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Keyword: dynamic programming

paper

A Decomposition Method for Finding Optimal Container Stowage Plans

Roberti, Roberto and Mingozzi, Aristide

In transportation of goods in large container ships, shipping industries need to minimize the time spent at ports to load/unload containers. An optimal stowage of containers on board minimizes unnecessary unloading/reloading movements, while satisfying many operational constraints. We address the basic container stowage planning problem (CSPP). Different heuristics and formulations have been proposed for the CSPP, but finding an optimal stowage plan remains an open problem even for small-sized instances. We introduce a novel formulation that decomposes CSPPs into two sets of decision variables: the first defining how single container stacks evolve over time and the second modeling port-dependent constraints. Its linear relaxation is solved through stabilized column generation and with different heuristic and exact pricing algorithms. The lower bound achieved is then used to find an optimal stowage plan by solving a mixed-integer programming model. The proposed solution method outperforms the methods from the literature and can solve to optimality instances with up to 10 ports and 5,000 containers in a few minutes of computing time.

Transportation Science Vol. 52, No. 6: 1297-1588 / 2018
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paper

A Decomposition Method for Finding Optimal Container Stowage Plans

Roberti, R; Pacino, Dario

In transportation of goods in large container ships, shipping industries need to minimize the time spent at ports to load/unload containers. An optimal stowage of containers on board minimizes unnecessary unloading/reloading movements, while satisfying many operational constraints. We address the basic container stowage planning problem (CSPP). Different heuristics and formulations have been proposed for the CSPP, but finding an optimal stowage plan remains an open problem even for small-sized instances. We introduce a novel formulation that decomposes CSPPs into two sets of decision variables: the first defining how single container stacks evolve over time and the second modeling port-dependent constraints. Its linear relaxation is solved through stabilized column generation and with different heuristic and exact pricing algorithms. The lower bound achieved is then used to find an optimal stowage plan by solving a mixed-integer programming model. The proposed solution method outperforms the methods from the literature and can solve to optimality instances with up to 10 ports and 5,000 containers in a few minutes of computing time.

Transportation Science 52 (6) 1444-1462 / 2018
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paper

The economic speed of an oceangoing vessel in a dynamic setting

Magirou, Evangelos F.; Psaraftis, Harilaos N.; Bouritas, Theodore

The optimal (economic) speed of oceangoing vessels has become of increased importance due to the combined effect of low freight rates and volatile bunker prices. We examine the problem for vessels operating in the spot market in a tramp mode. In the case of known freight rates between origin destination combinations, a dynamic programming formulation can be applied to determine both the optimal speed and the optimal voyage sequence. Analogous results are derived for random freight rates of known distributions. In the case of independent rates the economic speed depends on fuel price and the expected freight rate, but is independent of the revenue of the particular voyage. For freight rates that depend on a state of the market Markovian random variable, economic speed depends on the market state as well, with increased speed corresponding to good states of the market. The dynamic programming equations in our models differ from those of Markovian decision processes so we develop modifications of standard solution methods, and apply them to small examples.

Transportation Research Part B: Methodological, Volume 76 / 2015
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