A Continuum Approximation Approach to Competitive Facility Location Design under Facility Disruption Risks

摘要

This paper presents game-theoretical models based on a continuous approximation(CA) scheme to optimize service facility location design under spatial competition andfacility disruption risks. The share of customer demand in a market highly dependson the functionality of service facilities and the presence of nearby competitors, as cus29tomers normally seek the nearest functioning facility for service. Our game-theoreticalmodels incorporate these complicating factors into an integrated framework, and usecontinuous and dierentiable density functions to represent discrete location decisions.We rst analyze the existence of Nash equilibria in a symmetric two-company compe33tition. Then we build a leader-follower Stackelberg competition model to derive theoptimal facility location design when one of the companies have rst-move advantageover its competitor. Both models are solved eciently, and closed-form analytical solu36tions can be obtained for special case. Numerical experiments (with hypothetical andempirical data) are conducted to show the impacts of competition, facility disruptionrisks and transportation cost metrics on the optimal design. Interesting properties ofthe models cast managerial insights to real-world problems.