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

Objective

The objective is to minimize the following function:

\[ \Variable{TotalCost} = \Variable{FixedCost} + \Variable{VariableCost} \]

where

\begin{align*} \Variable{FixedCost} & = \sum _{\text {depot} \in \mr{DEPOTS}} \left(\Argument{open\_ cost[depot]} \cdot \Variable{IsOpen[depot]} - \Argument{close\_ savings[depot]} \cdot (1 - \Variable{IsOpen[depot]})\right) \\ & + \sum _{\mr{depot} \in \mr{EXPAND\_ DEPOTS}} \Argument{expand\_ cost[depot]} \cdot \Variable{Expand[depot]} \end{align*}

and

\[ \Variable{VariableCost} = \sum _{(i,j) \in \text {ARCS}} \Argument{cost[i,j]} \cdot \Variable{Flow[i,j]} \]