Michal Penn

Container ship stowage problem: complexity and connection to the coloring of circle graphs

This paper deals with a stowage plan for containers in a container ship. Since the approach to the containers on board the ship is only from above, it is often the case that containers have to be shifted. Shifting is defined as the temporary removal from and placement back of containers onto a stack of containers. Our aim is to find a stowage plan that minimizes the shifting cost. We show that the shift problem is NP-complete. We also show a relation between the stowage problem and the coloring of circle graphs problem. Using this relation we slightly improve Ungers upper bound on the coloring number of circle graphs.

A Genetic Algorithm with a Compact Solution Encoding for the Container Ship Stowage Problem

The purpose of this study is to develop an efficient heuristic for solving the stowage problem. Containers on board a container ship are stacked one on top of the other in columns, and can only be unloaded from the top of the column. A key objective of stowage planning is to minimize the number of container movements. A genetic algorithm technique is used for solving the problem. A compact and efficient encoding of solutions is developed, which reduces significantly the search space. The efficiency of the suggested encoding is demonstrated through an extensive set of simulation runs and its flexibility is demonstrated by successful incorporation of ship stability constraints.

Optimal Allocation of Proposals to Reviewers to Facilitate Effective Ranking

Peer review of research proposals and articles is an essential element in research and development processes worldwide. Here we consider a problem that, to the best of our knowledge, has not been addressed until now: how to assign subsets of proposals to reviewers in scenarios where the reviewers supply their evaluations through ordinal ranking. The solution approach we propose for this assignment problem maximizes the number of proposal pairs that will be evaluated by one or more reviewers. This new approach should facilitate meaningful aggregation of partial rankings of subsets of proposals by multiple reviewers into a consensus ranking. We offer two ways to implement the approach: an integer-programming set-covering model and a heuristic procedure. The effectiveness and efficiency of the two models are tested through an extensive simulation experiment.

Exact and approximate solutions of the container ship stowage problem

Abstract This paper deals with a stowage plan for containers in a container ship. Containers on board a container ship are placed in stacks, located in many bays. Since the access to the containers is only from the top of the stack, a common situation is that contianers designated for port J must be unloaded and reloaded at port I (before J) in order to access containers below them, designated for port I. This operation is called “shifting”. A container ship calling many ports, may encounter a large number of shifting operations, some of which can be avoided by efficient stowage planning. In general, the stowage plan must also take into account stability and strength requirements, as well as several other constraints on the placement of containers. In this paper we deal with stowage planning in order to minimize the number of shiftings, without considering stability constraints. First, a 0–1 binary linear programming formulating is presented that can find the optimal solution for stowage in a single rectangular bay of a vessel calling a given number of ports, assuming that the number of constainers to ship is known in advance. This model was successfully implemented using the GAMS software system. It was found, however, that finding the optimal solution using this model is quite limited, because of the large number of binary variables needed for the formulation. For this reason, several alternative heuristic algorithms were developed. The one presented here is based on a “reduced” transportation matrix. Containers with the same source and destination ports are stowed in full stacks as much as possible, and only the remaining containers are allocated by the binary linear programming model. This approach often allows the stowage planning of a much larger number of containers than using the exact formulation.

Creating a Consensus Ranking of Proposals from Reviewers' Partial Ordinal Rankings

Abstract Peer review of research proposals and articles is an essential element in R&D processes worldwide. In most cases, each reviewer evaluates a small subset of the candidate proposals. The review board is then faced with the challenge of creating an overall “consensus” ranking on the basis of many partial rankings. In this paper we propose a branch-and-bound model to support the construction of an aggregate ranking from the partial rankings provided by the reviewers. In a recent paper we proposed ways to allocate proposals to reviewers so as to achieve the maximum possible overlap among the subsets of proposals allocated to different reviewers. Here, we develop a special branch-and-bound algorithm that utilizes the overlap generated through our earlier methods to enable discrimination in ranking the competing proposals. The effectiveness and efficiency of the algorithm is demonstrated with small numerical examples and tested through an extensive simulation experiment.

NOTE Improved Approximation Algorithms for Weighted 2- and 3-Vertex Connectivity Augmentation Problems

The problem of finding a minimum augmenting edge-set to make a graphk-vertex connected is considered. This problem is denoted as the minimumk-augmentation problem. For weighted graphs, the minimumk-augmentation problem is NP-complete. Our main result is an approximation algorithm with a performance ratio of 3 for solving the minimum 3-augmentation problem. This improves the best previously known performance guarantee of 11/3. We also have the following marginal result: an approximation algorithm for the minimum 2-augmentation problem that achieves a factor of 2, and thus improves the previously known factor of 2+(1/n), withnas the number of vertices in the graph.

Tight integral duality gap in the Chinese Postman problem

AbstractLetG = (V, E) be a graph and letw be a weight functionw:E →Z+. Let

Network Optimization Models for Resource Allocation in Developing Military Countermeasures

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