Optimization under uncertainty: generality and application to multimodal transport

Document Type : Research Paper

Authors

1 Euromed University of Fes

2 Normandy University

Abstract

In a realistic environment, operational decision problems involve several sources of uncertainty, due to measurement errors, approximate parameters, or simply the unavailability of information at the time of decision-making. These disturbances are important in the optimization process and must be taken into consideration. To meet these needs, optimization under uncertainty has emerged as an important area of modern operations research and has gained increasing popularity in recent years by tackling complex optimization problems, such as multimodal chain management and container terminals management. In this regard, the present article provides a general overview of the different optimization paradigms and approaches used in the literature to support decision-making in the face of uncertainty. In particular, this article aims to present a state of the art on application of optimization under uncertainty in multimodal transport problems, with a particular focus on the application of Robust Optimization.

Keywords


Abbassi, A., El hilali Alaoui, A., & Boukachour, J. (2019). Robust optimisation of the intermodal freight transport problem: Modeling and solving with an efficient hybrid approach. Journal of computational science, 30, PP.127-142.
 
Aloulou, M. A., Kalaï, R., & Vanderpooten, D. (2005). Une nouvelle approche de robustesse: α-robustesse lexicographique. Bulletin du Groupe de Travail Européen Aide Multicritère à la Décision.
 
Appriou A. (1991). Probabilités et incertitudes en fusion de données multi-senseurs. Revue Scientifique et Technique de la Défense, 11, PP.27–40.
 
Ben-Tal, A., & Nemirovski, A. (1999). Robust solutions of uncertain linear programs. Operations research letters, 25(1), PP.1-13.
 
Bertsimas, D., & Sim, M. (2004). The price of robustness. Operations research, 52(1), pp.35-53.
 
Birge, J. R., & Louveaux, F. (2011). Introduction to stochastic programming. Springer Science & Business Media.
 
Bray, S., Caggiani, L., & Ottomanelli, M. (2015). Measuring transport systems efficiency under uncertainty by fuzzy sets theory based Data Envelopment Analysis: theoretical and practical comparison with traditional DEA model. Transportation Research Procedia, 5, pp.186-200.
 
Bruns, F., Goerigk, M., Knust, S., & Schöbel, A. (2014). Robust load planning of trains in intermodal transportation. OR spectrum, 36(3), PP.631-668.
 
Buckley, J. J., & Eslami, E. (2002). An introduction to fuzzy logic and fuzzy sets (Vol. 13). Springer Science & Business Media.
 
Caris, A., & Janssens, G. K. (2010). A deterministic annealing algorithm for the pre-and endhaulage of intermodal container terminals. International Journal of Computer Aided Engineering and Technology, 2(4), PP.340-355.
 
Charnes, A., & Cooper, W. W. (1959). Chance-constrained programming. Management science, 6(1), PP.73-79.
Cheemakurthy, H., & Garme, K. (2022). Fuzzy AHP-Based Design Performance Index for Evaluation of Ferries. Sustainability, 14(6), 3680.
 
Cheung, R. K., & Chen, C. Y. (1998). A two-stage stochastic network model and solution methods for the dynamic empty container allocation problem. Transportation science, 32(2), PP.142-162.
 
Coco, A. A., Solano-Charris, E. L., Santos, A. C., Prins, C., & de Noronha, T. F. (2014). Robust optimization criteria: state-of-the-art and new issues. Technical Report UTT-LOSI-14001, ISSN: 2266-5064.
 
Correia, I., & da Gama, F. S. (2015). Facility location under uncertainty. In Location science. Springer, Cham. pp. 177-203.
 
Dantzig G. B. (1955), Linear programming under uncertainty. Management Science, 1, pp 179– 206.
 
Dempster J A.P. (1967). Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics, 38, PP.325–339.
 
Ding, D., & Chou, M. C. (2015). Stowage planning for container ships: a heuristic algorithm to reduce the number of shifts. European Journal of Operational Research, 246(1), PP.242-249.
 
