Abstract
Today, many transportation systems use hub-and-spoke structures to transfer flow from origin to destination. In such systems, making the right and timely decisions about facilities during the planning horizon is crucial for Decision-Maker (DM); because the parameters influencing decision-making change over the planning horizon, and the initial design of the transportation network may not be desirable for the future. In this paper, we present a novel mathematical programming model for designing a multi-period hub network in a continuous-time planning horizon, considering linear time-dependent demand. The proposed model is a non-linear programming model in which sustainability aspects are addressed through the following objectives: economic (minimizing network costs), environmental (minimizing emissions), and social (maximizing fixed and variable job opportunities). After linearizing the model, using the aggregation function of the Torabi–Hassini (TH) method, the model becomes a parametric single-objective model, and some valid inequalities are introduced. To solve the single-objective model, an accelerated Benders decomposition algorithm and a rolling horizon heuristic algorithm are proposed. The proposed heuristic method can solve problems with twenty-five nodes and six time periods on the CAB dataset. Pareto solutions provide optimal decisions about facilities location, adjusting the operational capacity of facilities (through modules), and routing flows for DM. Also, the best time to implement decisions and the satisfaction degree of sustainability objectives are determined for each solution. We also perform sensitivity analysis on important parameters. The results show that the cost of designing a network with economic and social objectives is more than the cost of designing a network with economic and environmental objectives. Also, by increasing the module capacity after a threshold value, the network costs remain constant.
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References
Alumur S, Kara BY (2008) Network hub location problems: the state of the art. Eur J Oper Res 190:1–21
Alumur SA, Yaman H, Kara BY (2012) Hierarchical multimodal hub location problem with time-definite deliveries. Transp Res Part E Logist Transp Rev 48:1107–1120
Alumur SA, Nickel S, Saldanha-da-Gama F, Seçerdin Y (2016) Multi-period hub network design problems with modular capacities. Ann Oper Res 246:289–312
Amaldi E (1994) From finding maximum feasible subsystems of linear systems to feedforward neural network design. EPFL, Lausanne. https://doi.org/10.5075/epfl-thesis-1282
Aykin T (1994) Lagrangian relaxation based approaches to capacitated hub-and-spoke network design problem. Eur J Oper Res 79:501–523
Aykin T (1995) The hub location and routing problem. Eur J Oper Res 83:200–219
Bagherinejad J, Bashiri M, Abedpour Z (2020) Dynamic single allocation hub location problem considering life cycle and reconstruction hubs. Prod Oper Manag 11:71–87
Balasubramanian J, Grossmann IE (2004) Approximation to multistage stochastic optimization in multiperiod batch plant scheduling under demand uncertainty. Ind Eng Chem Res 43:3695–3713
Barth M, Boriboonsomsin K (2009) Energy and emissions impacts of a freeway-based dynamic eco-driving system. Transp Res Part D Transp Environ 14:400–410
Barth M, Younglove T, Scora G (2005) Development of a heavy-duty diesel modal emissions and fuel consumption model. California Partners for Advanced Transportation Technology, UC Berkeley. Retrieved from https://escholarship.org/uc/item/67f0v3zf
Bashiri M, Rezanezhad M, Tavakkoli-Moghaddam R, Hasanzadeh H (2018) Mathematical modeling for a p-mobile hub location problem in a dynamic environment by a genetic algorithm. Appl Math Model 54:151–169
Beasley JE (1990) OR-library: hub location. http://people.brunel.ac.uk/~mastjjb/jeb/info.html. Accessed 1 May 2015
Bektaş T, Laporte G (2011) The pollution-routing problem. Transp Res Part B Methodol 45:1232–1250
Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numer Math 4:238–252
Campbell JF (1990) Locating transportation terminals to serve an expanding demand. Transp Res Part B Methodol 24:173–192
Campbell JF (1994) Integer programming formulations of discrete hub location problems. Eur J Oper Res 72:387–405
Campbell JF (1996) Hub location and the p-hub median problem. Oper Res 44:923–935
Campbell JF, O’Kelly ME (2012) Twenty-five years of hub location research. Transp Sci 46:153–169
Campbell J, Ernst A, Krishnamoorthy M (2002) Hub location problems. In: Facility location: application and theory. Springer, Berlin
Chinneck JW (2007) Feasibility and infeasibility in optimization: algorithms and computational methods. Springer Science & Business Media
