In this paper, we investigate a multi-product, three-stage production/distribution system design problem (PDSD) with direct shipment and lateral transshipment capabilities. Our overall goal is to find the most efficient network design to minimize the total fixed facility and transportation costs. Specifically, we locate p capacitated distribution centers in the second stage from a set of candidate locations. At the same time, our design allows for direct shipments between first (suppliers) and third stages (customers) and lateral transshipments among the distribution centers in the second stage. The PDSD problem is known to be NP-hard, and prior studies have explored several heuristic methods including scatter search, tabu search, and genetic algorithms to solve the problem. In this paper, we propose two solution algorithms based on simulated annealing and GRASP heuristics. We apply both long-term and short-term memory lists to maintain an efficient local search, combined with a custom greedy solver that can effectively evaluate the quality of a solution candidate. We conduct a series of computational experiments to validate the proposed algorithms. Compared with the optimal solution, the simulated annealing algorithm presents an average optimality gap of 0.07% and an average time of 25.56% of optimal solution time, while the GRASP algorithm achieves a solution gap of 0.11% with 17.85% of optimal running time. The experimental results also show that the simulated annealing and GRASP algorithms outperform the best-reported heuristic in the literature based on scatter search regarding both solution quality and duration, especially for large-scale problem instances with tighter capacities.
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Ahmadi S, Osman IH (2005) Greedy random adaptive memory programming search for the capacitated clustering problem. Eur J Oper Res 162(1):30–44. Logistics: from theory to application
Arostegui MA, Kadipasaoglu SN, Khumawala BM (2006) An empirical comparison of Tabu search, simulated annealing, and genetic algorithms for facilities location problems. Int J Prod Econ 103(2):742–754
Brimberg J, Drezner Z (2013) A new heuristic for solving the p-median problem in the plane. Comput Oper Res 40:427–437
Camacho-Vallejo J-F, Munoz-Sancheza R, Gonzalez-Velarde JL (2015) A heuristic algorithm for a supply chain’s production-distribution planning. Comput Oper Res 61(9):110–121
Chen L, Monteiro T, Wang T, Marcon E (2018) Design of shared unit-dose drug distribution network using multi-level particle swarm optimization. Health Care Management Science Appeared Online, 1–14
Chiyoshi F, Galvao RD (2000) A statistical analysis of simulated annealing applied to the p-median problem. Ann Oper Res 96:61–74
Contreras IA, Diaz JA (2008) Scatter search for the single source capacitated facility location problem. Ann Oper Res 157:73–89
Diaz JA, Fernandez E (2006) Hybrid scatter search and path relinking for the capacitated p-median problem. Eur J Oper Res 169:570–585
Fahimnia B, Luong L, Marian R (2012) Genetic algorithm optimisation of an integrated aggregate production distribution plan in supply chains. Int J Prod Res 50(1):81–96
Feo TA, Resende MGC (1989) A probabilistic heuristic for a computationally difficult set covering problem. Oper Res Lett 8(2):67–71
Feo TA, Resende MGC (1995) Greedy randomized adaptive search procedures. J Global Optim 6(2):109–133
Festa P, Resende MGC (2009) An annotated bibliography of grasp-part ii : applications. Int Trans Oper Res 16:131–172
Firouz M, Keskin BB, Melouk SH (2017) An integrated supplier selection and inventory problem with multi-sourcing and lateral transshipments. Omega 70:77–93
Goetschalckx M, Vidal CJ, Dogan K (2002) Modeling and design of global logistic systems: a review of integrated strategic and tactical models and design algorithms. Eur J Oper Res 143:1–18
Jawahar N, Balaji A (2009) A genetic algorithm for the two-stage supply chain distribution problem associated with a fixed charge. Eur J Oper Res 194:496–537
Jin M, Eksioglu SD, Eksioglu B, Wang H (2010) Mode selection for automotive distribution with quantity discounts. Netw Spatial Econ 10(1):1–13
Kariv O, Hakimi L (1979) An algorithmic approach to network location problems. II: the p-medians. SIAM J Appl Math 37(3):539–560
Keskin BB, Üster H (2007a) Meta-heuristic approaches with memory and evolution for a multi-product production/distribution system design problem. Eur J Oper Res 182(2):663–682
Keskin BB, Üster H (2007b) A scatter search-based heuristic to locate capacitated transshipment points. Comput Oper Res 34(10):3112–3125
Melo MT, Nickel S, Saldanha da Gama F (2009) Facility location and supply chain management-a review. Eur J Oper Res 196(2):401–412
Miralinaghi M, Keskin BB, Lou Y, Roshandeh AM (2017) Capacitated refueling station location problem with traffic deviations over multiple time periods. Netw Spatial Econ 17(1):129–151
Miranda PA, Garrido RA (2006) A simultaneous inventory control and facility location model with stochastic capacity constraints. Netw Spatial Econ 6(1):39–53
Mladenovic N, Brimberg J, Hansen P, Moreno-Perez JA (2007) The p-median problem: a survey of metaheuristic approachest. Eur J Oper Res 179:927–939
Olhager J, Pashaei S, Sternberg H (2015) Design of global production and distribution networks: a literature review and research agenda. Int J Phys Distrib Logist Manag 45(1–2):138–158
Paterson C, Kiesmüller G, Teunter R, Glazebrook K (2011) Inventory models with lateral transshipments: a review. Eur J Oper Res 210(2):125–136
Pedrola O, Ruiz M, Velasco L, Careglio D, Gonzalez de Dios O, Comellas J (2013) A GRASP with path-relinking heuristic for the survivable IP/MPLS-over-WSON multi-layer network optimization problem. Comput Oper Res 40:3174–3187
Pessoa LS, Resende MGC, Ribeiro CC (2013) A hybrid lagrangean heuristic with grasp and path-relinking for set k-covering. Comput Oper Res 40:3132–3146
Resende MGC, Werneck RF (2004) A hybrid heuristic for the p-median problem. Ann Oper Res 10(1):59–88
Saez-Aguado J, Trandafir PC (2012) Some heuristic methods for solving p-median problems with a coverage constraint. Eur J Oper Res 220:320–327
Sahin G, Süral H (2007) A review of hierarchical facility location models. Comput Oper Res 34(8):2310–2331
Tragantalerngsak S, Rönnqvist JHM (1997) Lagrangian heuristics for the two-echelon, single-source, capacitated facility location problem. Eur J Oper Res 102 (3):611–625
Tragantalerngsak S, Holt J, Rönnqvist M (2000) An exact method for the two-echelon, single-source, capacitated facility location problem. Eur J Oper Res 123(3):473–489
Tsao Y-C, Linh VT (2016) Supply chain network designs developed for deteriorating items under conditions of trade credit and partial backordering. Netw Spatial Econ 16(3):933–956
We would like to thank the area editor and the two anonymous reviewers for their constructive feedback on the earlier versions of this manuscript.
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Zhi, J., Keskin, B.B. A Multi-Product Production/Distribution System Design Problem with Direct Shipments and Lateral Transshipments. Netw Spat Econ 18, 937–972 (2018). https://doi.org/10.1007/s11067-018-9436-8
- Simulated annealing
- Direct shipment
- Lateral transshipments