A Hybrid Mehta-Heuristic algorithm for optimization location-routing problem of facilities in four echelon supply chain

Subject Areas : Mathematical Optimization

Hamidreza Mohamadi ¹ , Reza Ehtesham Rasi ² , Ali Mohtashami ³

1 - Ph.D. Student, Department of Industrial Management, Qazvin Branch, Islamic Azad University, Qazvin, Iran.
2 - Department of Industrial Management, Qazvin Branch, Islamic Azad University, Qazvin, Iran
3 - Department of Industrial Management, Qazvin Branch, Islamic Azad University, Qazvin, Iran.

Received: 2020-11-07 Accepted : 2020-12-16 Published : 2020-12-01

Keywords: Mathematical Modeling, Location-routing, Multi-level Supply Chain, Multiproduct deteriorating items, Multiproduct,

Abstract :

During the last three decades, the concept of integrated decision making in the supply chain becomes one of the essential aspects of supply chain management (SCM). This concept explores the interdependence between facility location, flow allocation between facilities, transportation system structure, and inventory control system. This study presents a new form of the location-routing problem of facilities under uncertainty in a supply chain network for deteriorating items through taking environmental considerations, cost, and procurement time and customer satisfaction into account, to simultaneously minimize total system costs, maximal delivery time and emissions across the entire network and maximize customer satisfaction. The research problem is formulated in a mixed-integer nonlinear multi-objective programming. In order to solve the model, the combination of the two Benders decomposition algorithm and Lagrange multiplier liberalization, as well as the combination of red deer algorithm and annealing simulation, was proposed. For validation, the results of the proposed algorithm in different size examples are compared with the results of the exact method solution by MATLAB software. The mean error of the proposed algorithm for the objective function is less than 4% compared to the exact method in solving the sample problems. Besides, the results of the algorithm performance are investigated based on standard indices. The computational results show the efficiency of the algorithm for a wide range of problems with different sizes. The location decisions are interdependent, and the process of determining the optimal values of these variables interact together, which can lead to an optimal system.

References:

[1] An, K., & Ouyang, Y. (2016). Robust grain supply chain design considering post-harvest loss and harvest timing equilibrium. Transportation Research Part E: Logistics and Transportation Review, Vol.88, pp.110-128.

[2] Ardalan, Z., Karimi, S., Naderi, B., & Khamseh, A. A. (2016). Supply chain networks design with multi-mode demand satisfaction policy. Computers & Industrial Engineering, Vol.96, pp.108-117.

[3] As' ad, R., Hariga, M., & Alkhatib, O. (2019). Two stage closed loop supply chain models under consignment stock agreement and different procurement strategies. Applied Mathematical Modelling, Vol.65, pp.164-186.

[4] Asim, Z., Jalil, S. A., & Javaid, S. (2019). An uncertain model for integrated production-transportation closed-loop supply chain network with cost reliability. Sustainable Production and Consumption, Vol.17, pp.298-310.

[5] Baghalian, A., Rezapour, S., & Farahani, R. Z. (2013). Robust supply chain network design with service level against disruptions and demand uncertainties: A real-life case. European Journal of Operational Research,Vol. 227(1), pp.199-215.

[6] Balaji, M., & Arshinder, K. (2016). Modeling the causes of food wastage in Indian perishable food supply chain. Resources, Conservation and Recycling, Vol.114, pp.153-167.

[7] Benton, W. C., & Maloni, M. (2005). The influence of power driven buyer/seller relationships on supply chain satisfaction. Journal of Operations Management, Vol.23(1), pp.1-22.

[8] Ben-Tal,A.,Nemirovski.(2000).Robust solutions of Linear Programming problems contaminated with uncertain data. Math. Program. Vol.88, pp.411–424. https://doi.org/10.1007/PL00011380

[9] Borodin, V., Bourtembourg, J., Hnaien, F., & Labadie, N. (2016). Handling uncertainty in agricultural supply chain management: a state of the art. European Journal of Operational Research, Vol.254(2), pp.348-359.

[10] Chian-son Yu, Hann-Lin Li.(2010).A robust optimization model for stochastic logistic problems. Int. J. Production Economics, Vol.64(2), pp.385-397.

[11] Cole, R., & Aitken, J. (2019). The role of intermediaries in establishing a sustainable supply chain. Journal of Purchasing and Supply Management.Vol.26(2),pp.100-123.

[12] Dai, Z., Aqlan, F., Zheng, X., & Gao, K. (2018). A location-inventory supply chain network model using two heuristic algorithms for perishable products with fuzzy constraints. Computers & Industrial Engineering.Vol19(3),pp.338-352.

