Distribution Center Positioning and Territory Design in Supply Chain

Document Type : Research Paper


1 Ph.D. Candidate, Department of Industrial Engineering, Faculty of Industrial Engineering, Yazd University, Yazd, Iran

2 Prof., Department of Industrial Engineering, Faculty of Industrial Engineering, Yazd University, Yazd, Iran

3 Assistant Prof., Department of Industrial Engineering, Faculty of Industrial Engineering, Birjand Industrial University, Birjand, Iran

4 Associate Prof., Department of Industrial Engineering, Faculty of Industrial Engineering, Yazd University, Yazd, Iran


Objective: In this paper, we investigate a new optimization for territory design in the distribution system and allocation of the customers to supply centers which are considered as territory centers using MIP model. The objective is to balance the work load through minimizing the maximum differences the minimum customers allocated to the various centers. The study constraints guarantee continuity of the territories and the lack of gaps in the territories. Also, other constraints include allocation of a center to each territory and exclusive allocation of each customer to only one territory.
Methods: Since, territory design and positioning are among NP-hard issues, in order to solve real-world case and big problems we have to propose meta-heuristic algorithms. For this purpose, in this paper, a grey wolf optimizer and a salp optimizer algorithm are proposed. Based on the literature review, it is very difficult to use encoding-decoding solution  without any modifier algorithm. Therefore, we design a novel solution scheme based on a minimum spanning tree in order to obviate the complexities, guarantee the continuity of the territory structures and the lack of gaps, and generate feasible solutions.
Results: Computational results on random instances showed that the proposed algorithms can effectively help to generate reasonable responses.
Conclusion: The model proposed here could be a useful tool to aid the decision-making in distribution management, as well as for the better organization of any distribution.


