A Mathematical Modelling and Optimization Approach for a Maritime Facility Location Transshipment Problem

Al-Yakoob, Salem M.; Sherali, Hanif D.

doi:10.15388/Informatica.2018.184

Informatica

A Mathematical Modelling and Optimization Approach for a Maritime Facility Location Transshipment Problem

Volume 29, Issue 4 (2018), pp. 609–632

Salem M. Al-Yakoob Hanif D. Sherali

https://doi.org/10.15388/Informatica.2018.184

Pub. online: 1 January 2018 Type: Research Article

Open Access

Received
1 March 2018

Accepted
1 July 2018

Published
1 January 2018

Abstract

This paper presents an optimization based mathematical modelling approach for a single source single destination crude oil facility location transshipment problem. We began by formulating a mixed-integer nonlinear programming model and use a rolling horizon heuristic to find an optimal location for a storage facility within a restricted continuous region. We next design a hybrid two-stage algorithm that combines judicious facility locations resulting from the proposed model into a previously developed column generation approach. The results indicate that improved overall operational costs can be achieved by strategically determining cost-effective locations of the transshipment facility.

References

Agarwal, R. (2007). Network design and alliance formation for liner shipping. PhD Dissertation, School of Industrial and Systems Engineering: Georgia Institute of Technology, USA.

Aizemberg, L., Kramer, H., Pessoa, A., Uchoa, E. (2014). Formulations for a problem of petroleum transportation. European Journal of Operational Research, 237, 82–90.

Al Khayyal, F., Hwang, S. (2007). Inventory constrained maritime routing and scheduling for multi-commodity liquid bulk. Part I: applications and model. European Journal of Operational Research, 176, 106–130.

Al-Yakoob, S.M., Sherali, H.D. (2013). A column generation approach for determining optimal fleet mix, schedules, and transshipment facility locations for a vessel transportation problem. Applied Mathematical Modeling, 37, 2374–2387.

Andersson, H., Fagerholt, K., Hobbesland, K. (2015). Integrated maritime fleet deployment and speed optimization: case study from RoRo shipping. Computers and Operations Research, 55, 233–240.

Avella, P., Boccia, M., Sforza, A. (2004). Solving a fuel delivery problem by heuristic and exact approaches. European Journal of Operational Research, 152(1), 170–179.

Aykin, T., Brown, G.F. (1992). Interacting new facilities and location-allocation problems. Transportation Science, 26, 212–222.

Brønmo, G., Nygreen, B., Lysgaard, J. (2010). Column generation approaches to ship scheduling with flexible cargo sizes. European Journal of Operational Research, 200(1), 139–150.

Christiansen, M., Fagerholt, K., Ronen, D. (2004). Ship routing and scheduling: status and prospective. Transportation Science, 38(1), 1–18.

Christiansen, M., Fagerholt, K. (2009). Maritime inventory routing problems. In: Floudas, C.A., Pardalos, P.M. (Eds.), Encyclopedia of Optimization, pp. 1947–1955.

Christiansen, M., Fagerholt, K., Nygreen, B., Ronen, D. (2013). Ship routing and scheduling in the new millennium. European Journal of Operational Research, 228, 467–483.

Cornillier, F., Boctor, F.F., Laporte, G., Renaud, J. (2008a). An exact algorithm for the petrol station replenishment problem. Journal of the Operational Research Society, 59(5), 607–615.

Cornillier, F., Boctor, F.F., Laporte, G., Renaud, J. (2008b). A heuristic for the multi-period petrol station replenishment problem. European Journal of Operational Research, 191(2), 295–305.

Cornillier, F., Boctor, F.F., Laporte, G., Renaud, J. (2009). The petrol station replenishment problem with time windows. Computers and Operations Research, 36(3), 919–935.

Drezner, Z., Hamacher, H.W. (2004). Facility Location: Applications and Theory. Springer-Verlag, Berlin.

Fagerholt, K., Christiansen, M. (2000a). A combined ship scheduling and allocation problem. Journal of the Operational Research Society, 51(7), 834–842.

Fagerholt, K., Christiansen, M. (2000b). A traveling salesman problem with allocation time window and precedence constraints – an application to ship scheduling. International Transactions in Operational Research, 7(3), 231–244.

Furman, K.C., Song, J., Kocis, J.R., McDonald, M.K., Warrick, P.H. (2011). Feedstock routing in the ExxonMobil downstream sector. Interfaces, 41(2), 149–163.

Halvorsen-Weare, E.E., Fagerholt, K., Nonas, L.M., Asbjønslett, B.E. (2012). Optimal fleet composition and periodic routing of offshore supply vessels. European Journal of Operational Research, 223, 508–517.

Hennig, F., Furman, K.C., Kocis, G.R., Nygreen, B., Song, J. (2011). Crude oil tanker routing and scheduling. Information Systems and Operational Research, 49, 153–170.

Hennig, F., Nygreen, B., Christiansen, M., Fagerholt, K., Furman, K.C., Song, J., Kocis, G.R., Warrick, P.H. (2012). Maritime crude oil transportation – a split pickup and split delivery problem. Journal of the Operational Research Society, 218, 764–774.

Hennig, F., Nygreen, B., Furman, K.C., Song, J. (2015). Alternative approaches to the crude oil tanker routing and scheduling problem with split pickup and split delivery. European Journal of Operational Research, 243, 41–51.

Hoff, A., Andersson, H., Christiansen, M., Hasle, G., Løkketangen, A. (2010). Industrial aspects and literature survey: fleet composition and routing. Computers and Operations Research, 37, 2041–2061.

Hvattum, L.M., Fagerholt, K., Armentan, V.A. (2009). Tank allocation problems in maritime bulk shipping. Computers and Operations Research, 36(11), 3051–3060.

