Dantzig & Fulkerson (1954)Dantzig, G. B., & Fulkerson, D. R. (1954). Minimizing the number of tankers to meet a fixed schedule. Naval Research Logistics Quarterly, 1(3), 217-222. http://dx.doi.org/10.1002/nav.3800010309. http://dx.doi.org/10.1002/nav.3800010309...
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Scheduling of American Navy ships |
Linear optimization |
Flood (1954)Flood, M. M. (1954). Application of transportation theory to scheduling a military tanker fleet. Journal of the Operations Research Society of America, 2(2), 150-162. http://dx.doi.org/10.1287/opre.2.2.150. http://dx.doi.org/10.1287/opre.2.2.150...
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Transportation of oil by an American military fleet |
Linear optimization |
Briskin (1966)Briskin, L. (1966). Selecting delivery dates in the tanker scheduling problem. Management Science, 12(6), 224-235. http://dx.doi.org/10.1287/mnsc.12.6.B224. http://dx.doi.org/10.1287/mnsc.12.6.B224...
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Determination of dates and delivery volumes for oil tankers |
Scheduling with predefined routes |
Appelgren (1969)Appelgren, L. H. (1969). Column generation algorithm for a ship scheduling problem. Transportation Science, 3(1), 53-68. http://dx.doi.org/10.1287/trsc.3.1.53. http://dx.doi.org/10.1287/trsc.3.1.53...
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Assigning loads to ships with cost minimization |
Multi-commodity flow, Dantzig–Wolfe decomposition, and column generation |
Appelgren (1971)Appelgren, L. H. (1971). Integer programming methods for a vessel scheduling problem. Transportation Science, 5(1), 64-78. http://dx.doi.org/10.1287/trsc.5.1.64. http://dx.doi.org/10.1287/trsc.5.1.64...
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Extension of the 1969 article |
Method based on cutting plans and branch-and-bound |
Bellmore et al. (1971)Bellmore, M., Bennington, G., & Lubore, S. (1971). A multivehicle tanker scheduling problem. Transportation Science, 5(1), 36-47. http://dx.doi.org/10.1287/trsc.5.1.36. http://dx.doi.org/10.1287/trsc.5.1.36...
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Extension of the work of Dantzig and Fulkerson (1954)Dantzig, G. B., & Fulkerson, D. R. (1954). Minimizing the number of tankers to meet a fixed schedule. Naval Research Logistics Quarterly, 1(3), 217-222. http://dx.doi.org/10.1002/nav.3800010309. http://dx.doi.org/10.1002/nav.3800010309...
with heterogeneous fleet |
Relaxation of fixed program of visits, decomposition into subgraphs and branch-and-bound |
McKay & Hartley (1974)McKay, M. D., & Hartley, H. O. (1974). Computerized scheduling of seagoing tankers. Naval Research Logistics, 21(2), 255-264. http://dx.doi.org/10.1002/nav.3800210205. http://dx.doi.org/10.1002/nav.3800210205...
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Oil transportation in military ships around the world |
Mixed integer programming and variations with predefined routes |
Ronen (1986)Ronen, D. (1986). Short-term scheduling of vessels for shipping bulk or semi-bulk commodities originating in a single area. Operations Research, 34(1), 164-173. http://dx.doi.org/10.1287/opre.34.1.164. http://dx.doi.org/10.1287/opre.34.1.164...
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Scheduling for short-term for transport of commodities |
Allocation loading algorithms with random bias |
Brown et al. (1987)Brown, G. G., Graves, G. W., & Ronen, D. (1987). Scheduling ocean transportation of crude oil. Management Science, 33(3), 335-346. http://dx.doi.org/10.1287/mnsc.33.3.335. http://dx.doi.org/10.1287/mnsc.33.3.335...
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Oil transportation for export to Europe and the USA from Middle East. |
Model based on set partitioning |
Perakis & Bremer (1992)Perakis, A., & Bremer, W. M. (1992). An operational tanker scheduling optimization system: background, current practice and model formulation. Maritime Policy & Management, 19(3), 177-187. http://dx.doi.org/10.1080/751248659. http://dx.doi.org/10.1080/751248659...
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Scheduling of ships in Chevron company |
Mathematical formula based on Appelgren (1971)Appelgren, L. H. (1971). Integer programming methods for a vessel scheduling problem. Transportation Science, 5(1), 64-78. http://dx.doi.org/10.1287/trsc.5.1.64. http://dx.doi.org/10.1287/trsc.5.1.64...
and construction of a "schedule generator" to build feasible programs |
Haugen (1996)Haugen, K. K. (1996). A Stochastic Dynamic Programming model for scheduling of offshore petroleum fields with resource uncertainty. European Journal of Operational Research, 88(1), 88-100. http://dx.doi.org/10.1016/0377-2217(94)00192-8. http://dx.doi.org/10.1016/0377-2217(94)0...