Baños, R., Gil, C., Paechter, B., & Ortega, J. (2007). A hybrid meta-heuristic for multi-objective optimization: MOSATS. Journal of Mathematical Modelling and Algorithms, 6(2), 213-230.
Baqir, R. (2002). Districting and government overspending. Journal of political Economy, 110(6), 1318-1354.
Benzarti, E., Sahin, E., & Dallery, Y. (2013). Operations management applied to home care services: Analysis of the districting problem. Decision Support Systems, 55(2), 587-598.
Boonjing, V., Chanvarasuth, P. & Lertwongsatien, C. (2015). An Impact of Supply Chain Management Components on Firm Performance. Paper presented at the Proceedings of the 6th International Conference on Engineering, Project and Production Management.
Bozkaya, B., Erkut, E., & Laporte, G. (2003). A tabu search heuristic and adaptive memory procedure for political districting. European journal of operational research, 144(1), 12-26.
Brooks, S. P., & Morgan, B. J. (1995). Optimization using simulated annealing. The Statistician, 44(2), 241-257.
Butsch, A., Kalcsics, J., & Laporte, G. (2014). Districting for arc routing. INFORMS Journal on Computing, 26(4), 809-824.
Camacho-Collados, M., Liberatore, F., & Angulo, J. (2015). A multi-criteria police districting problem for the efficient and effective design of patrol sector. European journal of operational research, 246(2), 674-684.
Carbonara, N., Giannoccaro, I., & Pontrandolfo, P. (2002). Supply chains within industrial districts: A theoretical framework. International Journal of Production Economics, 76(2), 159-176.
Chen, X., & Yum, T.-S. P. (2010). Patrol districting and routing with security level functions. Paper presented at the Systems Man and Cybernetics (SMC), 2010 IEEE International Conference on.
Christopher, M. (2016). Logistics & supply chain management. Pearson UK.
Camacho-Collados, M., Liberatore, F., & Angulo, J. M. (2015). A multi-criteria police districting problem for the efficient and effective design of patrol sector. European journal of operational research, 246(2), 674-684.
Datta, D., Figueira, J., Gourtani, A., & Morton, A. (2013). Optimal administrative geographies: an algorithmic approach. Socio-Economic Planning Sciences, 47(3), 247-257.
Datta, D., & Figueira, J. R. (2011). Graph partitioning by multi-objective real-valued metaheuristics: A comparative study. Applied soft computing, 11(5), 3976-3987.
De Assis, L. S., Franca, P. M., & Usberti, F. L. (2014). A redistricting problem applied to meter reading in power distribution networks. Computers & Operations Research, 41, 65-75.
Farahani, R. Z., Fallah, S., Ruiz, R., Hosseini, S., & Asgari, N. (2018). OR models in urban service facility location: a critical review of applications and future developments. European journal of operational research, 276(1), 1-27.
Farughi, H., & Arkat, J. (2018). Healthcare Districting Optimization Using Gray Wolf Optimizer and Ant Lion Optimizer Algorithms (case study: South Khorasan Healthcare System in Iran). Journal of Optimization in Industrial Engineering, 12(1), 119-131.  
Flynn, B., Pagell, M., & Fugate, B. (2018). Survey Research Design in Supply Chain Management: The Need for Evolution in Our Expectations. Journal of Supply Chain Management, 54(1), 1-15.
Fragoso, R., Rego, C., & Bushenkov, V. (2016). Clustering of territorial areas: A multi-criteria districting problem. Journal of Quantitative Economics, 14(2), 179-198.
García‐Ayala, G., González‐Velarde, J. L., Ríos‐Mercado, R. Z., & Fernández, E. (2016). A novel model for arc territory design: promoting Eulerian districts. International Transactions in Operational Research, 23(3), 433-458.
Garfinkel, R.S., & Nemhauser, G.L. (1970). Optimal political districting by implicit enumeration techniques. Management Science, 16(8), B-495-B-508.
Ghiggi, C., Puliafito, P., & Zoppoli, R. (1975). A combinatorial method for health-care districting. Paper presented at the IFIP Technical Conference on Optimization Techniques, PP.116-130.
Graham, R. L., & Hell, P. (1985). On the history of the minimum spanning tree problem. Annals of the History of Computing, 7(1), 43-57.
Hugos, M. H. (2018). Essentials of supply chain management. John Wiley & Sons.
Jiang, S., Chin, K.-S., Wang, L., Qu, G., & Tsui, K. L. (2017). Modified genetic algorithm-based feature selection combined with pre-trained deep neural network for demand forecasting in outpatient department. Expert systems with applications, 82, 216-230.
Kalcsics, J. (2015). Districting problems Location science. Springer. (pp. 595-622).
Kim, K., Dean, D. J., Kim, H., & Chun, Y. (2016). Spatial optimization for regionalization problems with spatial interaction: a heuristic approach. International Journal of Geographical Information Science, 30(3), 451-473.
King, D. M., Jacobson, S. H., & Sewell, E. C. (2018). The geo-graph in practice: creating United States Congressional Districts from census blocks. Computational Optimization and Applications, 69(1), 25-49.
