Return to Index
Operations Research Models and Methods
Problems Section
Linear Programming Models
- Bus Driver Scheduling

A bus company must provide drivers for buses. The schedule varies from hour to hour because of customer demand as shown in the figure. Time 0 on the figure represents midnight, and times are shown with a 24-hour clock starting at midnight. This is only an example schedule. You are to write a model for a general problem with parameters describing the demand for the each four-hour period.

Driver requirements over a 24-hour period.

There are three classes of drivers: part time drivers who work a four hour shift, full time drivers who work a continuous eight hour shift, and split shift drivers who work four hours, are off four hours, and then return for another four hours of work. Parameters describing the characteristics and availability of the drivers are described below. You are to write your model in terms of these parameters. The parameters take on specific values for a specific instance of the problem.

The split shift wage is more than the full time wage. There is a limited supply of part time drivers. Full and split time drivers are drawn from the same pool of persons. An additional pool of drivers can be obtained to work full or split shifts at a premium wage of 1.25 times the wage of the regular drivers. A driver of any class can work at most one shift per day, although a shift started at the end of the day may continue into the next day.

a. Write the model that determines the number of drivers of each type to hire in each time period in order to satisfy demand. The goal is to minimize total wage cost. Solve the model for the following parameter values.

b. The company is considering raising the wages of full time drivers in order to encourage more people to work in that category. What full-time wage rate that will result in a different solution? Find the answer from the sensitivity analysis.

c. Consider again the base case without the change considered in part b. The company is considering placing an advertisement for more part time drivers. The advertisement costs $100 and is expected to add 10 more part time drivers to the pool. How can you use the sensitivity analysis for your solution to tell if the add should be placed? For the parameters given, is the add a good idea?

Return to Top

tree roots

Operations Research Models and Methods
by Paul A. Jensen
Copyright 2004 - All rights reserved