Erera, A. L., Morales, J. C., & Savelsbergh, M. (2009). Robust optimization for empty repositioning problems. Operations Research, 57(2), PP.468-483.
 
Ertem, M. A., Akdogan, M. A., & Kahya, M. (2022). Intermodal transportation in humanitarian logistics with an application to a Turkish network using retrospective analysis. International Journal of Disaster Risk Reduction, 72, 102828.
 
Expósito-Izquiero, C., Lalla-Ruiz, E., Lamata, T., Melián-Batista, B., & Moreno-Vega, J. M. (2016). Fuzzy optimization models for seaside port logistics: berthing and quay crane scheduling. In Computational Intelligence Springer, Cham, PP.323-343.
 
Fotuhi, F., & Huynh, N. (2017). Reliable intermodal freight network expansion with demand uncertainties and network disruptions. Networks and Spatial Economics, 17(2), PP.405-433.
 
Gabrel, V., & Murat, C. (2010). Robustness and duality in linear programming. Journal of the Operational Research Society, 61(8), PP.1288-1296.
 
Ghaderi, A., & Rahmaniani, R. (2016). Meta-heuristic solution approaches for robust single allocation p-hub median problem with stochastic demands and travel times. The International Journal of Advanced Manufacturing Technology, 82(9-12), PP.1627-1647.
 
Grossmann, I. E., Apap, R. M., Calfa, B. A., García-Herreros, P., & Zhang, Q. (2016). Recent advances in mathematical programming techniques for the optimization of process systems under uncertainty. Computers & Chemical Engineering, 91, pp.3-14.
 
Guo, W., Atasoy, B., van Blokland, W. B., & Negenborn, R. R. (2021). Anticipatory approach for dynamic and stochastic shipment matching in hinterland synchromodal transportation. Flexible Services and Manufacturing Journal, pp.1-35.
 
Guo, J., Xu, J., He, Z., & Liao, W. (2022). Research on cascading failure modes and attack strategies of multimodal transport network. Journal of Industrial & Management Optimization, 18(1), 397.
 
Heggen, H., Braekers, K., & Caris, A. (2017). An efficient heuristic for multi-objective train load planning: a parameter sensitivity analysis. Proceedings of the International Conference on Harbor Maritime and Multimodal Logistics Modelling and Simulation.
 
Iancu, D. A., & Trichakis, N. (2013). Pareto efficiency in robust optimization. Management Science, 60(1), PP.130-147.
 
Jin, J. G., Lee, D. H., & Hu, H. (2015). Tactical berth and yard template design at container transshipment terminals: A column generation based approach. Transportation Research Part E: Logistics and Transportation Review, 73, PP.168-184.
 
Kahfi, A., Tavakkoli-Moghaddam, R., & Seyed Hosseini, S. M. (2021). Robust Bi-Objective Location-Arc Routing Problem with Time Windows: A Case Study of an Iranian Bank. International Journal of Supply and Operations Management, 8(1), PP.1-17
 
Kouvelis, P., & Yu, G. (2013). Robust discrete optimization and its applications (Vol. 14). Springer Science & Business Media.
 
Lodwick, W. A., & Untiedt, E. (2010). Introduction to fuzzy and possibilistic optimization. In Fuzzy Optimization Springer, Berlin, Heidelberg, pp. 33-62.
 
Lu, B., & Park, N. K. (2013). Sensitivity analysis for identifying the critical productivity factors of container terminals. Journal of Mechanical Engineering, 59(9), pp.536-546.
 
Luhandjula, M. K., & Gupta, M. M. (1996). On fuzzy stochastic optimization. Fuzzy Sets and Systems, 81(1), PP.47-55.
 
Maiyar, L. M., & Thakkar, J. J. (2020). Robust optimisation of sustainable food grain transportation with uncertain supply and intentional disruptions. International Journal of Production Research, 58(18), PP.5651-5675.
 
