Optimization: Capacitated Facility Location Problem in Python

Find the optimal number and location of warehouses to reduce costs and meet demand

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Table of contents

1. Introduction
2. Problem statement
3. Implementation
   3.1. The dataset
   3.2. Customers, warehouses and demand
   3.3. Supply and fixed costs
   3.4. Transportation costs
   3.5. Optimization
4. Explore the results
5. Conclusions

1. Introduction

Facility Location Problems (FLPs) are classical optimization tasks. They aim at determining the best among potential sites for warehouses or factories.

Warehouses may or may not have a limited capacity. This distinguishes the capacitated (CFLP) from the uncapacitated (UFLP) variants of the problem.

The business goal to find the set of warehouse locations that minimize the costs. The original problem definition by Balinski (1965) minimizes the sum of two (annual) cost voices:

• Transportation costs
• Warehouse fixed costs

Transportation costs account for the expenses generated by reaching customers from the warehouse location. The warehouse fixed cost…