Integrated Production and Distribution Scheduling in Mobile Facilities

Document Type : Research Paper

Authors

Department of Industrial Engineering, K. N. Toosi University of Technology, Tehran, Iran

Abstract

Many supply chains lack flexibility and adaptability in today's competitive market, resulting in customer dissatisfaction, backorders, and several extra costs for the business. Additionally, the inability to quickly meet the customer's demands and the unnecessary transportation costs is also one of the significant challenges faced by the fixed facilities' supply chain. To address these challenges, this study analyzed the mobile facilities supply chain and the production, distribution, and delivery of goods conducted by trucks based on customer preferences. This study proposes a bi-objective mixed-integer linear programming model to ensure the mobile facilities' routing and manufacturing schedules are optimized to meet the customer's needs. Furthermore, this model minimizes production and distribution costs in the shortest amount of time. An exact decomposition algorithm based on Benders decomposition is used to find high-quality solutions in a reasonable amount of time to tackle the problem efficiently. We present several acceleration strategies for increasing the convergence rate of Benders' decomposition algorithm, including Pareto optimality cut and warm-up start. The warm-up start acceleration strategy itself is a meta-heuristic based on particle swarm optimization (PSO). Using the Benders decomposition, we demonstrate the superior accuracy of our solution methodology for large-scale cases with 10 kinds of products ordered by 30 customers using 10 mobile facilities.