Meng, Q., & Wang, T. (2010). A chance constrained programming model for short-term liner ship fleet planning problems. Marit. Pol. Mgmt., 37(4), PP.329-346.
 
Meng, Q., Wang, T., & Wang, S. (2012). Short-term liner ship fleet planning with container transshipment and uncertain container shipment demand. European Journal of Operational Research, 223(1), PP.96-105.
 
Meraklı, M., & Yaman, H. (2016). Robust intermodal hub location under polyhedral demand uncertainty. Transportation Research Part B: Methodological, 86, PP.66-85.
 
Min, H. (1991). International intermodal choices via chance-constrained goal programming. Transportation Research Part A: General, 25(6), PP.351-362.
 
Mudchanatongsuk, S., Ordóñez, F., & Liu, J. (2008). Robust solutions for network design under transportation cost and demand uncertainty. Journal of the Operational Research Society, 59(5), PP.652-662.
 
Munim, Z. H., & Haralambides, H. (2018). Competition and cooperation for intermodal container transhipment: A network optimization approach. Research in Transportation Business & Management, 26, PP.87-99.
 
Ordóñez, F., & Zhao, J. (2007). Robust capacity expansion of network flows. Networks: An International Journal, 50(2), PP.136-145.
 
Park, H. J., Cho, S. W., & Lee, C. (2021). Particle swarm optimization algorithm with time buffer insertion for robust berth scheduling. Computers & Industrial Engineering, 160, 107585.
 
Pishvaee, M. S., Rabbani, M., & Torabi, S. A. (2011). A robust optimization approach to closed-loop supply chain network design under uncertainty. Applied Mathematical Modelling, 35(2), PP.637-649.
 
Ries, J., González-Ramírez, R. G., & Miranda, P. (2014, September). A fuzzy logic model for the container stacking problem at container terminals. In International Conference on Computational Logistics. Springer, Cham, PP.93-111.
 
Rodrigues, F., & Agra, A. (2021). An exact robust approach for the integrated berth allocation and quay crane scheduling problem under uncertain arrival times. European Journal of Operational Research, 295(2), PP.499-516.
 
Rouky, N., Boukachour, J., Boudebous, D., & Alaoui, A. E. H. (2018). A Robust Metaheuristic for the Rail Shuttle Routing Problem with Uncertainty: A Real Case Study in the Le Havre Port. The Asian Journal of Shipping and Logistics, 34(2), PP.171-187.
 
Rouky, N., Abourraja, M., Boukachour, J., Boudebous, D., Alaoui, A., & Khoukhi, F. (2019). Simulation optimization based ant colony algorithm for the uncertain quay crane scheduling problem. International Journal of Industrial Engineering Computations, 10(1), PP.111-132.
 
Roy, B. (2010). Robustness in operational research and decision aiding: A multi-faceted issue. European Journal of Operational Research, 200(3), PP.629-638.
 
Ross, T. J. (2009). Fuzzy logic with engineering applications. John Wiley & Sons.
Sahinidis, N. V. (2004). Optimization under uncertainty: state-of-the-art and opportunities. Computers & Chemical Engineering, 28(6-7), PP.971-983.
 
Segura, F. G., Segura, E. L., Moreno, E. V., & Uceda, R. A. (2017, September). A fully fuzzy linear programming model for the berth allocation problem. In Computer Science and Information Systems (FedCSIS), 2017 Federated Conference on pp.453-458. IEEE.
 
Shapiro, A., Dentcheva, D., & Ruszczyński, A. (2009). Lectures on stochastic programming: modeling and theory. Society for Industrial and Applied Mathematics.
 
Shapiro, A., & Philpott, A. (2007). A tutorial on stochastic programming. Manuscript. Available at www2. isye. gatech. edu/ashapiro/publications. html, 17.
 
