Presenting a multi-objective locating-routing-arc model with a collaborative approach (a food distribution case study)

Document Type: Research Paper


Department of Industrial Engineering, Islamic Azad University, South Tehran Branch, Tehran, Iran


Transportation in the industrialized world plays an important role in the economic development of countries by enabling the consumption of products at very remote locations. Transportation costs are one of the most important parts of the finished products’ costs. In general, locating-routing-arc is highly important for industries that are heavily involved with the end customers such as the consumer product industries. In these industries, due to the insignificant difference between the products of the various companies, the maintenance of the market and the loyalty of customers depend on the timely availability of the required products. Hence, providing the customers ‘need at the right time and place with high level of responding is highly important to get customers’ satisfaction. In this study, the problem of locating-routing-arc is studied by using game theory. In the investigated problem, there are a number of demand points as customers, each of which has a specific demand (delivered, handover or return) of every type of products and each customer determines the delivery time for each product. To solve the Problem in Small dimensions, a mathematical model is presented in the form of the mixed integer, two-objective, multi-cyclic, and multi-commodity and for to solve the problem in big dimensions in the form of NP-HARD. The model is to test the validation of the proposed model, a ε-constraint method is used and Pareto solutions are calculated. Then due to the complexity of the problem in big dimensions. We used the meta-heuristics NSGA-II algorithm in cooperative and non-cooperative modes. Finally, the results if cooperative methods were used to allocate the amount of savings.


Main Subjects

Cooper, L. (1963). Location-allocation problems. Operations research11(3), 331-343.‏

Doulabi, S. H. H., & Seifi, A. (2013). Lower and upper bounds for location-arc routing problems with vehicle capacity constraints. European Journal of Operational Research224(1), 189-208.

Golden, B. L., & Wong, R. T. (1981). Capacitated arc routing problems. Networks11(3), 305-315.‏

Gupta, D., & Weerawat, W. (2006). Supplier–manufacturer coordination in capacitated two-stage supply chains. European Journal of Operational Research175(1), 67-89.‏

Ghorbani, A., & Jokar, M. R. A. (2016). A hybrid imperialist competitive-simulated annealing algorithm for a multisource multi-product location-routing-inventory problem. Computers & Industrial Engineering101, 116-127.‏

Liu, Y., & Zhang, Y. (2006, June). Supply chain coordination with contracts for online game industry. In Management of Innovation and Technology, 2006 IEEE International Conference on (Vol. 2, pp. 867-871). IEEE.‏

Lu, Y., & Li, Z. (2010, August). Coordination of price discount and sales promotion in a two-level supply chain system. In Emergency Management and Management Sciences (ICEMMS), 2010 IEEE International Conference on (pp. 9-12). IEEE.‏

Lozano, S., Moreno, P., Adenso-Díaz, B., & Algaba, E. (2013). Cooperative game theory approach to allocating benefits of horizontal cooperation. European Journal of Operational Research229(2), 444-452.‏

Lopes, R. B., Plastria, F., Ferreira, C., & Santos, B. S. (2014). Location-arc routing problem: Heuristic approaches and test instances. Computers & Operations Research43, 309-317.‏

Ma, Z., & Dai, Y. (2010). Stochastic dynamic location-routing-inventory problem in two-echelon multi-product distribution systems. In ICLEM 2010: Logistics For Sustained Economic Development: Infrastructure, Information, Integration (pp. 2559-2565).‏

Nagarajan, M. (2014). An operational research-based integrated approach for mass evacuation planning of a city (Doctoral dissertation, Aston University).‏

Proano, R. A., Jacobson, S. H., & Zhang, W. (2012). Making combination vaccines more accessible to low-income countries: The antigen bundle pricing problem. Omega40(1), 53-64.‏

Riquelme-Rodríguez, J. P., Gamache, M., & Langevin, A. (2016). Location arc routing problem with inventory constraints. Computers & Operations Research76, 84-94.‏

Salhi, S., & Rand, G. K. (1989). The effect of ignoring routes when locating depots. European journal of operational research39(2), 150-156.‏

Srinivas, N., & Deb, K. (1994). Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary computation2(3), 221-248.‏

Syam, S. S. (2008). A multiple server location–allocation model for service system design. Computers & Operations Research35(7), 2248-2265.‏

Seyedhosseini, S. M., Bozorgi-Amiri, A., & Daraei, S. (2014). An integrated location-Routing-Inventory problem by considering supply disruption. IBusiness6(02), 29.‏

Santoso, T., Ahmed, S., Goetschalckx, M., & Shapiro, A. (2005). A stochastic programming approach for supply chain network design under uncertainty. European Journal of Operational Research167(1), 96-115.‏

Shang, R., Du, B., Ma, H., Jiao, L., Xue, Y., & Stolkin, R. (2016). Immune clonal algorithm based on directed evolution for multi-objective capacitated arc routing problem. Applied Soft Computing49, 748-758.‏

Tuzun, D., & Burke, L. I. (1999). A two-phase tabu search approach to the location routing problem. European journal of operational research116(1), 87-99.‏

Tütüncü, G. Y., Carreto, C. A., & Baker, B. M. (2009). A visual interactive approach to classical and mixed vehicle routing problems with backhauls. Omega37(1), 138-154.‏

Ting, C. J., & Chen, C. H. (2013). A multiple ant colony optimization algorithm for the capacitated location routing problem. International Journal of Production Economics141(1), 34-44.‏

Tavakkoli-Moghaddam, R., & Raziei, Z. (2016). A new bi-objective location-routing-inventory problem with fuzzy demands. IFAC-PapersOnLine49(12), 1116-1121.‏

Umarani, R., & Selvi, V. (2010). Particle swarm optimization-evolution, overview and applications.‏

Willemse, E. J., & Joubert, J. W. (2016). Constructive heuristics for the mixed capacity arc routing problem under time restrictions with intermediate facilities. Computers & Operations Research68, 30-62.‏

Xu, Y., & Zhong, H. (2011, January). Benefit mechanism designing: for coordinating three stages supply chain. In Management Science and Industrial Engineering (MSIE), 2011 International Conference on (pp. 966-969). IEEE.‏

Xu, G., Yang, Y. Q., Liu, B. B., Xu, Y. H., & Wu, A. J. (2015). An efficient hybrid multi-objective particle swarm optimization with a multi-objective dichotomy line search. Journal of computational and applied mathematics280, 310-326.‏

Yao, Z., Lee, L. H., Jaruphongsa, W., Tan, V., & Hui, C. F. (2010). Multi-source facility location–allocation and inventory problem. European Journal of Operational Research207(2), 750-762.‏

Zhong, Y., & Cole, M. H. (2005). A vehicle routing problem with backhauls and time windows: a guided local search solution. Transportation Research Part E: Logistics and Transportation Review41(2), 131-144.‏

Zhao, Y., Wang, S., Cheng, T. E., Yang, X., & Huang, Z. (2010). Coordination of supply chains by option contracts: A cooperative game theory approach. European Journal of Operational Research207(2), 668-675.‏

Zhang, X., Zhang, Z., Zhang, Y., Wei, D., & Deng, Y. (2013). Route selection for emergency logistics management: A bio-inspired algorithm. Safety science54, 87-91.‏

Zibaei, S., Hafezalkotob, A., & Ghashami, S. S. (2016). Cooperative vehicle routing problem: an opportunity for cost saving. Journal of Industrial Engineering International12(3), 271-286.‏

Zhang, Y., Mei, Y., Tang, K., & Jiang, K. (2017). Memetic algorithm with route decomposing for periodic capacitated arc routing problem. Applied Soft Computing52, 1130-1142.‏