[13] Daryan Noori,M,.Talebizadeh,At allah.(2019). Optimizing pricing and ordering strategies in a three-level supply chain under return policy. Journal of Industrial Engineering International,Vol.15(1),pp.73–80.

[14] Das, K., & Chowdhury, A. H. (2012). Designing a reverse logistics network for optimal collection, recovery and quality-based product-mix planning. International Journal of Production Economics.Vol.135(1),pp. 209–221.

[15] Doss, D., & Dutta, P. (2013). A system dynamics framework for integrated reverse supply chain with three way recovery and product exchange policy. Computers and Industrial Engineering, 66(4), pp.720–733.

[16] De Keizer, M., Akkerman, R., Grunow, M., Bloemhof, J. M., Haijema, R., & van der Vorst, J. G. (2017). Logistics network design for perishable products with heterogeneous quality decay. European Journal of Operational Research, 262(2), pp.535-549.

[17] Dey, K., Saha, S. (2018). Influence of procurement decisions in two-period green supply chain. Journal of cleaner production, Vol.190(6),pp. 388-402.
[18] El-Sayed, M., Afia, N., & El-Kharbotly, A. (2010). A stochastic model for forward–reverse logistics network design under risk. Computers & Industrial Engineering, Vol.58(3), pp.423-431.
[19] Fredriksson, A. (2017). Location-allocation of public services–Citizen access, transparency and measurement. A method and evidence from Brazil and Sweden. Socio-Economic Planning Sciences,Vol.(59),pp.1-12.
[20] Gölgeci, I., Murphy, W. H., & Johnston, D. A. (2018). Power-based behaviors in supply chains and their effects on relational satisfaction: A fresh perspective and directions for research. European Management Journal, Vol.36(2), pp.278-287.
[21] Gumasta, K., Chan, F. T., & Tiwari, M. K. (2012). An incorporated inventory transport system with two types of customers for multiple perishable goods. International Journal of Production
Economics.Vol.139(2), pp.678-686.
[22] Hafezalkotob,Ashkan,Zamani,Soma.(2019). A multi-product green supply chain under government supervision with price and demand uncertainty.Journal of Industrial Engineering
International,Vol.15(1),pp.193–206.
[23] Katsaliaki, K., Mustafee, N., & Kumar, S. (2014). A game-based approach towards facilitating decision making for perishable products: An example of blood supply chain. Expert Systems with
Applications.Vol. 41(9),pp. 4043-4059.
[24] Kaur, H., & Singh, S. P. (2018). Heuristic modeling for sustainable procurement and logistics in a supply chain using big data. Computers & Operations Research.Vol.98, pp.301-321.
[25] Khosroshahi, H., Rasti-Barzoki, M., & Hejazi, S. R. (2019). A game theoretic approach for pricing decisions considering CSR and a new consumer satisfaction index using transparency-dependent demand in sustainable supply chains. Journal of Cleaner Production, Vol.208,pp.
1065-1080.
[26] Kovaˇci´c D, Bogataj M (2013) Reverse logistics facility location using cyclical model of extended MRP theory. Cent Eur J Oper Res.Vol. 21(1),pp.41–57.
[27] Kovačić, D., Hontoria, E., Ros-McDonnell, L., & Bogataj, M. (2015). Location and lead-time perturbations in multi-level assembly systems of perishable goods in Spanish baby food logistics. Central European journal of operations research, Vol.23(3), pp.607-623.
[28] Li, L., Dababneh, F., & Zhao, J. (2018). Cost-effective supply chain for electric vehicle battery remanufacturing. Applied energy, Vol.226, pp.277-286.
[29] Maranzana, F.E.1964. On the location of supply points to minimize transport costs. Operational Research Quarterly Vol.15, pp.261–270.
[30] Mogale, D. G., Kumar, M., Kumar, S. K., & Tiwari, M. K. (2018). Grain silo location-allocation problem with dwell time for optimization of food grain supply chain network. Transportation
Research Part E: Logistics and Transportation Review,Vol. 111, pp.40-69.
[31] Morganti, E., & Gonzalez-Feliu, J. (2015). City logistics for perishable products. The case of the Parma's Food Hub. Case Studies on Transport Policy, Vol.3(2), pp.120-128.

