Depot Location (Distribution 2): Where Should New Depots Be Built

Constraints

The following additional and modified constraints are used in this example:

  • bounds on variables

  • $\displaystyle { \sum _{i \in \mr{DEPOTS}} \Variable{IsOpen[i]} \le \Argument{max\_ num\_ depots} }$

  • for $i \in \mr{DEPOTS}$,

    \[ \sum _{(i,j) \in \text {ARCS}} \Variable{Flow[i,j]} \le \Argument{throughput[i]} \cdot \Variable{IsOpen[i]} + \left(\text {if } i \in \mr{EXPAND\_ DEPOTS}\text {, then }\Argument{expand\_ throughput[i]} \cdot \Variable{Expand[i]}\right) \]

  • for $i \in \mr{EXPAND\_ DEPOTS}$,

    \[ \Variable{Expand[i]} \le \Variable{IsOpen[i]} \]