Stackelberg Dynamic Location Planning under Cumulative Demand

TL;DR

This paper introduces a novel bilevel mixed-integer programming approach to competitive facility location with cumulative demand, highlighting the importance of considering market competition and demand dynamics for optimal planning.

Contribution

It formulates and analyzes a new competitive location model with cumulative demand, proving its computational complexity and developing efficient solution algorithms.

Findings

Monopolistic assumptions can lead to 50% profit loss.

Cooperation yields 6% higher joint profit.

Proposed algorithms outperform general-purpose solvers.

Abstract

Dynamic facility location problems predominantly suppose a monopoly over the service or product provided. Nonetheless, this premise can be a severe oversimplification in the presence of market competitors, as customers may prefer facilities installed by one of them. The monopolistic assumption can particularly worsen planning performance when demand depends on prior location decisions of the market participants, namely, when unmet demand from one period carries over to the next. Such a demand behaviour creates an intrinsic relationship between customer demand and location decisions of all market participants, and requires the decision-maker to anticipate the competitor's response. This work studies a novel competitive facility location problem that combines cumulative demand and market competition to devise high-quality solutions. We propose bilevel mixed-integer programming formulations for two variants of our problem, prove that the optimistic variant is $\Sigma^{p}_{2}$-hard, and develop branch-and-cut algorithms with tightened value-function cuts that significantly outperform general-purpose bilevel solvers. Our results quantify the severe cost of planning under a monopolistic assumption (profit drops by half on average) and the gains from cooperation over competition (6% more joint profit), while drawing managerial guidelines on how instance attributes and duopolistic modelling choices shape robust location schedules.