[32] Mukhopadhyay, S., & Ma, H. (2009). Joint procurement and production decisions in remanufacturing under quality and demand uncertainty. International Journal of Production Economics.Vol. 120(1), pp.5–17.
[33] Mousavi, M., & Rayat, F. (2017). A Bi-Objective Green Truck Routing and Scheduling Problem in a Cross Dock with the Learning Effect. Iranian Journal of Operations Research.Vol. 8(1), pp. 2-14.
[34] Nagurney, A. (2015). Design of sustainable supply chains for sustainable cities. Environment and Planning B: Planning and Design.Vol.42(1),pp. 40-57.
[35] Nenes, G., & Nikolaidis, Y. (2012). A multi-period model for managing used product returns. International Journal of Production Research, Vol.50(5), pp.1360–1376.
[36] Niu, B., Mu, Z., Chen, L., & Lee, C. K. (2019). Coordinate the economic and environmental sustainability via procurement outsourcing in a co-opetitive supply chain. Resources, Conservation and Recycling.Vol.146, pp.17-27.
[37] Oh, J., Jeong, B. (2019). Tactical supply planning in smart manufacturing supply chain. Robotics and Computer-Integrated Manufacturing, Vol.55, pp.217-233.
[38] Orjuela-Castro, J. A., Aranda-Pinilla, J. A., & Moreno-Mantilla, C. E. (2018). Identifying trade-offs between sustainability dimensions in the supply chain of biodiesel in Colombia. Computers and Electronics in Agriculture.

[39] Rasi,Ehtesha,Reza.(2018). A Cuckoo Search Algorithm Approach for Multi Objective Optimization in Reverse Logistics Network under Uncertainty Condition. International Journal of Supply and Operations Management (IJSOM).Vol.5(1),pp.66-80.
[40] Pellegrino, R., Costantino, N., & Tauro, D. (2019). Supply Chain Finance: A supply chain-oriented perspective to mitigate commodity risk and pricing volatility. Journal of Purchasing and Supply Management.Vol. 25(2), pp.118-133.
[41] Pettersson, A. I., & Segerstedt, A. (2013). Measuring supply chain cost. International Journal of Production Economics.Vol.143(2), pp.357-363.
[42] Pishvaee, M. S., & Rabbani, M. (2011). A graph theoretic-based heuristic algorithm for responsive supply chain network design with direct and indirect shipment. Advances in Engineering Software.Vol.42(3), pp.57-63.
[43] Pishvaee, M. S., & Razmi, J. (2012). Environmental supply chain network design using multi-objective fuzzy mathematical programming. Applied Mathematical Modelling.|Vol.36(8), pp.3433-
3446.
[44] Pishvaee, M.S., Jolai, F. and Razmi, J. (2009). “A stochastic optimization model for integrated forward/reverse logistics network design.” Journal of Manufacturing Systems, Vol. 28, pp. 107-114.
[45] Rafie-Majd, Z., Pasandideh, S. H. R., & Naderi, B. (2018). Modelling and solving the integrated inventory-location-routing problem in a multi-period and multi-perishable product supply chain with uncertainty: Lagrangian relaxation algorithm. Computers & Chemical Engineering.Vol.109, pp.9-22.
[46] Rand, G.K.(1976). Methodological choices in depot location studies. Operational Research Quarterly.Vol. 27, pp.241–249.
[47] Reimann, M., Xiong, Y., & Zhou, Y. (2019). Managing a closed-loop supply chain with process innovation for remanufacturing. European Journal of Operational Research.Vol.276(2), pp.510-518.
[48] Saif-Eddine, A. S., El-Beheiry, M. M., & El-Kharbotly, A. K. (2019). An improved genetic algorithm for optimizing total supply chain cost in inventory location routing problem. Ain Shams Engineering Journal.Vol.10(1), pp.63-76.
[49] Sun, S., Wang, X. (2019). Promoting traceability for food supply chain with certification. Journal of Cleaner Production.Vol. 217,  pp.658-665.
[50] Wang, C. X., Qian, Z., & Zhao, Y. (2018). Impact of manufacturer and retailer's market pricing power on customer satisfaction incentives in supply chains. International Journal of Production
Economics.Vol. 205, pp.98-112.
[51] Wang, X., Guo, H., Yan, R., & Wang, X. (2018). Achieving optimal performance of supply chain under cost information asymmetry. Applied Mathematical Modelling.Vol. 53, pp.523-539.
[52] Wu, T., Zhang, L. G., & Ge, T. (2019). Managing financing risk in capacity investment under green supply chain competition. Technological Forecasting and Social Change.Vol. 143,
pp.37-44.
[53] Yoo, S. H., Kim, D., & Park, M.-S. (2012). Lot sizing and quality investment with quality cost analyses for imperfect production and inspection processes with commercial return. International Journal of Production Economics.Vol.140(2),pp. 922–933.
[54] Zhang, S., Lee, C. K. M., Wu, K., & Choy, K. L. (2016). Multi-objective optimization for sustainable supply chain network design considering multiple distribution channels. Expert Systems with Applications.Vol. 65, pp.87-99.