A Bi-objective Robust Optimization Model for an Integrated Production-distribution Problem of Perishable Goods with Demand Improvement Strategies: A Case Study

Document Type : Original Article


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


This paper develops a bi-objective optimization model for the integrated production-distribution planning of perishable goods under uncertainty. The first objective seeks to maximize the profit in a specific supply chain with three levels: plants, distribution centers, and in the last level, customers. Since transportation is one of the major pollution sources in a distribution problem, the second objective is to minimize their emission. In the considered problem, the decisions of production, location, inventory, and transportation are made in an integrated structure. In developing the demand function, the effect of the product freshness and the price is formulated. Besides, to encourage customers, three strategies, including perished product return, discount, and credit policies, are proposed. Also, robust optimization is utilized to cope with the operational uncertainty of some cost parameters. To prove the applicability of this research and the feasibility of the environmental aspect, a case study is conducted. Finally, the numerical computations on the case study provide a trade-off between the environmental and economic goals and indicate a 37.5 percent increase in the profit using the developed model.



    1. Kazemi, A., Fazel Zarandi, M. H. and Moattar Husseini, S. M., "A Multi-Agent System to Solve the Production-Distribution Planning Problem for a Supply Chain: A Genetic Algorithm Approach." International Journal of Advanced Manufacturing Technology,Vol.44, No. 1-2, (2009), 180-193, doi: 10.1007/s00170-008-1826-5.
    2. Wei, W., Guimarães, L., Amorim, P. and Almada-Lobo, B., "Tactical Production and Distribution Planning with Dependency Issues on the Production Process." Omega,Vol. 67, (2017), 99-114, doi: 10.1016/j.omega.2016.04.004.
    3. Chen, Z., "Optimization of Production Inventory with Pricing and Promotion Effort for a Single-Vendor Multi-Buyer System of Perishable Products." International Journal of Production Economics, Vol. 203, (2018), 333–49, doi: 10.1016/j.ijpe.2018.06.002.
    4. Amorim, P., Günther, H.O. and Almada-Lobo, B., "Multi-Objective Integrated Production and Distribution Planning of Perishable Products." International Journal of Production Economics, Vol. 138, No. 1, (2012), 89-101, doi: 10.1016/j.ijpe.2012.03.005.
    5. Nahmias, S., "Perishable Inventory Theory: A Review." Operations Research, Vol. 30, No. 4, (1982), 680-708, doi: 10.1287/opre.30.4.680.
    6. Xie, J. and Wei, J.C., "Coordinating Advertising and Pricing in a Manufacturer–Retailer Channel." European Journal of Operational Research, Vol. 197, No. 2, (2009), 785-791, doi: 10.1016/j.ejor.2008.07.014.
    7. Amirtaheri, O., Zandieh, M., Dorri, B. and Motameni, A.R., "A Bi-Level Programming Approach for Production-Distribution Supply Chain Problem." Computers and Industrial Engineering, Vol. 110, (2017), 527-537, doi: 10.1016/j.cie.2017.06.030.
    8. Avinadav, T., Herbon, A. and Spiegel, U., "Optimal Inventory Policy for a Perishable Item with Demand Function Sensitive to Price and Time." International Journal of Production Economics, Vol. 144, No. 2, (2013), 497-506, doi: 10.1016/j.ijpe.2013.03.022.
    9. Esmaili, M. and Sahraeian, R., "A New Bi-Objective Model for a Two-Echelon Capacitated Vehicle Routing Problem for Perishable Products with the Environmental Factor." International Journal of Engineering, Transactions A: Basics, Vol. 30, No. 4, (2017), 523-531, doi: 10.5829/idosi.ije.2017.30.04a.10.
    10. Raa, B., Dullaert, W. and Aghezzaf, E.H., "A Matheuristic for Aggregate Production–Distribution Planning with Mould Sharing." International Journal of Production Economics, Vol. 145, No. 1, (2013), 29-37, doi: 10.1016/j.ijpe.2013.01.006.
    11. Fahimnia, B., Farahani, R.Z., Marian, R. and Luong, L., "A Review and Critique on Integrated Production–Distribution Planning Models and Techniques." Journal of Manufacturing Systems, Vol. 32, No. 1, (2013), 1-19, doi: 10.1016/j.jmsy.2012.07.005.
    12. Ahumada, O. and Villalobos, J.R., "Operational Model for Planning the Harvest and Distribution of Perishable Agricultural Products." International Journal of Production Economics, Vol. 133, No. 2, (2011), 677-687, doi: 10.1016/j.ijpe.2011.05.015.
    13. Fahimnia, B., Luong, L. and Marian, R., "Genetic Algorithm Optimisation of an Integrated Aggregate Production–Distribution Plan in Supply Chains." International Journal of Production Research, Vol. 50, No. 1, (2012), 81-96, doi: 10.1080/00207543.2011.571447.
    14. Amorim, P., Meyr, H., Almeder, C. and Almada-Lobo, B., "Managing Perishability in Production-Distribution Planning: A Discussion and Review." Flexible Services and Manufacturing Journal, Vol. 25, No. 3, (2013), 389-413, doi: 10.1007/s10696-011-9122-3.
    15. Bilgen, B. and Çelebi, Y., "Integrated Production Scheduling and Distribution Planning in Dairy Supply Chain by Hybrid Modelling." Annals of Operations Research, Vol. 211, No. 1, (2013), 55-82, doi: 10.1007/s10479-013-1415-3.
