Polyhedral Analysis of a Polytope from a Service Center Location Problem with a Type of Decision-Dependent Customer Demand

TL;DR

This paper investigates the polyhedral structure of a polytope arising from a service center location problem with location-dependent demand, introducing valid inequalities that capture demand variations.

Contribution

It provides a novel polyhedral analysis of the intersection polytope considering decision-dependent demand, with new facet-defining inequalities.

Findings

Identifies a new polyhedral structure for the problem

Develops valid inequalities reflecting demand changes

Enhances understanding of demand fulfillment in location problems

Abstract

The polytope from a service center location problem with a special location-dependent demand has been investigated in this paper. The location-dependent demand is defined based on a maximum-attraction-principle assumption. Along this direction, the intersection polytope of the capacity constraints and demand constraints yields a novel polyhedral structure. The structure is investigated in this paper via a family of valid and facet-defining inequalities that can reflect the change of demand fulfillment in a neighborhood.