A Column Generation Algorithm for a Ship Scheduling Problem

Appelgren, Leif

doi:10.1287/trsc.3.1.53

Cited by 127 publications

(59 citation statements)

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“…McKay and Hartley used binary route selection variables (an approach similar to the one taken here), but employed continuous solutions and an approximate heuristic. Similar, nonmilitary ship scheduling problems were dealt with by Laderman, Gleiberman and Egan (1966) who tried to minimize the number of ships used, Rao and Zionts (1968) and Dantzig, Blattner and Rao (1967) who tried to minimize operating and chartering costs, and Appelgren (1969Appelgren ( , 1971) who maximized profit contribution of optional cargos.…”

Section: Problem Formulationmentioning

confidence: 99%

Scheduling Ocean Transportation of Crude Oil

1987

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A crude oil tanker scheduling problem faced by a major oil company is presented and solved using an elastic set partitioning model. The model takes into account all fleet cost components, including the opportunity cost of ship time, port and canal charges, and demurrage and bunker fuel. The model determines optimal speeds for the ships and the best routing of ballast (empty) legs, as well as which cargos to load on controlled ships and which to spot charter. All feasible schedules are generated, the cost of each is accurately determined and the best set of schedules is selected. For the problems encountered, optimal integer solutions to set partitioning problems with thousands of binary variables have been achieved in less than a minute.transportation: planning, set partitioning, enumerative methods

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Section: Problem Formulationmentioning

confidence: 99%

Scheduling Ocean Transportation of Crude Oil

1987

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“…Early, classical, applications of this strategy include economic lot sizing ( [60]), the cutting stock problem ( [32,33]), and ship scheduling and routing ( [1,2]). The probably most widely known column generation method is the Dantzig-Wolfe decomposition method ( [18,19]) for block-angular linear programs.…”

Section: Background and Motivationmentioning

confidence: 99%

A generic column generation principle: derivation and convergence analysis

2015

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Given a non-empty, compact and convex set, and an a priori defined condition which each element either satisfies or not, we want to find an element belonging to the former category. This is a fundamental problem of mathematical programming which encompasses nonlinear programs, variational inequalities, and saddle-point problems.We present a conceptual column generation scheme, which alternates between solving a restriction of the original problem and a column generation phase which is used to augment the restricted problems. We establish the general applicability of the conceptual method, as well as to the three problem classes mentioned. We also establish a version of the conceptual method in which the restricted and column generation problems are allowed to be solved approximately, and of a version allowing for the dropping of columns.We show that some solution methods (e.g., Dantzig-Wolfe decomposition and simplicial decomposition) are special instances, and present new convergent column generation methods in nonlinear programming, such as a sequential linear programming (SLP) type method. Along the way, we also relate our quite general scheme in nonlinear programming presented in this paper with several other classic, and more recent, iterative methods in nonlinear optimization.

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“…Because all x i are integral and bounded, the principles of Dantzig-Wolfe decomposition apply (Dantzig and Wolfe [22]), as extended to integer programs by Appelgren [4]. (See Wolsey [60], Section 11.2, for a comprehensive discussion.)…”

Section: I∈imentioning

confidence: 99%

Solving a class of stochastic mixed-integer programs with branch and price

Silva¹,

Wood

2006

Math. Program.

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Abstract. We begin this paper by identifying a class of stochastic mixed-integer programs that have column-oriented formulations suitable for solution by a branch-and-price algorithm (B&P). We then survey a number of examples, and use a stochastic facility-location problem (SFLP) for a detailed demonstration of the relevant modeling and solution techniques. Computational results with a scenario representation of uncertain costs, demands and capacities show that B&P can be orders of magnitude faster than solving the standard formulation by branch and bound. We also demonstrate how B&P can solve SFLP exactly -as exactly as a deterministic mixed-integer program -when demands and other parameters can be represented as certain types of independent, random variables, e.g., independent, normal random variables with integer means and variances.

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A Column Generation Algorithm for a Ship Scheduling Problem

Cited by 127 publications

References 1 publication

Scheduling Ocean Transportation of Crude Oil

Scheduling Ocean Transportation of Crude Oil

A generic column generation principle: derivation and convergence analysis

Solving a class of stochastic mixed-integer programs with branch and price

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