Efficient solution of a class of location–allocation problems with stochastic demand and congestion

Abstract

We consider a class of location-allocation problems with immobile servers, stochastic demand and congestion that arises in several planning contexts: location of emergency medical clinics; preventive healthcare centers; refuse collection and disposal centers; stores and service centers; bank branches and automated teller machines; internet mirror sites; and distribution centers in supply chains. The problem seeks to simultaneously locate service facilities, equip them with appropriate capacities, and allocate customer demand to these facilities such that the total cost, which consists of the fixed cost of opening facilities with sufficient capacities, the access cost of users' travel to facilities, and the queuing delay cost, is minimized. Under Poisson user demand arrivals and general service time distributions, the problem is set up as a network of independent M/G/1 queues, whose locations, capacities and service zones need to be determined. The resulting mathematical model is a non-linear integer program. Using simple transformation and piecewise linear approximation, the model is linearized and solved to-optimality using a constraint generation method. Computational results are presented for instances up to 400 users, 25 potential service facilities, and 5 capacity levels with different coefficient of variation of service times and average queueing delay costs per customer. The results indicate that the proposed solution method is efficient in solving a wide range of problem instances.

A multi-service Healthcare Network Design with Patients' Choice to Exchange between Services

“…The input parameters are produced randomly in the following intervals in the ten test problems: the travel time between demand areas and health centers in the interval [0.25 -1.25] (hour), the travel time between health centers in the interval [0.2-1] (hour), the demand rates for four services per hour in the intervals [15][16][17][18][19][20][21][22][23][24][25], [10 -20], [5][6][7][8][9][10] and [3][4][5][6][7][8][9][10] respectively. The average service rate for four services is 6, 5, 5 and 4 patients per hour, standard waiting time in the system is 25, 30, 35 and 35 minutes and the minimum arrival rate required to provide services is 4, 3, 3 and 1 patient(s) per hour respectively.…”

“…The high congestion of these centers adversely affects clients' satisfaction, and in emergency cases, it may lead to irreparable damages. To guarantee service quality, we usually deal with one of these factors: (1) average queue length, (2) average waiting time in queues, or (3) the probability of receiving service in a standard time [4], [5]. These factors can be a part of constrains that are called "constraint-oriented" approaches [6], [7].…”

Stochastic Location Models with Congestion

“…Balanced-objective models are listed in Table 17.3 and include the following references: Aboolian et al (2008), Abouee-Mehrizi et al (2011), Castillo et al (2009), Elhedhli (2006, Kim (2013), Marianov and Rios (2000), Pasandideh and Chambaria (2010), Rabieyan and Seifbarghy (2010), Vidyarthi and Jayaswal (2013), and Wang et al (2004).…”

A capacitated location-allocation problem with stochastic demands using sub-sources: An empirical study

“…Constraints (15) show the maximum number of capacities each sub-source can provide to other facilities. The binary restriction imposed by expressions (1) is replaced by (16), insuring that when a facility is to provide its capacities to other facilities, i gets to be 1, and it gets to be 0, otherwise. To ensure that when a sub-source is to provide its capacities to other facilities, ω i is set to be 1, and it gets to be 0, otherwise.…”

“…Authors proposed some heuristics to solve the problem. Vidyarthi and Jayaswal [16] proposed a non-linear integer programming model to solve an LA problem with immobile servers, stochastic demands and congestions. Authors considered that customer demands occur continuously over time according to an independent Poisson process and service times at facilities follow an exponential distribution.…”