Shafer, G. (1976). A mathematical theory of evidence. Princeton university press.
Shang, X. T., Cao, J. X., & Ren, J. (2016). A robust optimization approach to the integrated berth allocation and quay crane assignment problem. Transportation Research Part E: Logistics and Transportation Review, 94, PP.44-65.
 
Sharma, G., Sharma, V., Pardasani, K. R., & Alshehri, M. (2020). Soft set based intelligent assistive model for multiobjective and multimodal transportation problem. IEEE Access, 8, pp.102646-102656.
 
Sheikhtajian, S., Nazemi, A., & Feshari, M. (2020). Marine Inventory-Routing Problem for Liquefied Natural Gas under Travel Time Uncertainty. International Journal of Supply and Operations Management, 7(1), PP.93-111.
 
Smets, P., & Kennes, R. (1994). The transferable belief model. Artificial intelligence, 66(2), PP.191-234.
 
Smets, P. (1998). Application of the transferable belief model to diagnostic problems. International journal of intelligent systems, 13(2‐3), PP.127-157.
 
Soyster, A. L. (1973). Convex programming with set-inclusive constraints and applications to inexact linear programming. Operations research, 21(5), PP.1154-1157.
 
Tang, J., Wang, D. W., Fung, R. Y., & Yung, K. L. (2004). Understanding of fuzzy optimization: theories and methods. Journal of Systems Science and Complexity, 17(1), PP.117- 136.
 
Tirkolaee, E. B., & Aydin, N. S. (2022). Integrated design of sustainable supply chain and transportation network using a fuzzy bi-level decision support system for perishable products. Expert Systems with Applications, 195, 116628.
 
Tsang, H. T., & Mak, H. Y. (2015). Robust Optimization Approach to Empty Container Repositioning in Liner Shipping. In Handbook of Ocean Container Transport Logistics pp. 209-229. Springer, Cham.
 
Van Hui, Y., Gao, J., Leung, L., & Wallace, S. (2014). Airfreight forwarder’s shipment planning under uncertainty: A two-stage stochastic programming approach. Transportation Research Part E: Logistics and Transportation Review, 66, PP.83-102.
 
Vis, I. F. (2006). A comparative analysis of storage and retrieval equipment at a container terminal. International Journal of Production Economics, 103(2), PP. 680-693.
 
Wang, C. N., Nhieu, N. L., Tran, K. P., & Wang, Y. H. (2022). Sustainable Integrated Fuzzy Optimization for Multimodal Petroleum Supply Chain Design with Pipeline System: The Case Study of Vietnam. Axioms, 11(2), 60.
 
Wang, B., & Yang, T. (2012). Stochastic optimization of empty container repositioning of sea carriage. In Advanced Materials Research (Vol. 340, pp. 324-330. Trans Tech Publications.
 
Wang, R., Yang, K., Yang, L., & Gao, Z. (2018). Modeling and optimization of a road-rail intermodal transport system under uncertain information. Engineering Applications of Artificial Intelligence, 72, PP.423-436.
 
Wu, Z., Song, T., & Zhao, K. (2006). Selection of Container Shipping Routes [J]. Journal of Southwest Jiaotong University, 41(3), pp. 269-272.
 
Yu, G., & Yang, J. (1998). On the robust shortest path problem. Computers & Operations Research, 25(6), PP.457-468.
 
Zetina, C. A., Contreras, I., Cordeau, J. F., & Nikbakhsh, E. (2017). Robust uncapacitated hub location. Transportation Research Part B: Methodological, 106, PP.393-410.
 
Zhang, H., Yang, K., Gao, Y. and Yang, L., 2022. Accelerating Benders decomposition for stochastic incomplete multimodal hub location problem in many-to-many transportation and distribution systems. International Journal of Production Economics248, p.108493.
 
Zweers, B. G., & van der Mei, R. D. (2022). Minimum costs paths in intermodal transportation networks with stochastic travel times and overbookings. Eu