Question

The Barberton Municipal Division of Road Maintenance is charged with road repair in the city of Barberton and the surrounding area. Cindy Kramer, road maintenance director, must submit a staffing plan for the next year based on a set schedule for repairs and on the city budget. Kramer estimates that the labor hours required for the next four quarters are 6,000, 12,000, 19,000, and 9,000, 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 $18 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 $3,000, and the cost of laying off a worker is $2,000. Subcontracting is not permitted. Find a level staffing 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 and how many undertime hours does it call for? Use a chase strategy that varies the workforce level without using overtime or undertime. What is the total cost of this plan? Propose a plan of your own. Compare your plan with those in part (a) and part (b) and discuss its comparative merits.

Answer 1

Find a level staffing plan that relies just on overtime and the minimum amount of under time possible. Overtime can be used to its limits in any quarter. What is the total cost of the plan and how many under time hours does it call for?

       The peak demand in the third quarter is 19,000. Each employee can work 600 hours per quarter. (500 regular time and 100 on overtime). The level workforce that relies just on overtime, does not allow delays and minimum under time is 19,000/600 = 31.67 or 32 employees.

Regular wages – (6,000 per quarter)(32)(4 quarters) = $768,000.

Over time    -   (3,000 per hr in quarter 3)(18 per hour) =54,000.

Costs of hire – (3,000 per hire)(21 hires) = 63,000.

Total = 885,000.

Thirty two workers can produce (32)(500) = 16,000 hours of regular time in any quarter. However, the 19,000 hours in quarter 3 exceeds the amount by 3,000 hours.

The under time hours can be calculated as 10,000 hours in the first quarter, 32(500) – 6,000 = 10,000 hours. In the second quarter 32(500) – 12,000 = 4,000 hours. In quarter 4, 32(500) – 9,000 = 7,000. The total overall is 21,000 hours.

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

     The chase strategy is:

1^st quarter – demand per hr is 6,000. The workforce is 12 with 1 hire and no layoffs. 2^nd quarter – the demand per hr is 12,000, workforce – 24 with 12 hires and no layoffs. 3^rd quarter - 19,000 demand per hour – work force 38 with 14 hired and no layoffs. 4^th quarter – demand per hour 9,000 – work force 18 with no hires, and 20 layoffs. The total for all 4 quarters is a work force of 92 with 27 hires and 20 layoffs.

Calculations:

Regular wages – (6,000 per quarter)(92) = 552,000.

Hire costs – (3,000 per hire)(27 hires)   =   81,000.

Layoff costs – (2,000 per layoff)(20) = 40,000

Total = 673,000.

Propose a plan of your own. Compare your plan with those in part (a) and part (b) and discuss in comparative merits.

Proposed plan:

This plan consists of a mixed strategy. Although chase strategy was used in the first and second quarter, seven extra workers were hired in the third quarter using 3,500 hours of overtime equivalent to 6.2 workers to fill the gap. The savings in the hiring and layoffs costs has exceeded the extra costs for overtime.

Quarter                        demand per hr           workforce       hires     layoffs      overtime hr

      1                                     6,000                      12                1            0                0

    

      2                                    12,000                     24               12           0                0

      3                                    19,000                   31                 7            0                3,500

      4                                       9,000                   18                 0            13              0

Total                                                                  85                 20           13             3,500

Cost                                                        Calculation                                          Amount

Regular wages                                (6,000 per quarter)(85)                              510,000

Hire costs                                        (3,000 per hire)(20 hires)                            60,000

Layoff costs                                    (2,000 per layoff)(13 layoffs)                     26,000

Overtime                                         (18 per hour)(3,500 hours)                         63,000

                                                      Total = 659,000

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