Prescriptive Analytics Integer Programming

$2.$ A ride$-$hailing service in the DFW metroplex is able to schedule drivers in two$-$hour blocks based on rider demand. In scheduling for this company, drivers are not full$-$time employees, and based on demand, slots are set up for which any authorized$/$approved driver can sign up for work. Drivers can sign up for multiple two$-$hour slots if desired; however, they must be able to complete the full two hours of driving.

The operations manager wants to plan slots for drivers at the DFW airport for a particular day in April $2023.$ Based on past experience, the company anticipates $0\mathrm{.}5$ ride hails per aircraft that lands in a given hour. Aircraft arrivals by hour are provided in Tables $5-6.$ In reading the table, $13$ aircraft landed between $12$:$00$ AM and $12$:$59$ AM$.$

$2$a$.$ Develop a model and program it$,$ delivering the operations manager a plan that informs them about the minimum number of drivers required per hiring hour. Start times for blocks of slots cover $2$ hours and begin at $12$ AM$,2$ AM$,4$ AM$,$ etc. In total, you are delivering $12$ values that define the number of recommended drivers in each start time block.

$2$b$.$ Revise the model allowing start times to occur every hour. Under this configuration, there will potentially be $24$ start times. Minimize the number of slots.

$2$c: Revise problem $2$b$.$ so that the objective minimizes cost. Pay is based on demand with higher traffic hours receiving higher pay. As pay, drivers operating from $9$ AM through $7$ PM are paid, on average, $$19\mathrm{.}36$ per hour. Drivers working from $7$ PM until $12$ AM are paid $$16\mathrm{.}76$ per hour, while those from $12$ AM to $9$ AM are paid, on average, $$15\mathrm{.}21.$

Table $5-6.$ DFW Average Daily Hourly Arrival Counts April $2023$