Column generation approaches to ship scheduling with flexible cargo sizes

We present a Dantzig-Wolfe procedure for the ship scheduling problem with flexible cargo sizes. This problem is similar to the well-known pickup and delivery problem with time windows, but the cargo sizes are defined by an interval instead of a fixed value. We show that the introduction of flexible cargo sizes to the column generation framework is not straightforward, and we handle the flexible cargo sizes heuristically when solving the subproblems. This leads to convergence issues in the branch-and-price search tree, and the optimal solution cannot be guaranteed. Hence we have introduced a method that generates an upper bound on the optimal objective. We have compared our method with an a priori column generation approach, and our computational experiments on real world cases show that the Dantzig-Wolfe approach is faster than the a priori generation of columns, and we are able to deal with larger or more loosely constrained instances. By using the techniques introduced in this paper, a more extensive set of real world cases can be solved either to optimality or within a small deviation from optimalityTransportation; integer programming; dynamic programming

Scheduling participants of Assessment Centres

Assessment Centres are used as a tool for psychologists and coaches to ob- serve a number of dimensions in a person's behaviour and test his/her potential within a number of chosen focus areas. This is done in an intense course, with a number of dierent exercises which expose each participant's ability level in the chosen focus areas. The participants are observed by assessors with the purpose of gathering material for reaching a conclusion on each participant's personal pro le. We consider the particular case that arises at the company Human Equity (www.humanequity.dk), where Assessment Centres usually last two days and involve 3-6 psychologists or trained coaches as assessors. An entire course is composed of a number of rounds, with each round having its individual duration. In each round, the participants are divided into a number of groups with prespeci ed pairing of group sizes and assessors. The scheduling problem amounts to determining the allocation of participants to groups in each round. We have developed a model and solution approach for this particular scheduling problem, which may be viewed as a rather extensive generalization of the Social Golfer Problem.No keywords;

Sustainable maritime crude oil transportation: a split pickup and split delivery problem with time windows

This paper studies a novel sustainable vessel routing problem modeling considering the multi-compartment, split pickup and split delivery, and time windows concepts. In the presented problem, oil tankers transport crude oil from supply ports to demand ports around the globe. The objective is to find ship routes, as well as port arrival and departure times, in a way that minimizes transportation costs. As a second objective, we considered the sustainability aspect by minimizing the vessel energy efficiency operational indicator. Multiple products are transported by a heterogeneous fleet of tankers. Small realistic test instances are solved with the exact method

Modelling of dual-cycle strategy for container storage and vehicle scheduling problems at automated container terminals

This study proposes a new approach to determine the dispatching rules of AGVs and container storage locations, considering both unloading and loading processes simultaneously. We formulate this problem as a mixed integer programming model, aiming to minimise the ship’s berth time. Optimal solutions can be obtained in small sizes, however, large-sized problems are hard to solve optimally in a reasonable time. Therefore, a heuristic method, i.e. genetic algorithm is designed to solve the problem in large sizes. A series of numerical experiments are carried out to evaluate the effectiveness of the integration approach and algorithm

Modelling of integrated vehicle scheduling and container storage problems in unloading process at an automated container terminal

Effectively scheduling vehicles and allocating storage locations for containers are two important problems in container terminal operations. Early research efforts, however, are devoted to study them separately. This paper investigates the integration of the two problems focusing on the unloading process in an automated container terminal, where all or part of the equipment are built in automation. We formulate the integrated problem as a mixed-integer programming (MIP) model to minimise ship’s berth time. We determine the detailed schedules for all vehicles to be used during the unloading process and the storage location to be assigned for all containers. A series of experiments are carried out for small-sized problems by using commercial software. A genetic algorithm (GA) is designed for solving large-sized problems. The solutions from the GA for the small-sized problems are compared with the optimal solutions obtained from the commercial software to verify the effectiveness of the GA. The computational results show that the model and solution methods proposed in this paper are efficient in solving the integrated unloading problem for the automated container terminal