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Natural gas distribution in Europe |
Stochastic dynamic programming applied to programming projects (Stochastic Project Scheduling Problem) |
Sherali et al. (1999)Sherali, H. D., Al-Yakoob, S. M., & Hassan, M. M. (1999). Fleet management models and algorithms for an oil-tanker routing and scheduling problem. IIE Transactions, 5(31), 395-406. http://dx.doi.org/10.1080/07408179908969843. http://dx.doi.org/10.1080/07408179908969...
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Scheduling oil and natural gas exporters ships in Kuwait |
Based on Brown et al. (1987)Brown, G. G., Graves, G. W., & Ronen, D. (1987). Scheduling ocean transportation of crude oil. Management Science, 33(3), 335-346. http://dx.doi.org/10.1287/mnsc.33.3.335. http://dx.doi.org/10.1287/mnsc.33.3.335...
, presents exact and heuristic method for rolling time horizon |
Christiansen (1999)Christiansen, M. (1999). Decomposition of a combined inventory and time constrained ship routing problem. Transportation Science, 33(1), 3-16. http://dx.doi.org/10.1287/trsc.33.1.3. http://dx.doi.org/10.1287/trsc.33.1.3...
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Problem with pickup and delivery of integrated disposal of ammonia in a Norwegian company |
Mixed integer model method with column generation |
Lasschuit & Thijssen (2004)Lasschuit, W., & Thijssen, N. (2004). Supporting supply chain planning and scheduling decisions in the oil and chemical industry. Computers & Chemical Engineering, 28(6-7), 863-870. http://dx.doi.org/10.1016/j.compchemeng.2003.09.026. http://dx.doi.org/10.1016/j.compchemeng....
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Strategic planning of global supply chain of oil and chemical industry |
Programming nonlinear mixed integer based on GMOS / NetSim |
Persson & Göthe-Lundgren (2005)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. http://dx.doi.org/10.1016/j.ejor.2004.02.008. http://dx.doi.org/10.1016/j.ejor.2004.02...
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Scheduling ships for bitumen runoff |
Mixed integer model with valid inequalities and columns generation |
Al-Khayyal & Hwang (2007)Al-Khayyal, F., & Hwang, S. J. (2007). Inventory constrained maritime routing and scheduling for multi-commodity liquid bulk, Part I: Applications and model. European Journal of Operational Research, 176(1), 106-130. http://dx.doi.org/10.1016/j.ejor.2005.06.047. http://dx.doi.org/10.1016/j.ejor.2005.06...
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Maritime transport of various liquids in bulk |
Programming mixed integer linear and non-linear |
Gribkovskaia et al. (2007)Gribkovskaia, I., Laporte, G., & Shlopak, A. (2007). A tabu search heuristic for a routing problem arising in servicing of offshore oil and gas platforms. The Journal of the Operational Research Society, 59(11), 1449-1459. http://dx.doi.org/10.1057/palgrave.jors.2602469. http://dx.doi.org/10.1057/palgrave.jors....
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Provisioning of oil and gas platforms in the Norwegian Sea |
Constructive heuristics and algorithm based on tabu search |
Rocha et al. (2009)Rocha, R., Grossmann, I. E., & Poggi De Aragão, M. V. S. (2009). Petroleum allocation at PETROBRAS: mathematical model and a solution algorithm. Computers & Chemical Engineering, 33(12), 2123-2133. http://dx.doi.org/10.1016/j.compchemeng.2009.06.017. http://dx.doi.org/10.1016/j.compchemeng....
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Oil allocation to the logistics process of Petrobras |
Programming mixed integer and heuristic based on local search |
Brønmo et al. (2010)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. http://dx.doi.org/10.1016/j.ejor.2008.12.028. http://dx.doi.org/10.1016/j.ejor.2008.12...
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Scheduling pickups and deliveries of ships with load flexibility |
Programming integer with Dantzig-Wolfe decomposition |
Kobayashi & Kubo (2010)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(1), 161-173. http://dx.doi.org/10.1007/s13160-010-0008-7. http://dx.doi.org/10.1007/s13160-010-000...
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Operational scheduling of an oil cabotage fleet in Japan |
Programming integer and heuristics developed by the own authors |
Andersson et al. (2010)Andersson, H., Hoff, A., Christiansen, M., Hasle, G., & Løkketangen, A. (2010). Industrial aspects and literature survey: Combined inventory management and routing. Computers & Operations Research, 37(9), 1515-1536. http://dx.doi.org/10.1016/j.cor.2009.11.009. http://dx.doi.org/10.1016/j.cor.2009.11....
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Bibliographic review of models of inventory routing problem type integrated with inventory management, with emphasis on practical aspects of industrial applications for marine and land modes |
Hoff et al. (2010)Hoff, A., Andersson, H., Christiansen, M., Hasle, G., & Løkketangen, A. (2010). Industrial aspects and literature survey: Fleet composition and routing. Computers & Operations Research, 37(12), 2041-2061. http://dx.doi.org/10.1016/j.cor.2010.03.015. http://dx.doi.org/10.1016/j.cor.2010.03....