Kobayashi, K., Kubo, M. (2010). Optimization of oil tanker schedules by decomposition, column generation, and time-space network techniques. Japan Journal of Industrial and Applied Mathematics, 27, 161–173.

Li, C.L., Pang, K.W. (2011). An integrated model for ship routing and berth allocation. International Journal of Shipping and Transport Logistics, 3, 245–260.

Malépart, V., Boctor, F.F., Renaud, J., Labilois, S. (2003). Nouvelles approches pour l’approvisionnement des stations d’essence. Revue Française de Gestion Industrielle, 22, 15–31.

Ng, W., Leung, S., Lam, J., Pan, S. (2008). Petrol delivery tanker assignment and routing: a case study in Hong Kong. Journal of the Operational Research Society, 59(9), 1191–1200.

Pang, K., Li, C. (2011). Constraint programming based column generation heuristics for a ship routing and berthing time assignment problem. In: Proceedings of the 2011 International Conference on Industrial Engineering and Operations Management. Kuala Lumpur, Malaysia, pp. 22–24.

Pang, K.W., Xu, Z., Li, C.L. (2011). Ship routing problem with berthing time clash avoidance constraints. International Journal of Production Economics, 131, 752–762.

Pantuso, G., Fagerholt, K., Hvattum, L.M. (2014). A survey on maritime fleet size and mix problems. Journal of the Operational Research Society, 235, 341–349.

Persson, J.A., Göthe-Lundgren, M. (2005). Shipment planning at oil refineries using column generation and valid inequalities. European Journal of Operational Research, 163(3), 631–652.

Rodrigue, J.P., Comtois, C., Slack, B. (2017). The Geography of Transport Systems, 4th ed. Taylor & Francis, New York.

Ronen, D. (1983). Cargo ships routing and scheduling: survey of models and problems. European Journal of Operational Research, 12(2), 119–126.

Ronen, D. (1993). Ship scheduling: the last decade. European Journal of Operational Research, 71(3), 325–333.

Ronen, D. (2002). Marine inventory routing: shipment planning. Journal of the Operational Research Society, 53(1), 108–114.

Sherali, H.D., Adams, W.P. (1984). A decomposition algorithm for a discrete location-allocation problem. Operations Research, 32(4), 878–900.

Sherali, H.D., Smith, J.C. (2001). Improving discrete model representations via symmetry considerations. Management Science, 47(10), 1396–1407.

Sherali, H.D., Al-Yakoob, S.M. (2006a). Determining an optimal fleet mix and schedules. Part I: single source and destination. In: Karlof, J. (Ed.), Integer Programming: Theory and Practice. Taylor and Francis Group, pp. 137–166.

Sherali, H.D., Al-Yakoob, S.M. (2006b). Determining an optimal fleet mix and schedules. Part II: multiple sources and destinations, and the option of leasing transshipment depots. In: Karlof, J. (Ed.), Integer Programming: Theory and Practice. Taylor and Francis Group, pp. 167–193.

Sherali, H.D., Adams, W.P., Driscoll, P.J. (1998). Exploiting special structures in constructing a hierarchy of relaxations for 0-1 mixed integer problems. Operations Research, 46(3), 396–405.

Shetty, C.M., Sherali, H.D. (1977). Rectilinear distance location-allocation problem: a simplex based algorithm. Economics and Mathematical Systems, Extremal Methods and Systems Analysis, 174, 442–464.

Song, J., Furman, K. (2013). A maritime inventory routing problem: practical approach. Computers and Operations Research, 40(3), 657–665.

Soroush, H.M., Al-Yakoob, S.M. (2018). A Maritime scheduling transportation-inventory problem with normally distributed demands and fully loaded/unloaded vessels. Applied Mathematical Modeling, 53, 540–566.

Taqa-allah, D., Renaud, J., Boctor, F.F. (2000). Le problème d’approvisionnement des stations d’essence. APII-JESA. Journal Européen des Systémes Automatisés, 34, 11–33.

Trade Map (2017). Trade Statistics for International Business Development. International Trade Center, World Trade Organization and United Nations. http://www.trademap.org/Index.aspx.

Xinlian, X., Tangfei, W., Daisong, C. (2000). A dynamic model and algorithm for fleet planning. Maritime Policy and Management, 27(1), 53–63.

Biographies

Al-Yakoob Salem M.

salem@al-yakoob.com

S. Al-Yakoob is an associate professor at the Department of Mathematics at Kuwait University. His research interests include mathematical programming and optimization with applications to real world problems such as location, transportation, scheduling, and timetabling problems.

Sherali Hanif D.

hanifs@vt.edu

H.D. Sherali is a university distinguished professor emeritus in the Industrial and Systems Engineering Department at Virginia Polytechnic Institute and State University. His areas of research interest are in mathematical optimization modelling, analysis, and design of algorithms for specially structured linear, nonlinear, and continuous and discrete nonconvex programs, with applications to transportation, location, engineering and network design, production, economics, and energy systems. He has published over 349 refereed articles in various operations research journals and has (co-) authored nine books, with a total Google Scholar citation count of over 31,788 and an H-index of 68. He is an elected member of the National Academy of Engineering, a fellow of both INFORMS and IIE, and a member of the Virginia Academy of Science Engineering and Medicine.

Full article Related articles Cited by

Open access article under the CC BY license.

Keywords

mixed-integer programming vessel scheduling transportation inventory

Metrics

since January 2020

1245 Article info views	627 Full article views
562 PDF downloads	242 XML downloads

RSS

Authors

Abstract

References

Biographies

Export citation

Copy and paste formatted citation

Download citation in file