    16. Díaz-Madroñero, M., Peidro, D. and Mula, J., "A Review of Tactical Optimization Models for Integrated Production and Transport Routing Planning Decisions." Computers & Industrial Engineering, Vol. 88, (2015), 518-535, doi: 10.1016/j.cie.2015.06.010.
    17. Makui, A., Heydari, M., Aazami, A., & Dehghani, E., "Accelerating Benders decomposition approach for robust aggregate production planning of products with a very limited expiration date." Computers & Industrial Engineering, Vol. 100, (2016), 34-51, doi: 10.1016/j.cie.2016.08.005.
    18. Fattahi, P., Bashiri, M. and Tanhatalab, M., "Bi-Objectives Approach for a Multi-Period Two Echelons Perishable Product Inventory-Routing Problem with Production and Lateral Transshipment." International Journal of Engineering, Transactions C: Aspects, Vol. 30, No. 6, (2017), 876-886, doi: 10.5829/ije.2017.30.06c.08.
    19. Devapriya, P., Ferrell, W. and Geismar, N., "Integrated Production and Distribution Scheduling with a Perishable Product." European Journal of Operational Research, Vol. 259, No. 3, (2017), 906-916, doi: 10.1016/j.ejor.2016.09.019.
    20. Ensafian, H., and Yaghoubi, S., "Robust optimization model for integrated procurement, production and distribution in platelet supply chain." Transportation Research Part E: Logistics and Transportation Review, Vol. 103, (2017), 32-55, doi: 10.1016/j.tre.2017.04.005.
    21. Guarnaschelli, A., Salomone, H.E. and Méndez, C.A., "A Stochastic Approach for Integrated Production and Distribution Planning in Dairy Supply Chains." Computers and Chemical Engineering, Vol. 140, (2020), doi: 10.1016/j.compchemeng.2020.106966.
    22. Biuki, M., Kazemi, A. and Alinezhad, A., "An Integrated Location-Routing-Inventory Model for Sustainable Design of a Perishable Products Supply Chain Network." Journal of Cleaner Production, Vol. 260, (2020), doi: 10.1016/j.jclepro.2020.120842.
    23. Liu, P., Hendalianpour, A., Razmi, J., and Sangari, M. S., "A solution algorithm for integrated production-inventory-routing of perishable goods with transshipment and uncertain demand." Complex & Intelligent Systems, (2021), 1-17, doi: 10.1007/s40747-020-00264-y.
    24. Bakker, M., Riezebos, J. and Teunter, R.H., "Review of Inventory Systems with Deterioration since 2001." European Journal of Operational Research, Vol. 221, No. 2, (2012), 275-284, doi: 10.1016/j.ejor.2012.03.004.
    25. Coelho, L.C. and Laporte, G., "Optimal Joint Replenishment, Delivery and Inventory Management Policies for Perishable Products." Computers and Operations Research, Vol. 47, (2014), 42-52, doi: 10.1016/j.cor.2014.01.013.
    26. Janssen, L., Claus, T. and Sauer, J., "Literature Review of Deteriorating Inventory Models by Key Topics from 2012 to 2015." International Journal of Production Economics, Vol. 182, (2016), 86-112, doi: 10.1016/j.ijpe.2016.08.019.
    27. Gharehyakheh, A., Krejci, C. C., Cantu, J., and Rogers, K. J., "A Multi-Objective Model for Sustainable Perishable Food Distribution Considering the Impact of Temperature on Vehicle Emissions and Product Shelf Life." Sustainability, Vol. 12, No. 16, (2020), doi: 10.3390/su12166668.
    28. Navazi, F., Sazvar, Z., & Tavakkoli-Moghaddam, R., "A sustainable closed-loop location-routing-inventory problem for perishable products." Scientia Iranica, (2021), doi: 10.24200/SCI.2021.55642.4353.
    29. Bertsimas, D. and Sim, M., "The Price of Robustness." Operations Research, Vol. 52, No. 1, (2004), 35-53, doi: 10.1287/opre.1030.0065.
    30. Aazami, A., and Saidi-Mehrabad, M., "Benders decomposition algorithm for robust aggregate production planning considering pricing decisions in competitive environment: A case study." Scientia Iranica, Vol. 26, No. 5, (2019), 3007-3031, doi: 10.24200/SCI.2018.5563.1346.
    31. Aazami, A., & Saidi-Mehrabad, M., "A production and distribution planning of perishable products with a fixed lifetime under vertical competition in the seller-buyer systems: A real-world application." Journal of Manufacturing Systems, Vol. 58, (2021), 223-247, doi: 10.1016/j.jmsy.2020.12.001.
    32. Kaviyani-Charati, M., Heidarzadeh Souraki, F. and Hajiaghaei-Keshteli, M., "A Robust Optimization Methodology for Multi-Objective Location-Transportation Problem in Disaster Response Phase under Uncertainty." International Journal of Engineering, Transactions B: Applications, Vol. 31, No. 11, (2018), 1953-1961, doi: 10.5829/ije.2018.31.11b.20.
    33. Yanıkoğlu, İ., Gorissen, B.L. and den Hertog, D., "A Survey of Adjustable Robust Optimization." European Journal of Operational Research, Vol. 277, No. 3, (2019), 799-813, doi: 10.1016/j.ejor.2018.08.031.
    34. Beyer, H.G. and Sendhoff, B., "Robust Optimization-a Comprehensive Survey." Computer Methods in Applied Mechanics and Engineering, Vol. 196, No. 33-34, (2007), 3190-3218, doi: 10.1016/j.cma.2007.03.003.
    35. Ben-Tal, A., El Ghaoui, L. and Nemirovski, A., Robust Optimization., Vol. 28, Princeton University Press, (2009), ISBN-13: 978-0691143682.
    36. Nikas, A., Fountoulakis, A., Forouli, A. and Doukas, H., "A Robust Augmented  -Constraint Method (AUGMECON-R) for Finding Exact Solutions of Multi-Objective Linear Programming Problems." Operational Research, (2020), 1-42, doi: 10.1007/s12351-020-00574-6.