Document Type: Original Article

Authors

1 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran.

2 School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran.

Abstract

Non-uniform distribution of customers in a region and variation of their maximum willingness to pay at distinct areas make regional pricing a practical method to maximize the profit of the distribution system. By subtracting the classic objective function, which minimizes operational costs from revenue function, profit maximization is aimed. A distribution network is designed by determining the number of trucks to each established distribution center, allocating customers in routes, and inventory levels of customers. Also, environmental impacts, including fuel consumption and CO2 emission, aimed to be minimized. So, a new quadratic mixed-integer programming model is presented for the Green Transportation Location-Inventory-Routing Problem integrated with dynamic regional pricing problem (GTLIRP+DRP). The model is applied to the real case study, to show its competent application. To tackle this problem, a Hybrid Bees Algorithm (HBA) is developed and verified by the genetic algorithm. Finally, managers suggested using HBA that achieves better solutions in the less computational time.

Keywords

Phillips, R. L. (2005). Pricing and revenue optimization. Stanford University Press.

Ahmadi Javid, A. and Azad, N., (2010). "Incorporating location, routing and inventory decisions in supply chain network design", Transportation Research Part E: Logistics and Transportation Review, Elsevier Ltd, Vol. 46, No. 5, pp. 582–597, DOI: 10.1016/j.tre.2009.06.005.

Ahmadzadeh, E. and Vahdani, B., (2017). "A location-inventory-pricing model in a closed loop supply chain network with correlated demands and shortages under a periodic review system", Computers and Chemical Engineering, Elsevier Ltd, Vol., 101, pp. 148–166.

Bektas, T. and Laporte, G., (2011). "The Pollution-Routing Problem", Transportation Research Part B, Vol. 45, pp. 1232–1250, DOI: 10.1016/j.trb.2011.02.004.

Cheng, C., Yang, P., Qi, M., and Rousseau, L. M., (2017). "Modeling a green inventory routing problem with a heterogeneous fleet", Transportation Research Part E: Logistics and Transportation Review, Vol. 97, pp. 97-112.

Crama, Y., Rezaei, M., Savelsbergh, M., and Woensel, T. V., (2018). Stochastic inventory routing for perishable products. Transportation Science, Vol. 52, No. 3, pp. 526-546.

Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. A. M. T., (2002). "A fast and elitist multiobjective genetic algorithm: NSGA-II", IEEE transactions on evolutionary computation, Vol. 6, No. 2, pp. 182-197.

Eskandarpour, M., Dejax, P., Miemczyk, J., and Péton, O., (2015). "Sustainable supply chain network design: An optimization-oriented review", Omega (United Kingdom), Elsevier, pp. 11–32. DOI: 10.1016/j.omega.2015.01.006.

Etebari, F. and Dabiri, N., (2016). "A hybrid heuristic for the inventory routing problem under dynamic regional pricing", Computers and Chemical Engineering, Elsevier Ltd, Vol. 95, pp. 231–239, DOI: 10.1016/j.compchemeng.2016.09.018.

Farrokhi-Asl, H., Makui, A., Jabbarzadeh, A., and Barzinpour, F., (2018). "Solving a multi-objective sustainable waste collection problem considering a new collection network’, Operational Research, pp. 1–39. doi: 10.1007/s12351-018-0415-0.

Gen, M. and Cheng, R., (1997). Genetic Algorithms and Engineering Design.pdf. wiley.

Gholamian, M.R., Heydari, M., (2017). "An inventory model with METRIC approach in location ‐ routing ‐ inventory problem", Advances in Production Engineering & Management.

Ghorbani, A. and Akbari Jokar, M. R. (2016). "A hybrid imperialist competitive-simulated annealing algorithm for a multisource multi-product location-routing-inventory problem", Computers & Industrial Engineering, Vol. 101, pp. 116–127, DOI: 10.1016/j.cie.2016.08.027.

Govindan, K., Jafarian, A., Khodaverdi, R., and Devika, K., (2014). "Two-echelon multiple-vehicle location-routing problem with time windows for optimization of sustainable supply chain network of perishable food", International Journal of Production Economics, Vol. 152, pp. 9–28, DOI: 10.1016/j.ijpe.2013.12.028.

Guerrero, W. J., Prodhon, C., Velasco, N., and Amaya, C. A., (2013). "hybrid heuristic for the inventory location-routing problem with deterministic demand", Intern. Journal of Production Economics, Vol. 146, pp. 359–370.

Guerrero, W. J., Prodhon, C., Velasco, N., and Amaya, C. A., (2015). "A relax-and-price heuristic for the inventory-location-routing problem", International Transactions in Operational Research, Vol. 22, No. 1, DOI: 10.1111/itor.12091.

Hiassat, A. and Diabat, A., (2011). "A location-inventory-routing-problem with perishable products", in 41st International Conference on Computers and Industrial Engineering 2011.

Hiassat, A., Diabat, A. and Rahwan, I., (2017). "A genetic algorithm approach for location-inventory-routing problem with perishable products", Journal of Manufacturing Systems, The Society of Manufacturing Engineers, Vol. 42, pp. 93–103. doi: 10.1016/j.jmsy.2016.10.004.

Khalili-Damghani, K., Abtahi, A.-R. and Ghasemi, A., (2015). "A New Bi-objective Location-routing Problem for Distribution of Perishable Products: Evolutionary Computation Approach", Journal of Mathematical Modelling and Algorithms in Operations Research, Vol. 14, No. 3, DOI: 10.1007/s10852-015-9274-3.

