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.

buses 4 4 4 4 8 8 8 8 10 10 10 10  7  7  7  7 12 12 12 12  4  4  4  4
time  1 2 3 4 5 6 7 8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
 
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.

parameters:

d-t: demand for drivers during the interval starting at time t.
w-p: hourly wages for part-timr drivers.
w-f: hourly wages for full-time drivers.
w-s: hourly wages for split time drivers.
u-p: number of part time drivers available.
u-number of full and split time drivers available.
a-number of full and split time drivers willing to work at the premium wage.