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A Column Generation Algorithm for a Ship Scheduling Problem
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1969
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Mathematical ProgrammingEngineeringDecomposition AlgorithmColumn Generation AlgorithmBranch And CutOperations ResearchLogisticsSystems EngineeringCombinatorial OptimizationShip Scheduling ProblemOptimizationInteger OptimizationInteger ProgrammingScheduling ProblemProduction SchedulingMixed Integer OptimizationPacking ProblemsScheduling (Production Processes)Linear Programming
The paper presents an algorithm for a ship‑scheduling problem derived from a Swedish shipowning company. The algorithm applies Dantzig–Wolfe decomposition to a ship‑scheduling linear program, solving simple network‑flow subproblems via dynamic programming and a binary‑matrix master LP, with additional integer‑programming experiments to address fractional solutions. Experiments show that fractional solutions occur in only 1–2 % of cases, and instances with ~40 ships and 50 cargoes solve in ~2.5 min on an IBM 7090, with further integer‑programming results pending publication.
This paper describes an algorithm for a ship scheduling problem, obtained from a Swedish shipowning company. The algorithm uses the Dantzig-Wolfe decomposition method for linear programming. The subprograms are simple network flow problems that are solved by dynamic programming. The master program in the decomposition algorithm is an LP problem with only zero-one elements in the matrix and the right-hand side. Integer solutions are not guaranteed, but generation and solution of a large number of problems indicates that the frequency of fractional solutions is as small as 1–2 per cent. Problems with about 40 ships and 50 cargoes are solved in about 2.5 minutes on an IBM 7090. In order to resolve the fractional cases, some integer programming experiments have been made. The results will be reported in a forthcoming paper.