Heterogeneous Multi-Resource Allocation with Subset Demand Requests

TL;DR

This paper addresses the complex problem of allocating multiple heterogeneous resources over space and time to meet subset demands, proposing models, algorithms, and computational analysis to optimize reward maximization.

Contribution

It introduces a formal integer programming model for multi-resource allocation with subset demands, analyzes its complexity, and develops approximation algorithms including travel cost considerations.

Findings

The problem is NP-hard.

Approximation algorithms achieve near-optimal solutions.

Travel cost extension improves practical applicability.

Abstract

We consider the problem of allocating multiple heterogeneous resources geographically and over time to meet demands that require some subset of the available resource types simultaneously at a specified time, location, and duration. The objective is to maximize the total reward accrued from meeting (a subset of) demands. We model this problem as an integer program, show that it is NP-hard, and analyze the complexity of various special cases. We introduce approximation algorithms and an extension to our problem that considers travel costs. Finally, we test the performance of the integer programming model in an extensive computational study.