The Outcome Range Problem in Interval Linear Programming

TL;DR

This paper investigates the outcome range problem in interval linear programming, focusing on uncertainty in right-hand side data, and proposes approximation algorithms with practical applications in healthcare decision making.

Contribution

It defines the outcome range problem for interval LPs, analyzes its computational complexity, and develops two approximation methods for solving it.

Findings

The problem is computationally hard to solve exactly.

The proposed algorithms perform well on random instances.

Application to healthcare demonstrates practical relevance.

Abstract

Quantifying extra functions, herein referred to as outcome functions, over optimal solutions of an optimization problem can provide decision makers with additional information on a system. This bears more importance when the optimization problem is subject to uncertainty in input parameters. In this paper, we consider linear programming problems in which input parameters are described by real-valued intervals, and we address the outcome range problem which is the problem of finding the range of an outcome function over all possible optimal solutions of a linear program with interval data. We give a general definition of the problem and then focus on a special class of it where uncertainty occurs only in the right-hand side of the underlying linear program. We show that our problem is computationally hard to solve and also study some of its theoretical properties. We then develop two approximation methods to solve it: a local search algorithm and a super-set based method. We test the methods on a set of randomly generated instances. We also provide a real case study on healthcare access measurement to show the relevance of our problem for reliable decision making.