Keywords


  • [1] Behzad, A. and Pirayesh, M.A., 2016. Designing supply chain network of mobile factories, 2nd international conference of industrial & systems engineering. https://civilica.com/doc/540369 (In persian)
  • [2] Adulyasak, Y., Cordeau, J.F. and Jans, R., 2015. The production routing problem: A review of formulations and solution algorithms. Computers & Operations Research55, pp.141-152.
  • [3] Fu, L.L., Aloulou, M.A. and Triki, C., 2017. Integrated production scheduling and vehicle routing problem with job splitting and delivery time windows. International Journal of Production Research55(20), pp.5942-5957.
  • [4] Lei, C., Lin, W.H. and Miao, L., 2016. A two-stage robust optimization approach for the mobile facility fleet sizing and routing problem under uncertainty. Computers & Operations Research67, pp.75-89.
  • [5] Halper, R., Raghavan, S. and Sahin, M., 2015. Local search heuristics for the mobile facility location problem. Computers & Operations Research62, pp.210-223.
  • [6] Raghavan, S., Sahin, M. and Salman, F.S., 2019. The capacitated mobile facility location problem. European Journal of Operational Research277(2), pp.507-520.
  • [7] Halper, R. and Raghavan, S., 2011. The mobile facility routing problem. Transportation Science45(3), pp.413-434.
  • [8] Mohammadi, S., Al-e-Hashem, S.M. and Rekik, Y., 2020. An integrated production scheduling and delivery route planning with multi-purpose machines: A case study from a furniture manufacturing company. International Journal of Production Economics219, pp.347-359.
  • [9] Lei, C., Lin, W.H. and Miao, L., 2014. A multicut L-shaped based algorithm to solve a stochastic programming model for the mobile facility routing and scheduling problem. European Journal of Operational Research238(3), pp.699-710.
  • [10] Friggstad, Z. and Salavatipour, M.R., 2011. Minimizing movement in mobile facility location problems. ACM Transactions on Algorithms (TALG)7(3), pp.1-22.
  • [11] Singgih, I.K., 2020, June. Mobile Laboratory Routing Problem for COVID-19 Testing Considering Limited Capacities of Hospitals. In 2020 3rd International Conference on Mechanical, Electronics, Computer, and Industrial Technology (MECnIT)(pp. 80-83). IEEE.
  • [12] Low, C., Chang, C.M., Li, R.K. and Huang, C.L., 2014. Coordination of production scheduling and delivery problems with heterogeneous fleet. International Journal of Production Economics153, pp.139-148.
  • [13] Liu, P. and Lu, X., 2016. Integrated production and job delivery scheduling with an availability constraint. International Journal of Production Economics176, pp.1-6.
  • [14] Soukhal, A., Oulamara, A. and Martineau, P., 2005. Complexity of flow shop scheduling problems with transportation constraints. European Journal of Operational Research161(1), pp.32-41.
  • [15] Hassanzadeh, A., Rasti-Barzoki, M. and Khosroshahi, H., 2016. Two new meta-heuristics for a bi-objective supply chain scheduling problem in flow-shop environment. Applied soft computing49, pp.335-351.
  • [16] Güden, H. and Süral, H., 2019. The dynamic p-median problem with mobile facilities. Computers & Industrial Engineering.
  • [17] Demir, , Eyers, D. and Huang, Y., 2021. Competing through the last mile: Strategic 3D printing in a city logistics context. Computers & Operations Research131, p.105248.
  • [18] Tang, C.S., Veelenturf, L.P., 2019. The strategic role of logistics in the industry 4.0 era. Transportation Research Part E: Logistics and Transportation Review, 129, 1–11.
  • [19] Savelsbergh, M., Van Woensel, T., 2016. 50th anniversary invited article–city logistics: Challenges and opportunities. Transportation Science 50, 579–590.
  • [20] Durocher, S., Kirkpatrick, D., 2006. The steiner centre of a set of points: stability, eccentricity, and applications to mobile facility location. International Journal of Computational Geometry & Applications, 16 (04), 345–371.
  • [21] Bashiri,, Rezanezhad, M., Tavakkoli-Moghaddam, R. and Hasanzadeh, H., 2018. Mathematical modeling for a p-mobile hub location problem in a dynamic environment by a genetic algorithm. Applied Mathematical Modelling, 54, pp.151-169.
  • [22] Shahmoradi-Moghadam, H. and Schönberger, J., 2021. Joint Optimization of Production and Routing Master Planning in Mobile Supply Chains. Operations Research Perspectives, p.100187.
  • [23] Jackson M, Wiktorsson M, Bellgran M. Factory-in-a-box — Demonstrating the next
    generation manufacturing provider. Manuf. Syst. Technol. New Front., London:
    Springer London; 2008, p. 341–6. https://doi.org/10.1007/978-1-84800-267-8_70.
  • [24] Fox S. Reliable Autonomous Production Systems: Combining Industrial Engineering Methods and Situation Awareness Modelling in Critical Realist Design of
    Autonomous Production Systems. Systems 2018;6:26.
    https://doi.org/10.3390/systems6030026.
