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A New Ship Scheduling Set Packing Model Considering Limited Risk
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 Title & Authors
A New Ship Scheduling Set Packing Model Considering Limited Risk
Kim, Si-Hwa; Hwang, Hee-Su;
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In this paper, we propose a new ship scheduling set packing model considering limited risk or variance. The set packing model is used in many applications, such as vehicle routing, crew scheduling, ship scheduling, cutting stock and so on. As long as the ship scheduling is concerned, there exits many unknown external factors such as machine breakdown, climate change and transportation cost fluctuation. However, existing ship scheduling models have not considered those factors apparently. We use a quadratic set packing model to limit the variance of expected cost of ship scheduling problems under stochastic spot rates. Set problems are NP-complete, and additional quadratic constraint makes the problems much harder. We implement Kelley's cutting plane method to replace the hard quadratic constraint by many linear constrains and use branch-and-bound algorithm to get the optimal integral solution. Some meaningful computational results and comments are provided.
0-1 integer set packing model;Quadratic programming;Branch-and-cut;Kelley's cut;Limited risk;
 Cited by
Bausch, D. O., Brown, G. G. and Ronen, D. (1998), 'Scheduling Short-Term Maritime Transport of Bulk Products,' Maritime Policy and Management 25, 335-348 crossref(new window)

Christiansen, M., Fagerholt, K. and Ronen, D. (2004), 'Ship routing and scheduling: Status and perspectives', Transportation Science 38(1), 1-18 crossref(new window)

Christiansen, M. and Fagerholt, K. (2002), 'Robust ship scheduling with multiple time windows', Naval Research Logistics 49(6), 611-625 crossref(new window)

Fisher, M. and Rosenwein, M. (1989), 'An interactive optimization system for bulk-cargo ship scheduling', Naval Research Logistics 36, 27-42 crossref(new window)

Fagerholt, K. (2001), 'Ship scheduling with soft time windows: an optimisation based approach', Eur. J. Oper. Res. 13, 559-571

Fagerholt, K. and Christiansen, M. (2000a), 'A combined ship scheduling and allocation problem', J. Oper. Res. Soc. 51(7), 834-842 crossref(new window)

Fagerholt, K. and Christiansen, M. (2000b), 'A travelling salesman problem with allocation, time window and precedence constraints: an application to ship scheduling', Int. Trans. Oper. Res. 7(3), 231-244 crossref(new window)

Kelley, J. E., Jr. (1960), 'The cutting plane method for solving convex programs', J. of the society for Industrial and Applied Mathematics, Vol. 8, No. 4, 703-712 crossref(new window)

Kim, S. and Lee, K. (1997), 'An optimization-based decision support system for ship scheduling', Computers and Industrial Engineering, 33(3-4), 689-692 crossref(new window)

Kim, S. H. (1999), 'Optimization-Based Decision Support System For Maritime Transportation Problems In Tramp Shipping', Ph.D. thesis, Industrial Engieering, Pusan National University, Pusan, South Korea

Mulvey, J., Vanderbei, R. and Zenios, S. (1995) 'Robust optimization of large-scale system'. Operations Research, 43(2):264-281 crossref(new window)

Sharpe, W. F. (1970), 'Portfolio Theory and Capital Markets', McGraw-Hill

Winston, W. L. (1994) 'Operations Research: Applications and Algorithms'. International Thomson Publishing, 3rd ed