Car Rental 1

Objective

The objective is to maximize the following function:

\begin{align*} \Variable{Profit} & = \sum _{\substack{i \in \text {DEPOTS},\\ j \in \text {DEPOTS},\\ \text {day} \in \text {DAYS},\\ \text {length} \in \text {LENGTHS}}} (\Argument{rental\_ price[i,j,day,length]} - \Argument{cost[length]}) \cdot \Variable{NumCarsRented[i,j,day,length]}\\ & + \sum _{\substack{i \in \text {DEPOTS},\\ \text {day} \in \text {DAYS}}} \Argument{damage\_ prob} \cdot \Argument{damage\_ charge} \cdot \Variable{NumCarsRented\_ i\_ day[i,day]}\\ & - \sum _{\substack{i \in \text {DEPOTS},\\ j \in \text {DEPOTS} \setminus \{ i\} ,\\ \text {day} \in \text {DAYS}}} \Argument{transfer\_ cost[i,j]} \cdot \Variable{NumCarsTransferred[i,j,day]}\\ & - \Argument{opportunity\_ cost\_ per\_ week} \cdot \Variable{NumCars} \end{align*}