The Warehouse Location Problem

Prerequisites

• Please look at Getting Started first for the most basic functions and the setup of OPTANO.Modeling

The mathematical Model

Sets: \begin{array}{l} C = \text{Set of Customers}\newline N = \text{Set of depots} \end{array}

Parameters: $$f_{j} = \text{fixed cost for opening depot }j$$ $$c_{ij} = \text{transportation cost from depot }j\text{ to customer }i$$ $$d_{j} = \text{demand of customer }j$$ $$M = \text{big M is a constant}$$

Variables: $$y_{j} = \begin{cases} 1, \text{ if depot }j\text{ is used}\newline 0, \text{ else} \end{cases}$$

$$x_{ij} \in \mathbb{R}^+ = \text{ amount of supply customer }i\in C\text{ receives from depot }j\in N$$

Objective: $$min \sum\limits_{i\in C} \sum\limits_{j\in N} c_{ij} x_{ij} + \sum\limits_{j\in N} f_{j} y_{j}$$

Restrictions: \begin{array}{l} \sum\limits_{j\in N} x_{ij} = d_{j} & \qquad \forall i \in C & \text{(Satisfy the demands)}\newline \sum\limits_{i\in C} x_{ij} \le M y_{j} & \qquad \forall j\in N & \text{(Mapping of customers and depots)} \end{array}

The Warehouse Location Problem

• Step 1: Create Business objects for your Model
• Step 2: Create your Model Class
• Step 3: Retrieve the Solution of your Model