  • [25] Koren Y, Gu X, Guo W. Reconfigurable manufacturing systems: Principles, design, and future trends. Front Mech Eng 2018;13:121–36. https://doi.org/10.1007/s11465-
    018-0483-0.
  • [26] Antzoulatos N, Castro E, Scrimieri D, Ratchev S. A multi-agent architecture for plug and produce on an industrial assembly platform. Prod Eng 2014;8:773–81.
    https://doi.org/10.1007/s11740-014-0571-x.
  • [27] Moons S, Ramaekers K, Caris A, Arda Y. Integrating production scheduling and
    vehicle routing decisions at the operational decision level: A review and discussion.
    Computers and Industrial Engineering, 2017;104:224–45. https://doi.org/10.1016/j.cie.2016.12.010.
  • [28] Behzad, A., Pirayesh, M. and Ranjbar, M., 2017. Routing and Production Scheduling for a Mobile Factory. International Journal of Industrial Engineering & Production Research28(3), pp.299-308.
  • [29] Ivanov D, Tsipoulanidis A, Schönberger J. Erratum to: Global Supply Chain and
    Operations Management, 2017, p. E1–E1. https://doi.org/10.1007/978-3-319-
    24217-0_15.
  • [30] Shahmoradi-Moghadam H, Samani O, Schönberger J. A Hybrid Robust-Stochastic
    Optimization Approach for the Noise Pollution Routing Problem with a
    Heterogeneous Vehicle Fleet. International Conference Dynamics Logistics, 2020, p. 124–34.
    https://doi.org/10.1007/978-3-030-44783-0_12.
  • [31] Braekers K, Ramaekers K, Van Nieuwenhuyse I. The vehicle routing problem: State of
    the art classification and review. Computers and Industrial Engineering, 2016;99:300–13.
    https://doi.org/10.1016/j.cie.2015.12.007.
  • [32] Fazli Besheli, B., Jahan, A. (2018). 'multi-item multi-objective optimization-location dynamic model with reliability', Advances in Industrial Engineering, 52(3), pp. 445-458. doi: 10.22059/jieng.2019.226472.1314
  • [33] Demaine, E.D., Hajiaghayi, M., Mahini, H., Sayedi-Roshkhar, A.S., Oveisgharan, S. and Zadimoghaddam, M., 2009. Minimizing movement. ACM Transactions on Algorithms (TALG)5(3), pp.1-30.
  • [34] Mohammadi, S., Al-e-Hashem, S.M. and Rekik, Y., 2020. An integrated production scheduling and delivery route planning with multi-purpose machines: A case study from a furniture manufacturing company. International Journal of Production Economics219, pp.347-359.
  • [35] Sağlam, Ü. and Banerjee, A., 2018. Integrated multiproduct batch production and truck shipment scheduling under different shipping policies. Omega74, pp.70-81.
  • [36] Karaoğlan, İ. and Kesen, S.E., 2017. The coordinated production and transportation scheduling problem with a time-sensitive product: a branch-and-cut algorithm. International Journal of Production Research55(2), pp.536-557.
  • [37] Benders, F. (1962). Partitioning procedures for solving mixed-variables programming
    problems. Numerische Mathematik, 4(1), 238–252
  • [38] De Camargo, Ricardo Saraiva, Gilberto de Miranda Jr, and Henrique Pacca L. Luna. "Benders decomposition for hub location problems with economies of scale." Transportation Science1(2009): 86-97.
  • [39] Rebennack, S. “Combining sampling-based and scenario-based nested Benders
    decomposition methods: application to stochastic dual dynamic programming,”
    Program.
    , 156(1–2), pp. 343–389 (2016).
  • [40] Magnanti, T.L. and Wong, R.T., 1981. Accelerating Benders decomposition: Algorithmic enhancement and model selection criteria. Operations Research29(3), pp.464-484.
  • [41] Watson, F.R. and Rogers, D.F., 2006. Pareto-Optimality of the Balinski Cut for the Uncapacitated Facility Location Problem.
  • [42] Geoffrion, A.M., 2010. Lagrangian relaxation for integer programming. In 50 Years of Integer Programming 1958-2008(pp. 243-281). Springer, Berlin, Heidelberg.
  • [43] O’Kelly, M.E., Luna, H.P.L., De Camargo, R.S. and De Miranda, G., 2015. Hub location problems with price sensitive demands. Networks and Spatial Economics15(4), pp.917-945.
  • [44] Contreras, I., Cordeau, J.F. and Laporte, G., 2011. Benders decomposition for large-scale uncapacitated hub location. Operations Research59(6), pp.1477-1490.
  • [45] Easwaran, G. and Üster, H., 2010. A closed-loop supply chain network design problem with integrated forward and reverse channel decisions. IIE Transactions42(11), pp.779-792.
  • [46] Eberhart, R. and Kennedy, J., 1995, November. Particle swarm optimization. In Proceedings of the IEEE International Conference on Neural Networks(Vol. 4, pp. 1942-1948). Citeseer.
  • [47] A. C. Coello, G. T. Pulido and M. S. Lechuga, "Handling multiple objectives with particle swarm optimization," IEEE Transactions on Evolutionary Computation, vol. 8, no. 3, pp. 256-279, June 2004, doi: 10.1109/TEVC.2004.826067.
  • [48] Gong, Y.J., Zhang, J., Liu, O., Huang, R.Z., Chung, H.S.H. and Shi, Y.H., 2011. Optimizing the vehicle routing problem with time windows: A discrete particle swarm optimization approach. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 42(2), pp.254-267.