Question

Tarheel Limousine has a fleet of cars that it operates in the RDU area. It hires drivers for its cars on a monthly salary. The CEO wishes to determine how many drivers to employ in the next 5 months. Based on his forecast, the CEO believes he would need at least the following number of drivers:

February: 45 Drivers

March: 65 Drivers

April: 70 Drivers

May: 50 Drivers

June: 55 Drivers

At the beginning of each month, the company must decide how many drivers should be fired or hired. Tarheel Limousine incurs administrative costs of $500 to hire and train a driver and $300 to fire a driver. A driver’s salary is $3000 per month. At the beginn ing of February, Tarheel Limousine has 50 drivers.

A driver hired at the beginning of a month may be used to meet the current month’s requirements and is paid full salary for the current month. It is feasible (but expensive) to have too many drivers

a) Formulate an LP to minimize Tarheel Limousine’s labor costs over the next five months. (15pts)

b) Solve the LP in Excel and give the optimal solution. Explain in plain English what the CEO needs to do. (7pts)

c) A labor organization believes that drivers who are fired need to be paid an extra $300 as compensation, i.e., the cost of firing increases from $300 to $600, of which $300 is paid to the fired worker. Now solve the LP in Excel assuming that the company pays each fired worker $300. How does the optimal solution you found in the previous part change? Will the total labor cost increase under the labor organization’s plan? Will the total compensation paid to the drivers increase under the labor organization’s plan? Explain (5pts)

Answer 1

a) Formulate LP as below:

Let Hi, Fi and Wi be the number of drivers Hired (Hi), Fired (Fi) and net available (Wi) (after hiring and firing) at the beginning of month i

Minimize 500H1+500H2+500H3+500H4+500H5+300F1+300F2+300F3+300F4+300F5+3000W1+3000W2+3000W3+3000W4+3000W5

s.t.

W1-H1+F1 = 50

W2-H2+F2-W1 = 0

W3-H3+F3-W2 = 0

W4-H4+F4-W3 = 0

W5-H5+F5-W4 = 0

W1 >= 45

W2 >= 65

W3 >= 70

W4 >= 50

W5 >= 55

Hi, Fi, Wi >= 0

b) Solution using Excel Solver is following:

EXCEL FORMULAS:

The CEO needs to Fire 5 and 20 drivers at the beginning of Feb and May respectively,

and, he needs to Hire 20, 5 and 5 drivers at the beginning of March, April and June respectively.

Total cost of this plan = $ 877,500

c) The solution based on increased cost of firing is following:

The optimal solution does not change.

Total labor cost increases because of the increased firing cost to $ 885,000

Yes, the total compensation paid to the drivers increase under the labor organization's plan.