Solving a new bi-objective hierarchical hub location problem with an M∕M∕c queuing framework

Abstract This paper presents a bi-objective hierarchical hub location problem with hub facilities as servicing centers. The objectives are to minimize the total cost (i.e., fixed cost of establishing hub facilities and transportation cost) and the maximum route length, simultaneously. Hub facilities are categorized as central and local ones. The queuing frameworks for these types of facilities are considered as M ∕ M ∕ c and M ∕ M ∕ 1 , respectively. Moreover, density functions for the traveling time and number of entities are assumed to be Exponential and Poisson functions. The presented mathematical model is solved by a new game theory variable neighborhood fuzzy invasive weed optimization (GVIWO) as introduced in this paper. To evaluate the efficiency of this proposed algorithm, some experiments are conducted and the related results are compared with the non-dominated sorting genetic algorithm (NSGA-II) and hybrid simulated annealing (HSA) algorithm with respect to some comparison metrics. The results show that the proposed GVIWO algorithm outperforms the NSGA-II and HSA. Finally, the conclusion is provided.

[1]  James F. Campbell,et al.  Integer programming formulations of discrete hub location problems , 1994 .

[2]  James F. Campbell,et al.  Location and allocation for distribution systems with transshipments and transportion economies of scale , 1993, Ann. Oper. Res..

[3]  Reza Tavakkoli-Moghaddam,et al.  Design of a fuzzy bi-objective reliable p-hub center problem , 2016, J. Intell. Fuzzy Syst..

[4]  Vladimir Marianov,et al.  Location models for airline hubs behaving as M/D/c queues , 2003, Comput. Oper. Res..

[5]  Fariborz Jolai,et al.  A new stochastic approach for a reliable p-hub covering location problem , 2015, Comput. Ind. Eng..

[6]  Jiuping Xu,et al.  Approximation based fuzzy multi-objective models with expected objectives and chance constraints: Application to earth-rock work allocation , 2013, Inf. Sci..

[7]  Soheil Davari,et al.  AN EMPIRICAL COMPARISON OF SIMULATED ANNEALING AND ITERATED LOCAL SEARCH FOR THE HIERARCHICAL SINGLE ALLOCATION HUB MEDIAN LOCATION PROBLEM , 2015 .

[8]  Reza Tavakkoli-Moghaddam,et al.  Design of a reliable logistics network with hub disruption under uncertainty , 2016 .

[9]  Cheng-Chang Lin,et al.  The integrated secondary route network design model in the hierarchical hub-and-spoke network for dual express services , 2010 .

[10]  Rafay Ishfaq,et al.  Design of intermodal logistics networks with hub delays , 2012, Eur. J. Oper. Res..

[11]  M. F. Zarandi,et al.  The single-allocation hierarchical hub median location problem with fuzzy demands , 2012 .

[12]  Reza Tavakkoli-Moghaddam,et al.  Solving a Redundancy Allocation Problem by a Hybrid Multi-objective Imperialist Competitive Algorithm , 2013 .

[13]  Reza Tavakkoli-Moghaddam,et al.  An interactive possibilistic programming approach for a multi-objective hub location problem: Economic and environmental design , 2017, Appl. Soft Comput..

[14]  Hande Yaman,et al.  The hierarchical hub median problem with single assignment , 2009 .

[15]  Samir Elhedhli,et al.  Hub-and-spoke network design with congestion , 2005, Comput. Oper. Res..

[16]  Reza Tavakkoli-Moghaddam,et al.  Mathematical modeling for a p-mobile hub location problem in a dynamic environment by a genetic algorithm , 2018 .

[17]  Mehrdad Mohammadi,et al.  Multi-objective hub network design under uncertainty considering congestion: An M/M/c/K queue system , 2016 .

[18]  Amir Azaron,et al.  Robust and fuzzy goal programming optimization approaches for a novel multi-objective hub location-allocation problem: A supply chain overview , 2015, Appl. Soft Comput..

[19]  Reza Tavakkoli-Moghaddam,et al.  A game-based meta-heuristic for a fuzzy bi-objective reliable hub location problem , 2016, Eng. Appl. Artif. Intell..

[20]  Oded Berman,et al.  Flow-Interception Problems , 1995 .

[21]  Sibel A. Alumur,et al.  Hierarchical multimodal hub location problem with time-definite deliveries , 2012 .

[22]  Reza Tavakkoli-Moghaddam,et al.  Optimization of a multi-modal tree hub location network with transportation energy consumption: A fuzzy approach , 2016, J. Intell. Fuzzy Syst..

[23]  Fariborz Jolai,et al.  An M/M/c queue model for hub covering location problem , 2011, Math. Comput. Model..

[24]  Sheu Hua Chen,et al.  The hierarchical network design problem for time-definite express common carriers , 2004 .

[25]  Sheu Hua Chen,et al.  A Heuristic Algorithm for Hierarchical Hub-and-spoke Network of Time-definite Common Carrier Operation Planning Problem , 2010 .

[26]  Vladimir Marianov,et al.  Probabilistic, Maximal Covering Location—Allocation Models forCongested Systems , 1998 .

[27]  Yue‐Hong Chou,et al.  The hierarchical-hub model for airline networks , 1990 .

[28]  Vladimir Marianov,et al.  Location–Allocation of Multiple-Server Service Centers with Constrained Queues or Waiting Times , 2002, Ann. Oper. Res..

[29]  Reza Tavakkoli-Moghaddam,et al.  A self-adaptive evolutionary algorithm for a fuzzy multi-objective hub location problem: An integration of responsiveness and social responsibility , 2017, Eng. Appl. Artif. Intell..

[30]  Vladimir Marianov,et al.  PROBABILISTIC MAXIMAL COVERING LOCATION-ALLOCATION FOR CONGESTED SYSTEMS , 1998 .

[31]  María Jesús Álvarez,et al.  Hub Location Under Capacity Constraints , 2007 .

[32]  Abbas Ahmadi,et al.  A multi-objective model for facility location-allocation problem with immobile servers within queuing framework , 2014, Comput. Ind. Eng..

[33]  R. Tavakkoli-Moghaddam,et al.  A new multi-mode and multi-product hub covering problem: A priority M/M/c queue approach , 2015 .

[34]  M. O'Kelly,et al.  A quadratic integer program for the location of interacting hub facilities , 1987 .