# Solving multi-resource allocation and location problems in disaster management through linear programming

## TL;DR

This paper introduces a linear programming approach using the simplex method to efficiently solve large-scale multi-resource allocation and location problems in disaster management, bypassing the need for complex integer programming solvers.

## Contribution

It demonstrates that many disaster management problems can be exactly solved with linear programming and extends linear programming techniques to cluster analysis via k-medoids.

## Key findings

- Large-scale disaster management problems can be solved with linear programming.
- The simplex method can be used for clustering without integer solvers.
- Numerical experiments validate the approach.

## Abstract

In this paper we propose a new efficient linear programming based approach for multi-resource allocation and location problems in disaster management. Such problems require an integer solution and therefore, in most cases, the computations rely on integer and mixed-integer linear programming solvers. In general, these solvers can not handle large scaled problem. In this paper we demonstrate that there exists a large class of disaster management problems whose exact solutions can be obtained by applying the simplex method (linear programming). The results of numerical experiments are provided. Another important contribution of this paper is related to general cluster analysis and allocation. Namely, we demonstrate that the classical $k$-medoid clustering method can be implemented using linear programming techniques (simplex method) without relying on integer solvers.