. Payroll costs are $ 6,000   in wages per worker for regular time worked up to 500   ​hours, with an overtime pay rate of $ 19   for each overtime hour. Overtime is limited to 20   percent of the​ regular-time capacity in any quarter. Although unused overtime capacity has no​ cost, unused regular time is paid at $ 12   per hour. The cost of hiring a worker is $ 3,600 ​, and the cost of laying off a worker is $ 1,000. Subcontracting is not permitted. ​(Hint: When calculating the number of​ workers, make sure to round up to the next whole number before proceeding with any further​ calculations.)   A. Find a level workforce plan that relies just on overtime and the minimum amount of undertime possible. Overtime can be used to its limits in any quarter. What is the total cost of the​ plan? ​   How many undertime hours does it call​ for?___hours   B. Use a chase strategy that varies the workforce level without using overtime or undertime. What is the total cost of this​ plan?   C. Consider the following proposed​ plan, for a different demand​ schedule, that combines the strategy of​ hiring, layoffs, and utilizing overtime. Payroll costs are $6,000 in wages per worker for regular time​ worked, with an overtime pay rate of $19 for each overtime hour. The cost of hiring a worker is $3,600, and the cost of laying off a worker is $1,000.   Quarter Demand ​(hours) Workforce Hires Layoffs Overtime ​(hours) 1 ​6,000 12 1     2 ​12,000 24 12     3 ​19,000 31 7   ​3,500 4 ​9,000 18   13   Total   85 20 13 ​3,500   The total cost for this plan would be?

Practical Management Science
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ISBN:9781337406659
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Chapter12: Queueing Models
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The Barberton Municipal division of Road Maintenance is charged with road repair in the city of Barberton and the surrounding area. Vijay​ Gupta, road maintenance​ director, must submit a staffing plan for the next year based on a set schedule for repairs and on the city budget. Gupta estimates that the labor hours required for the next four quarters are 6,500 ​, 12,500 ​, 19,500 ​, and 10,000 ​, respectively. Each of the 11   workers on the workforce can contribute 500   hours per quarter. Payroll costs are $ 6,000   in wages per worker for regular time worked up to 500   ​hours, with an overtime pay rate of $ 19   for each overtime hour. Overtime is limited to 20   percent of the​ regular-time capacity in any quarter. Although unused overtime capacity has no​ cost, unused regular time is paid at $ 12   per hour. The cost of hiring a worker is $ 3,600 ​, and the cost of laying off a worker is $ 1,000. Subcontracting is not permitted. ​(Hint: When calculating the number of​ workers, make sure to round up to the next whole number before proceeding with any further​ calculations.)

 

A. Find a level workforce plan that relies just on overtime and the minimum amount of undertime possible. Overtime can be used to its limits in any quarter. What is the total cost of the​ plan? ​

 

How many undertime hours does it call​ for?___hours

 

B. Use a chase strategy that varies the workforce level without using overtime or undertime. What is the total cost of this​ plan?

 

C. Consider the following proposed​ plan, for a different demand​ schedule, that combines the strategy of​ hiring, layoffs, and utilizing overtime. Payroll costs are $6,000 in wages per worker for regular time​ worked, with an overtime pay rate of $19 for each overtime hour. The cost of hiring a worker is $3,600, and the cost of laying off a worker is $1,000.

 

Quarter

Demand

​(hours)

Workforce

Hires

Layoffs

Overtime

​(hours)

1

​6,000

12

1

   

2

​12,000

24

12

   

3

​19,000

31

7

 

​3,500

4

​9,000

18

 

13

 

Total

 

85

20

13

​3,500

 

The total cost for this plan would be?

 

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