Skip to content

Latest commit

 

History

History
82 lines (58 loc) · 4.05 KB

README.md

File metadata and controls

82 lines (58 loc) · 4.05 KB
Raw

Warehouse Location Problem

An online retail company in the US is planning to open warehouses in potential locations to optimize their logistics and service delivery. This project aims to solve the warehouse location problem using mathematical modeling and optimization techniques.

Problem Description

The company is considering opening warehouses in the following cities: Chicago, Atlanta, New York, St. Louis, Detroit, Cincinnati, Pittsburgh, Charlotte, and Boston. The goal is to minimize the total weighted distance between demand points and their nearest warehouse while considering budgetary constraints and service level requirements.

Data

Distance Matrix (in miles):

City Chicago Atlanta New York St. Louis Detroit Cincinnati Pittsburgh Charlotte Boston
Chicago 0 720 790 297 283 296 461 769 996
Atlanta 720 0 884 555 722 461 685 245 1099
New York 790 884 0 976 614 667 371 645 219
St. Louis 297 555 976 0 531 359 602 715 1217
Detroit 283 722 614 531 0 263 286 629 721
Cincinnati 296 461 667 359 263 0 288 479 907
Pittsburgh 461 685 371 602 286 288 0 448 589
Charlotte 769 245 645 715 629 479 448 0 867
Boston 996 1099 219 1217 721 907 589 867 0

Demand at each location:

City Demand
Chicago 2,870,000
Atlanta 572,000
New York 8,450,000
St. Louis 350,000
Detroit 901,000
Cincinnati 333,000
Pittsburgh 306,000
Charlotte 723,000
Boston 610,000

Objectives

  1. Minimize Total Weighted Distance: The objective is to minimize the total weighted distance between demand points and their nearest warehouse, with weight being the demand of each location. The company can open only ( p ) warehouses due to budgetary limitations.

  2. Maximize Service Distance: Ensure that no demand location is more than 500 miles away from a warehouse and maximize the total demand that can be covered within a 200-mile distance (high service distance).

Mathematical Model

Variables:

  • ( x_{ij} ): Binary variable indicating whether a warehouse is placed in city ( i ) to serve city ( j ).
  • ( y_i ): Binary variable indicating whether a warehouse is opened in city ( i ).

Parameters:

  • ( d_{ij} ): Distance between city ( i ) and city ( j ).
  • ( w_j ): Demand at city ( j ).
  • ( p ): Number of warehouses to be opened.
  • ( D_{\text{max}} ): Maximum distance a demand point can be from a warehouse.
  • ( D_{\text{service}} ): High service distance.

Objective Function:

  • Minimize total weighted distance: ( \sum_{i} \sum_{j} d_{ij} \cdot w_j \cdot x_{ij} ).

Constraints:

  1. Each demand point must be assigned to exactly one warehouse: ( \sum_{i} x_{ij} = 1 \quad \forall j ).

  2. A warehouse must be open in city ( i ) if it serves any city ( j ): ( x_{ij} \leq y_i \quad \forall i, j ).

  3. The total number of warehouses must be exactly ( p ): ( \sum_{i} y_i = p ).

  4. Maximum distance constraint: ( d_{ij} \cdot x_{ij} \leq D_{\text{max}} \quad \forall i, j ).

  5. High service distance constraint: ( \sum_{i} \sum_{j: d_{ij} \leq D_{\text{service}}} w_j \cdot x_{ij} ).

Files

  • warehouse_location.mod: The OPL model file.
  • warehouse_location.dat: The data file containing distance matrix and demand values.