Contreras I, Cordeau J-F, Laporte G (2011) The dynamic uncapacitated hub location problem. Transp Sci 45:18–32
Correia I, Nickel S, Saldanha-da-Gama F (2018) A stochastic multi-period capacitated multiple allocation hub location problem: formulation and inequalities. Omega 74:122–134
Demir E, Bektaş T, Laporte G (2011) A comparative analysis of several vehicle emission models for road freight transportation. Transp Res Part D Transp Environ 16:347–357
Drezner Z, Wesolowsky GO (1991) Facility location when demand is time dependent. Nav Res Logist 38:763–777
Dukkanci O, Peker M, Kara BY (2019) Green hub location problem. Transp Res Part E Logist Transp Rev 125:116–139
Ebrahimi-Zade A, Hosseini-Nasab H, Zahmatkesh A (2016) Multi-period hub set covering problems with flexible radius: a modified genetic solution. Appl Math Model 40:2968–2982
Ernst AT, Krishnamoorthy M (1996) Efficient algorithms for the uncapacitated single allocation p-hub median problem. Locat Sci 4:139–154
Farahani RZ, Drezner Z, Asgari N (2009) Single facility location and relocation problem with time dependent weights and discrete planning horizon. Ann Oper Res 167:353–368
Farahani RZ, Hekmatfar M, Arabani AB, Nikbakhsh E (2013) Hub location problems: a review of models, classification, solution techniques, and applications. Comput Ind Eng 64:1096–1109
Fattahi P, Shakeri Kebria Z (2020) A bi objective dynamic reliable hub location problem with congestion effects. Int J Ind Eng Prod Res 31:63–74
Fotuhi F, Huynh N (2018) A reliable multi-period intermodal freight network expansion problem. Comput Ind Eng 115:138–150
Gelareh S, Nickel S (2008) Multi-period public transport planning: a model and greedy neighborhood heuristic approaches. Technical report, Department of Optimization, Fraunhofer Institute for Industrial Mathematics (ITWM), D 67663 Kaiserslautern, Germany
Gendreau M, Laporte G, Semet F (2001) A dynamic model and parallel tabu search heuristic for real-time ambulance relocation. Parallel Comput 27:1641–1653
Gelareh S, Monemi RN, Nickel S (2015) Multi-period hub location problems in transportation. Transp Res Part E Logist Transp Rev 75:67–94
Ghodratnama A, Tavakkoli-Moghaddam R, Azaron A (2013) A fuzzy possibilistic bi-objective hub covering problem considering production facilities, time horizons and transporter vehicles. Int J Adv Manuf Technol 66:187–206
Guua S-M, Wu Y-K (1999) Two-phase approach for solving the fuzzy linear programming problems. Fuzzy Sets Syst 107:191–195
Hakimi SL (1964) Optimum locations of switching centers and the absolute centers and medians of a graph. Oper Res 12:450–459
Holden E, Linnerud K, Banister D (2014) Sustainable development: our common future revisited. Glob Environ Chang 26:130–139
ISO (2010) ISO, 2010. Final Draft International Standard ISO/FDIS 26000:2010(E), Guidance on Social Responsibility.
Kara BY, Taner MR (2011) Hub location problems: the location of interacting facilities. In: Eiselt HA, Marianov V (eds) Foundations of location analysis. Springer, pp 273–288
Khosravian Y, Shahandeh Nookabadi A, Moslehi G (2019) Mathematical model for bi-objective maximal hub covering problem with periodic variations of parameters. Int J Eng 32:964–975
Klincewicz JG (1991) Heuristics for the p-hub location problem. Eur J Oper Res 53:25–37
Klincewicz JG (1992) Avoiding local optima in thep-hub location problem using tabu search and GRASP. Ann Oper Res 40:283–302
Kostin AM, Guillén-Gosálbez G, Mele FD et al (2011) A novel rolling horizon strategy for the strategic planning of supply chains. Application to the sugar cane industry of Argentina. Comput Chem Eng 35:2540–2563
Lai Y-J, Hwang C-L (1993) Possibilistic linear programming for managing interest rate risk. Fuzzy Sets Syst 54:135–146
Mohammadi M, Tavakkoli-Moghaddam R, Rostami R (2011) A multi-objective imperialist competitive algorithm for a capacitated hub covering location problem. Int J Ind Eng Comput 2:671–688
Mohammadi M, Jolai F, Tavakkoli-Moghaddam R (2013a) Solving a new stochastic multi-mode p-hub covering location problem considering risk by a novel multi-objective algorithm. Appl Math Model 37:10053–10073
Mohammadi M, Tavakkoli-Moghaddam R, Razmi J (2013b) Multi-objective invasive weed optimization for stochastic green hub location routing problem with simultaneous pick-ups and deliveries. Econ Comput Econ Cybernet Stud Res 47(3):247–266
Mohammadi M, Torabi SA, Tavakkoli-Moghaddam R (2014) Sustainable hub location under mixed uncertainty. Transp Res Part E Logist Transp Rev 62:89–115
Musavi M, Bozorgi-Amiri A (2017) A multi-objective sustainable hub location-scheduling problem for perishable food supply chain. Comput Ind Eng 113:766–778