Kong, Y., Zhu, Y., & Wang, Y. (2018). A center-based modeling approach to solve the districting problem. International Journal of Geographical Information Science, 1-17. Published online: 21 May 2018.
Konur, D., & Geunes, J. (2016). Integrated districting, fleet composition, and inventory planning for a multi-retailer distribution system. Annals of Operations Research, 1-33.
Lambert, D. M., & Cooper, M. C. (2000). Issues in supply chain management. Industrial marketing management, 29(1), 65-83.
Lei, H., Wang, R., & Laporte, G. (2016). Solving a multi-objective dynamic stochastic districting and routing problem with a co-evolutionary algorithm. Computers & Operations Research, 67, 12-24.
Li, W., Church, R. L., & Goodchild, M. F. (2014). An extendable heuristic framework to solve the p-compact-regions problem for urban economic modeling. Computers, Environment and Urban Systems, 43, 1-13.
Liberatore, F., & Camacho-Collados, M. (2016). A comparison of local search methods for the multicriteria police districting problem on graph. Mathematical Problems in Engineering, 2016(3), 1-13.
Lin, H.-Y., & Kao, J.-J. (2008). Subregion districting analysis for municipal solid waste collection privatization. Journal of the Air & Waste Management Association, 58(1), 104-111.
Lin, M., Chin, K.-S., Fu, C., & Tsui, K.-L. (2017). An effective greedy method for the Meals-On-Wheels service districting problem. Computers & Industrial Engineering, 106, 1-19.
Mehregan, M., Jafarnejad, A., Mohammadi, M. (2018). Proposing a Multi-objective Model for Ground Transportation of Hazardous Materials in the Hub Network (Case Study: National Iranian Oil Products Distribution Company). Industrial Management Journal, 10(2), 201-220. (in Persian)
Minciardi, R., Puliafito, P., & Zoppoli, R. (1981). A districting procedure for social organizations. European journal of operational research, 8(1), 47-57.
Mirjalili, S., Gandomi, A. H., Mirjalili, S. Z., Saremi, S., Faris, H., & Mirjalili, S. M. (2017). Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems. Advances in Engineering Software, 114, 163-191.
Mirjalili, S., Mirjalili, S. M., & Lewis, A. (2014). Grey wolf optimizer. Advances in Engineering Software, 69, 46-61.
Pezzella, F., Bonanno, R., & Nicoletti, B. (1981). A system approach to the optimal health-care districting. European journal of operational research, 8(2), 139-146.
Ptak, C. A., & Schragenheim, E. (2016). ERP: tools, techniques, and applications for integrating the supply chain. Crc Press.
Razavi, M., Soukhakian, M. A. & Ziarati, K. (2011). A Meta Heuristic Algorithms Based on Ant Colony System For Solving Multi Depots Location-routing Problem with Multiple Using of Vehicle. Industrial Management, 3(6), 17-38. (in Persian)
Ríos-Mercado, R. Z., & López-Pérez, J. F. (2013). Commercial territory design planning with realignment and disjoint assignment requirements. Omega, 41(3), 525-535.
Shahin, M., Jabalameli, M. S., Jabbarzadeh, A. (2017). Multi-modal and multiproduct hierarchical hub location under uncertainty. Industrial Management, 8(4), 625-658.
(in Persian)
Shirabe, T. (2009). Districting modeling with exact contiguity constraints. Environment and Planning B: Planning and Design, 36(6), 1053-1066.
Shirabe, T. (2012). Prescriptive modeling with map algebra for multi-zone allocation with size constraints. Computers, Environment and Urban Systems, 36(5), 456-469.
Steiner, M. T. A., Datta, D., Neto, P. J. S., Scarpin, C. T., & Figueira, J. R. (2015). Multi-objective optimization in partitioning the healthcare system of Parana State in Brazil. Omega, 52, 53-64.
Tan, K. C. (2001). A framework of supply chain management literature. European Journal of Purchasing & Supply Management, 7(1), 39-48.
Tran, T.-C., Dinh, T. B., & Gascon, V. (2017). Meta-heuristics to Solve a Districting Problem of a Public Medical Clinic. Paper presented at the Proceedings of the Eighth. International Symposium on Information and Communication Technology.
Vakili, P., Hosseini-Motlagh,S.M., Gholamian, M.R, Jokar,A. (2017). A developed model and heuristic algorithm for inventory routing problem in a cold chain with pharmaceutical products. Industrial Management, 9(2), 383-407.(in Persian)
Wang, G., Gunasekaran, A., Ngai, E. W., & Papadopoulos, T. (2016). Big data analytics in logistics and supply chain management: Certain investigations for research and applications. International Journal of Production Economics, 176, 98-110.
Wang, T., Wu, Z., & Mao, J. (2007). A new method for multi-objective tdma scheduling in wireless sensor networks using pareto-based pso and fuzzy comprehensive judgement. High Performance Computing and Communications (pp. 144-155): Springer.
Wisner, J. D., Tan, K.-C., & Leong, G. K. (2014). Principles of supply chain management: A balanced approach. Cengage Learning.
Zhao, J., Wang, D., & Peng, Q. (2018). Optimizing the Train Dispatcher Desk Districting Problem in High-Speed Railway Network. Transportation Research Board 97th Annual Meeting, 2018-1-7 to 2018-1-11.