Lin, C., Choy, K. L., Ho, G. T., Chung, S. H., and Lam, H. Y., (2014). "Survey of Green Vehicle Routing Problem : Past and future trends", Expert Systems with Applications, Vol. 41, pp. 1118–1138, DOI: 10.1016/j.eswa.2013.07.107.

Lin, R. H., (2012). "An integrated model for supplier selection under a fuzzy situation", International Journal of Production Economics, Vol. 138, No. 1, pp. 55–61.

Liu, S. and Chen, J., (2011). "A heuristic method for the inventory routing and pricing problem in a supply chain", Expert Systems With Applications, Elsevier Ltd, Vol. 38, No. 3, pp. 1447–1456, DOI: 10.1016/j.eswa.2010.07.051.

Martínez-Salazar, I. A., Molina, J., Ángel-Bello, F., Gómez, T., and Caballero, R., (2014). "Solving a bi-objective transportation location routing problem by metaheuristic algorithms", European Journal of Operational Research, Vol. 234, No. 1, DOI: 10.1016/j.ejor.2013.09.008.

Navazi, F., Tavakkoli-Moghaddam, R., Sazvar, Z., and Memari, P., (2019). "Sustainable Design for a Bi-level Transportation-Location-Vehicle Routing Scheduling Problem in a Perishable Product Supply Chain’, in Borangiu, T. et al. (eds) Service Orientation in Holonic and Multi-Agent Manufacturing. Cham: Springer International Publishing, pp. 308–321.

Navazi, F., Tavakkoli-Moghaddam, R. and Sazvar, Z., (2018). "A Multi-Period Location-Allocation-Inventory Problem for Ambulance and Helicopter Ambulance Stations: Robust Possibilistic Approach", IFAC-PapersOnLine, Elsevier B.V., Vol. 51, No. 11, pp. 322–327, DOI: 10.1016/j.ifacol.2018.08.303.

Nekooghadirli, N., Tavakkoli-Moghaddam, R., Ghezavati, V. R., and Javanmard, A. S., (2014). "Solving a new bi-objective location-routing-inventory problem in a distribution network by meta-heuristics", Computers & Industrial Engineering, Vol. 76, pp. 204–221, DOI: 10.1016/j.cie.2014.08.004.

Nemmich, M. A., Debbat, F., and Slimane, M., (2019). "A Permutation-Based Bees Algorithm for Solving Resource-Constrained Project Scheduling Problem", International Journal of Swarm Intelligence Research (IJSIR),Vol. 10, No. 4, pp.1-24, DOI:10.4018/IJSIR.2019100101.

Pham, D. T., Ghanbarzadeh, A., Koç, E., Otri, S., Rahim, S., and Zaidi, M.  (2011). "The Bees Algorithm – A Novel Tool for Complex Optimisation Problems", Paper presented at the Intelligent Production Machines and Systems-2nd I* PROMS Virtual International Conference (3-14 July 2006).

Prodhon, C., and Prins, C., (2014). "A survey of recent research on location-routing problems", European Journal of Operational Research, Elsevier B.V., Vol. 238, No. 1, pp. 1–17, DOI: 10.1016/j.ejor.2014.01.005.

Rabbani, M., Navazi, F., Farrokhi-Asl, H., and Balali, M., (2018). "A sustainable transportation-location-routing problem with soft time windows for distribution systems", Uncertain Supply Chain Management, Vol. 6, No. 3, pp. 229–254, DOI: 10.5267/j.uscm.2017.12.002.

Rabbani, M., Farshbaf-geranmayeh, A., and Haghjoo, N., (2016). "Vehicle routing problem with considering multi-middle depots for perishable food delivery", Uncertain Supply Chain Management, 4, pp. 171–182, DOI: 10.5267/j.uscm.2016.3.001.

Rafie-Majd, Z., Pasandideh, S. H. R. and 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 and Chemical Engineering, Elsevier Ltd, 109, pp. 9–22. doi: 10.1016/j.compchemeng.2017.10.013.

Saif-Eddine, A. S., El-Beheiry, M. M., and El-Kharbotly, A. K., (2019)."An improved genetic algorithm for optimizing total supply chain cost in inventory location routing problem", Ain Shams Engineering Journal, Ain Shams University, Vol. 10, No. 1, pp. 63–76, DOI: 10.1016/j.asej.2018.09.002.

Tavakkoli-moghaddam, R., and Raziei, Z., (2016). "A New Bi-Objective Bi-Objective Location-Routing-Inventory Problem with Fuzzy Demands", IFAC-PapersOnLine. Elsevier B.V., Vol. 49, No. 12, pp. 1116–1121, DOI: 10.1016/j.ifacol.2016.07.646.

Taylor, P., Ahmadi-javid, A., and Seddighi, A. H., (2013). "A location-routing-inventory model for designing multisource distribution networks", Engineering Optimization, (February 2013), pp. 37–41.

Nagurney, A., Flores, E. A., and Soylu, C., (2016). "Sustainable design of a closed-loop location-routing-inventory supply chain network under mixed uncertainty", Transportation Research Part E: Logistics and Transportation Review, Vol. 89, pp. 182–214, DOI: 10.1016/j.tre.2016.02.011.

Zhang, Y., Qi, M., Miao, L., and Liu, E., (2014). "Hybrid metaheuristic solutions to inventory location routing problem", Transportation Research Part E: Logistics and Transportation Review, Vol. 70, pp. 305–323, DOI: 10.1016/j.tre.2014.07.010.

Zheng, X., Yin, M., and Zhang, Y., (2019). "Integrated optimization of location, inventory and routing in supply chain network design", Transportation Research Part B: Methodological, Elsevier Ltd, 121, pp. 1–20, DOI: 10.1016/j.trb.2019.01.003.