Decentralized Fuzzy P-hub Centre Problem: Extended Model and Genetic Algorithms

International Journal of Supply and Operations Management IJSOM February 2017, Volume 4, Issue 1, pp. 90-104 ISSN-Print: 2383-1359 ISSN-Online: 2383-2525 www.ijsom.com Decentralized Fuzzy P-hub Centre Problem: Extended Model and Genetic Algorithms Sara Mousavinia a, *, Majid Khalili a, Mohammad Shafiee a a Department of industrial engineering, Islamic Azad University of Karaj, Karaj, Iran Abstract This paper studies the incapacitated P-hub centre problem in a network under decentralized management assuming time as a fuzzy variable. In this network, transport companies act independently, each company makes its route choices according to its own criteria. In this model, time is presented by triangular fuzzy number and used to calculate the fraction of users that probably choose hub routes instead of direct routes. To solve the problem, two genetic algorithms are proposed. The computational results compared with LINGO indicate that the proposed algorithm solves large-scale instances within promising computational time and outperforms LINGO in terms of solution quality. Keywords: Decentralized management; Fuzzy number; Genetic algorithm; P-hub network; Hub location problem. 1. Introduction Hub location problems (HLP) are of great importance in the field of operation management with a wide range of applications and ever-growing body of literature. (See for example Zarrinpour 2011, Alumur 2012, Campbell 2012, Hernandez 2012). Zanjirani Farahani et al. (2013) provided a complete and detailed discussion of the various aspects of the problem and the state of the art of its different formulations and solution methods. Table1. Different types of HLPs (Zanjirani Farahani et al. (2013)) Capacity of hub node Assignment of non-hub Type of the HLP Number of hub node to hub nodes nodes Capacitated (C) Single allocation (SA) Median (M) Single (1) Incapacitated (U) Multiple allocation (MA) Center (T) More than one (P) Covering (V) Set covering (SV) Maximum covering (MV) As it was marked in table.1, the problem we discussed in this paper is based on Incapacitated Multiple allocation P hub centre problem. So, in the rest of this section, the recent studies pertinent to our studied DFUMHLP 1will be reviewed. According to Zanjirani et al. (2013), majority of studies have dealt with incapacitated cases of HLPs. One of the most recent studies in this area has been done by O’Kelly et al. (2014) who formulated a model to analyse the role of fixed costs in the design of optimal transportation hub networks. Campbell et al. (2015) presented a new model for hub location and network design that uses fixed and variable transportation costs on all arcs, fixed costs for hubs, and also allowed direct arcs. 1 Decentralized Fuzzy Incapacitated Multiple Hub Location Problem *Corresponding author email address: 90 Decentralized Fuzzy P-hub Centre Problem ... In real world applications, all the parameters of a network may not be known precisely due to uncontrollable factors. Because due to rapid changes, lack of data, and incomplete and/or noisy factors in the available information, if any decision is made based on the deterministic models, demands may not be reached at the right location, at the right time, and at the best costs (2013b). Yang et al. (2011) studied the p-hub centre problem with discrete random travel time. Qin and Gao (2014) formulated a new incapacitated p-hub location model with flows described by uncertain variables. Hult et al. (2014) proposed a reformulation for the p-hub centre problem when the uncertainty of travel times was considered. In short, these studies point out that if a decision maker ignores the uncertainty, it causes huge regrets in long run (2013a). For many cases, the estimations of probability distributions for decision factors may not be easy due to the lack of data. So this type of imprecise data has not always been well represented by random variable selected from a probability distribution. This kind of data can effectively be presented by fuzzy features (Kaur and Kumar 2011). Yang et al. (2013) presented a new risk aversion p-hub centre problem with fuzzy travel times. Nematian (2016) presented an incapacitated p-hub center problem in case of single allocation and also multiple allocations in which travel times or transportation costs were considered as fuzzy parameters. Both the facility location and network design problems as sub problems of the facility location–network design problem are NP-hard (Ghaderi2013, Rabbani2015). So, UMHLP is known to be NP-hard, with exception of special cases, for example when matrix of flows is sparse (Kratica 2005). Even though integer programming optimization approaches are applied to solve small hub problems, larger instances of HLPs need to be solved by heuristic procedures or meta-heuristic procedures. As a matter of fact, while large-size instances can be dealt with specialized exact methods (e.g., benders decomposition and branch and price methods), development of meta-heuristics has helped many real-world applications, in which optimal/near-optimal solutions can even be obtained in less computational time (Zanjirani et al. 2013). The most related and recent GA solution approaches are summarized in table2. Article Table 2. Genetic algorithms in HLPs Problem Solution algorithm Kratica et al. (2005) Topcuoglu et al. (2005) Eraslan S. (2010) Bashiri et al. (2013) Yang et al. (2013) Rabbani et al. (2015) incapacitated incapacitated incapacitated capacitated no capacities involved incapacitated genetic algorithm- applied caching technique genetic algorithm genetic algorithm genetic algorithm- hybrid approach genetic algorithm- hybrid approach genetic algorithm and simulated annealing According to the literature of HLP solution approaches, we think that UMHLP problem under decentralized management has not yet been solved for large-sized scale problems, but it is a very common case in the analysis of networks of regional or greater scope. Besides, few studies have considered hub location problems with uncertain parameters (Contreras 2011) so; another contribution of this paper is that we considered travel time in the network as a fuzzy parameter in order to study the network in a more real situation. It may contribute to estimate the network time and cost more accurately. The existing model is only applicable to networks by the deterministic factors. In this paper, we are aimed to develop the mathematical formulation of the Vosconcelos’s problem (2011)incapacitated multiple allocation p-hub location problem under decentralized management- with uncertainty in travel time parameter. This parameter is characterized by a triangular fuzzy number while the objective function of this problem minimizes the expected costs. Then we present a novel solution based on a genetic search framework for DFUMHLP. We compared the quality of solutions from our method by comparing the both solutions; by exact time factor and fu (...truncated)