Niakan F, Vahdani B, Mohammadi M (2015) A multi-objective optimization model for hub network design under uncertainty: an inexact rough-interval fuzzy approach. Eng Optim 47:1670–1688
Nickel S, da Gama FS (2015) Multi-period facility location. In: Laporte G, Nickel S, da Gama FS (eds) Location science. Springer, pp 289–310
Niknamfar AH, Niaki STA (2016) Fair profit contract for a carrier collaboration framework in a green hub network under soft time-windows: dual lexicographic max–min approach. Transp Res Part E Logist Transp Rev 91:129–151
O’kelly ME (1986a) The location of interacting hub facilities. Transp Sci 20:92–106
O’kelly ME (1986b) Activity levels at hub facilities in interacting networks. Geogr Anal 18:343–356
O’kelly ME (1987) A quadratic integer program for the location of interacting hub facilities. Eur J Oper Res 32:393–404
O’kelly ME, (1992) Hub facility location with fixed costs. Pap Reg Sci 71:293–306
Orda A, Rom R (1989) Location of central nodes in time varying computer networks. In: INFOCOM’89. Proceedings of the Eighth Annual Joint Conference of the IEEE Computer and Communications Societies. Technology: Emerging or Converging, IEEE. IEEE, pp 193–199
Puerto J, Rodríguez-Chía AM (1999) Location of a moving service facility. Math Methods Oper Res 49:373–393
Rahimi Y, Tavakkoli-Moghaddam R, Mohammadi M, Sadeghi M (2016) Multi-objective hub network design under uncertainty considering congestion: an M/M/c/K queue system. Appl Math Model 40:4179–4198
Roni MS, Eksioglu SD, Cafferty KG, Jacobson JJ (2017) A multi-objective, hub-and-spoke model to design and manage biofuel supply chains. Ann Oper Res 249:351–380
Saharidis GKD, Ierapetritou MG (2010) Improving Benders decomposition using maximum feasible subsystem (MFS) cut generation strategy. Comput Chem Eng 34:1237–1245
Sakawa M, Yano H, Yumine T (1987) An interactive fuzzy satisficing method for multiobjective linear-programming problems and its application. IEEE Trans Syst Man Cybern 17:654–661
Sangaiah AK, Khanduzi R (2022) Tabu search with simulated annealing for solving a location–protection–disruption in hub network. Appl Soft Comput 114:108056
Scora G, Barth M (2006) Comprehensive modal emissions model (cmem), version 3.01. User Guid Cent Environ Res Technol Univ California, Riverside 1070
Sedehzadeh S, Tavakkoli-Moghaddam R, Mohammadi M, Jolai F (2014) Solving a new priority M/M/C Queue model for a multi-mode hub covering location problem by multi-objective parallel simulated annealing. Econ Comput Econ Cybern Stud Res 48:299–318
Sherali HD (2001) On mixed-integer zero-one representations for separable lower-semicontinuous piecewise-linear functions. Oper Res Lett 28:155–160
Taghipourian F, Mahdavi I, Mahdavi-Amiri N, Makui A (2012) A fuzzy programming approach for dynamic virtual hub location problem. Appl Math Model 36:3257–3270
Toh RS, Higgins RG (1985) The impact of hub and spoke network centralization and route monopoly on domestic airline profitability. Transp J 24(4):16–27
Torabi SA, Hassini E (2008) An interactive possibilistic programming approach for multiple objective supply chain master planning. Fuzzy Sets Syst 159:193–214
Torkestani SS, Seyedhosseini SM, Makui A, Shahanaghi K (2018) The reliable design of a hierarchical multi-modes transportation hub location problems (HMMTHLP) under dynamic network disruption (DND). Comput Ind Eng 122:39–86
Wang J, Shu Y-F (2007) A possibilistic decision model for new product supply chain design. Eur J Oper Res 177:1044–1061
Yaman H, Carello G (2005) Solving the hub location problem with modular link capacities. Comput Oper Res 32:3227–3245
Zanjirani Farahani R, Szeto WY, Ghadimi S (2015) The single facility location problem with time-dependent weights and relocation cost over a continuous time horizon. J Oper Res Soc 66:265–277
Zhalechian M, Tavakkoli-Moghaddam R, Rahimi Y (2017a) A self-adaptive evolutionary algorithm for a fuzzy multi-objective hub location problem: an integration of responsiveness and social responsibility. Eng Appl Artif Intell 62:1–16
Zhalechian M, Tavakkoli-Moghaddam R, Rahimi Y, Jolai F (2017b) An interactive possibilistic programming approach for a multi-objective hub location problem: economic and environmental design. Appl Soft Comput 52:699–713
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Khaleghi, A., Eydi, A. Hybrid solution methods for a continuous-time multi-period hub location problem with time-dependent demand and sustainability considerations. J Ambient Intell Human Comput 15, 115–155 (2024). https://doi.org/10.1007/s12652-022-03879-w
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DOI: https://doi.org/10.1007/s12652-022-03879-w