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?