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Continuation of the work of Andersson et al. (2010)Andersson, H., Hoff, A., Christiansen, M., Hasle, G., & Løkketangen, A. (2010). Industrial aspects and literature survey: Combined inventory management and routing. Computers & Operations Research, 37(9), 1515-1536. http://dx.doi.org/10.1016/j.cor.2009.11.009. http://dx.doi.org/10.1016/j.cor.2009.11....
, with a focus on studies that integrate routing problems with fleet composition |
Hennig et al. (2012)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. European Journal of Operational Research, 01(218), 764-774. http://dx.doi.org/10.1016/j.ejor.2011.09.046. http://dx.doi.org/10.1016/j.ejor.2011.09...
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pickup and delivery problem with split loads |
Mixed integer programming with pre-generated routes |
Stålhane et al. (2012)Stålhane, M., Andersson, H., Christiansen, M., Cordeau, J.-F., & Desaulniers, G. (2012). A branch-price-and-cut method for a ship routing and scheduling problem with split loads. Computers & Operations Research, 39(12), 3361-3375. http://dx.doi.org/10.1016/j.cor.2012.04.021. http://dx.doi.org/10.1016/j.cor.2012.04....
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pickup and delivery problem with split loads |
Method branch-and-price-and-cut |
Song & Furman (2013)Song, J.-H., & Furman, K. C. (2013). A maritime inventory routing problem: practical approach. Computers & Operations Research, 40(3), 657-665. http://dx.doi.org/10.1016/j.cor.2010.10.031. http://dx.doi.org/10.1016/j.cor.2010.10....
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IRP type models |
Proposal for a flexible framework to guide the applications of models based on IRP with formulation of multi-commodity flow |
Christiansen et al. (2013)Christiansen, M., Fagerholt, K., Nygreen, B., & Ronen, D. (2013). Ship routing and scheduling in the new millennium. European Journal of Operational Research, 228(3), 467-483. http://dx.doi.org/10.1016/j.ejor.2012.12.002. http://dx.doi.org/10.1016/j.ejor.2012.12...
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Recent bibliographic survey of routing problems and scheduling of ships and related problems that illustrate the main areas of the area. |
Agra et al. (2012)Agra, A., Christiansen, M., & Delgado, A. (2012). Mixed integer formulations for a short sea fuel oil distribution problem. Transportation Science, 47(1), 108-204. http://dx.doi.org/10.1287/trsc.1120.0416. http://dx.doi.org/10.1287/trsc.1120.0416...
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Problem of oil distribution of short distance between the islands of the archipelago of Cape Verde |
Mixed integer programming model with search strategies to better limits, extension of formulations and valid inequalities |
Agra et al. (2013a)Agra, A., Andersson, H., Christiansen, M., & Wolsey, L. (2013a). A maritime inventory routing problem: discrete time formulations and valid inequalities. Networks, 62(4), 297-314. http://dx.doi.org/10.1002/net.21518. http://dx.doi.org/10.1002/net.21518...
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Routing of single product inventory problem with variable rates of consumption and production over the planning horizon |
Mixed integer programming model with two discrete formulations and use of relaxations based on sizing to propose valid inequalities |
Agra et al. (2013b)Agra, A., Christiansen, M., Delgado, A., & Simonetti, L. (2013b). Hybrid heuristics for a short sea inventory routing problem. European Journal of Operational Research, 236(3), 924-935. http://dx.doi.org/10.1016/j.ejor.2013.06.042. http://dx.doi.org/10.1016/j.ejor.2013.06...
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Same problem addressed by Agra et al. (2012)Agra, A., Christiansen, M., & Delgado, A. (2012). Mixed integer formulations for a short sea fuel oil distribution problem. Transportation Science, 47(1), 108-204. http://dx.doi.org/10.1287/trsc.1120.0416. http://dx.doi.org/10.1287/trsc.1120.0416...
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Formulation based on arc-load flow with use of valid inequalities and hybrid heuristics (rolling horizon, local branching and feasibility pump) |
Stålhane et al. (2015)Stålhane, M., Andersson, H., & Christiansen, M. (2015). A branch-and-price method for a ship routing and scheduling problem with cargo coupling and synchronization constraints. EURO Journal on Transportation and Logistics, 4(4), 421-443. http://dx.doi.org/10.1007/s13676-014-0061-5. http://dx.doi.org/10.1007/s13676-014-006...
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Pickup and delivery problem with time windows, load combination and synchronized delivery for specialized and unique loads |
Method branch-and-price with subproblem based on a shortest path problem with resource restrictions, solved by dynamic programming |
Rakke et al. (2014)Rakke, J. G., Andersson, H., Christiansen, M., & Desaulniers, G. (2014). A new formulation based on customer delivery patterns for a maritime inventory routing problem. Transportation Science
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Routing problem of inventory for one of the largest global producers of liquefied petroleum gas (LPG) |
Formulation based on the decomposition of the problem for patterns of demand with usage of method branch-price-and-cut |