Johan Oppen | Searcharxiv

arXiv2016

The matching relaxation for a class of generalized set partitioning problems

This paper introduces a discrete relaxation for the class of combinatorial optimization problems which can be described by a set partitioning formulation under packing constraints. We present two combinatorial relaxations based on computing maximum weighted matchings in suitable graphs. Besides providing dual bounds, the relaxations are also used on a variable reduction technique and a matheuristic. We show how that general method can be tailored to sample applications, and also perform a successful computational evaluation with benchmark instances of a problem in maritime logistics.

cs.DS↗

arXiv2016

A Decomposition Approach to Solve The Quay Crane Scheduling Problem

In this work we propose a decomposition approach to solve the quay crane scheduling problem. This is an important maritime transportation problem faced in container terminals where quay cranes are used to handle cargo. The objective is to determine a sequence of loading and unloading operations for each crane in order to minimize the completion time. We solve a mixed integer programming formulation for the quay crane scheduling problem, decomposing it into a vehicle routing problem and a corresponding scheduling problem. The routing sub-problem is solved by minimizing the longest crane completion time without taking crane interference into account. This solution provides a lower bound for the makespan of the whole problem and is sent to the scheduling sub-problem, where a completion time for each task and the makespan are determined. This scheme resembles Benders' decomposition and, in particular, the scheme underlying combinatorial Benders' cuts. We evaluate the proposed approach by solving instances from the literature and comparing the results with other available methods.

math.OC↗