# Rowntown Cab Company has 70 drivers that it must schedule in three 8-hour shifts. However, the demand

## Question:

Thus, the drivers who start their shift during the period from 4:00 A.M. to 8:00 A.M. average $500 in total fares, and drivers who start at 8:00 A.M. average $420. Drivers who start at noon average $300, and drivers who start at 4:00 P.M. average $270. Drivers who start at the beginning of the 8:00 P.M. to midnight period earn an average of $210 in fares during their 8-hour shift.

To retain customers and acquire new ones, Rowntown must maintain a high customer service level. To do so, it has determined the minimum number of drivers it needs working during every 4-hour time segment-10 from midnight to 4:00 A.M., 12 from 4:00 to 8:00 A.M., 20 from 8:00 A.M. to noon, 25 from noon to 4:00 P.M., 32 from 4:00 to 8:00 P.M., and 18 from 8:00 P.M. to midnight.

a. Formulate and solve an integer programming model to help Rowntown Cab schedule its drivers.

b. If Rowntown has a maximum of only 15 drivers who will work the late shift from midnight to 8:00 A.M., reformulate the model to reflect this complication and solve it.

c. All the drivers like to work the day shift from 8:00 A.M. to 4:00 P.M., so the company has decided to limit the number of drivers who work this 8-hour shift to 20. Reformulate the model in (b) to reflect this restriction and solve it.

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