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Location and Capacity Planning of Facilities with General Service-Time Distributions Using Conic Optimization

Amir Ahmadi-Javid (ahmadi_javid***at***aut.ac.ir)
Oded Berman (Berman***at***rotman.utoronto.ca)
Pooya Hoseinpour (pooya.hoseinpour***at***mcgill.ca)

Abstract: This paper studies a stochastic congested location problem in the network of a service system that consists of facilities to be established in a finite number of candidate locations. Population zones allocated to each open service facility together creates a stream of demand that follows a Poisson process and may cause congestion at the facility. The service time at each facility is stochastic and depends on the service capacity and follows a general distribution that can differ for each facility. The service capacity is selected from a given (bounded or unbounded) interval. The objective of our problem is to optimize a balanced performance measure that compromises between facility-induced and customer-related costs. Service times are represented by a flexible location-scale stochastic model. The problem is formulated using quadratic conic optimization. Valid inequalities and a cut-generation procedure are developed to increase computational efficiency. A comprehensive numerical study is carried out to show the efficiency and effectiveness of the solution procedure. Moreover, our numerical experiments using real data of a preventive healthcare system in Toronto show that the optimal service network configuration is highly sensitive to the service-time distribution. Our method for convexifying the waiting-time formulas of M/G/1 queues is general and extends the existing convexity results in queueing theory such that they can be used in optimization problems where the service rates are continuous.

Keywords: Service system design; Stochastic location models; Congested networks; M\M\1 and M\G\1 queue systems; Location problems with congestion; Integer nonlinear programming; Second-order cone programming (Conic quadratic programming or Mixed 0-1 conic optimization); Mixed-integer convex optimization.

Category 1: Applications -- OR and Management Sciences

Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 3: Applications -- Science and Engineering (Facility Planning and Design )


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Entry Submitted: 08/31/2018
Entry Accepted: 08/31/2018
Entry Last Modified: 08/31/2018

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