Matias Sevel Rasmussen

Bio: Matias Sevel Rasmussen is an academic researcher from Technical University of Denmark. The author has contributed to research in topics: Column generation & Vehicle routing problem. The author has an hindex of 4, co-authored 6 publications receiving 403 citations.

The vehicle routing problem with time windows and temporal dependencies

Abstract: In this article, we formulate the vehicle routing problem with time windows and temporal dependencies. The problem is an extension of the well studied vehicle routing problem with time windows. In addition to the usual constraints, a scheduled time of one visit may restrain the scheduling options of other visits. Special cases of temporal dependencies are synchronization and precedence constraints. Two compact formulations of the problem are introduced and the Dantzig–Wolfe decompositions of these formulations are presented to allow for a column generation-based solution approach. Temporal dependencies are modeled by generalized precedence constraints. Four different master problem formulations are proposed and it is shown that the formulations can be ranked according to the tightness with which they describe the solution space. A tailored time window branching is used to enforce feasibility on the relaxed master problems. Finally, a computational study is performed to quantitatively reveal strengths and weaknesses of the proposed formulations. It is concluded that, depending on the problem at hand, the best performance is achieved either by relaxing the generalized precedence constraints in the master problem, or by using a time-indexed model, where generalized precedence constraints are added as cuts when they become severely violated. © 2011 Wiley Periodicals, Inc. NETWORKS, Vol. 58(4), 273–289 2011 © 2011 Wiley Periodicals, Inc.

The Home Care Crew Scheduling Problem

Abstract: In the Home Care Crew Scheduling Problem (HCCSP) a staff of caretakers has to be assigned a number of tasks, such that the total number of assigned tasks is maximised. The tasks have different locations and positions in time, and travelling time and time windows must be respected. The challenge when assigning tasks to caretakers lies in the existence of several soft constraints and indeed also in timewise constraints connecting the tasks. Preferably all of these constraints are satisfied, however for different reasons, this is not always possible. We call a solution to the problem home care optimal, if it satisfies all soft constraints. The problem originates from the scheduling of tasks in the home care sector and has many similarities with the well-studied Vehicle Routing Problem with Time Windows (VRPTW) and the Crew Scheduling Problem with Time Windows (CSPTW). Former approaches to solving the HCCSP involve the use of heuristic methods. In this thesis, we will show that by using an exact algorithm as the basis and then modifying this intelligently, it is possible to generate home care optimal solutions which are in general better than the solutions found by the use of heuristics. The thesis constitutes a proof-of-concept and only focuses on the efficiency of the algorithm to some extent. The developed exact algorithm is based on a branch-and-price approach using column generation. The algorithm is tested on real-life problem instances supplied by the Danish company Zealand Care and we obtain solutions that are near to home care optimal in most cases. The problem is decomposed into a master and a subproblem. We model a very general precedence constraint that captures all timewise constraints from real-life, and we handle precedence constraints in the branching, which we have not seen elsewhere in the literature. We devise an exact label setting algorithm for solving the Elementary Shortest Path Problem with Resource Constraints (ESPPRC) subproblem. Solving the subproblem constitutes a substantial impact on the overall running time of the branch-and-price algorithm. To counteract this, intelligent reductions of the ESPPRC networks are introduced. When reducing the ESPPRC networks, the number of unassigned tasks may increase, hence the branch-and-price algorithm is extended to handle tasks that are unassigned as a consequence of the reductions of the ESPPRC networks. The reductions in the ESPPRC networks and the changes to the branchand-price algorithm result in improvements of both the quality of the solutions, many of which are close to being home care optimal, and the overall efficiency of the algorithm.

Subsequence Generation for the Airline Crew Pairing Problem

Abstract: Good and fast solutions to the airline crew pairing problem are highly interesting for the airline industry, as crew costs are the biggest expenditure after fuel for an airline. The crew pairing problem is typically modelled as a set partitioning problem and solved by column generation. However, the extremely large number of possible columns naturally has an impact on the solution time. In the solution method of this work we severely limit the number of allowed subsequent flights, i.e. the subsequences, thereby significantly decreasing the number of possible columns. Set partitioning problems with limited subsequence counts are known to be easier to solve, resulting in a decrease in solution time. The problem though, is that a small number of deep subsequences might be needed for an optimal or near-optimal solution and these might not have been included by the subsequence limitation. Therefore, we try to identify or generate such subsequences that potentially can improve the solution value. We benchmark the subsequence generation approach against a classical column generation approach on real-life test instances. We consider the LP relaxation and compare the quality and the integrality of the solutions. The LP solutions from the subsequence generation approach are less fractional, but it comes at the cost of a worse solution quality. ∗Corresponding author: E-mail: jesla@man.dtu.dk. Address: Department of Management Engineering, Technical University of Denmark, Produktionstorvet, Building 424, DK-2800 Kgs. Lyngby, Denmark. Tel.: +45-45253385. Fax: +45-45933435.

An IP Framework for the Crew Pairing Problem Using Subsequence Generation

Abstract: In this paper we consider an important problem for the airline industry. The widely studied crew pairing problem is typically formulated as a set partitioning problem and solved using the branchand-price methodology. Here we develop a new integer programming framework, based on the concept of subsequence generation, for solving the set partitioning formulation. In subsequence generation one restricts the number of permitted subsequent flights, that a crew member can turn to after completing any particular flight. By restricting the number of subsequences, the number of pairings in the problem decreases. The aim is then to dynamically add attractive subsequences to the problem, thereby increasing the number of possible pairings and improving the solution quality. Encouraging results are obtained on 19 real-life instances supplied by Air New Zealand and show that the described methodology is a viable alternative to column generation.

A comprehensive taxonomy for multi-robot task allocation

Abstract: Task allocation is an important aspect of many multi-robot systems. The features and complexity of multi-robot task allocation (MRTA) problems are dictated by the requirements of the particular domain under consideration. These problems can range from those involving instantaneous distribution of simple, independent tasks among members of a homogenous team, to those requiring the time-extended scheduling of complex interrelated multi-step tasks for members of a heterogenous team related by several constraints. The existing widely used taxonomy for task allocation in multi-robot systems was designed for problems with independent tasks and does not deal with problems with interrelated utilities and constraints. While that taxonomy was a ground-breaking contribution to the MRTA literature, a survey of recent work in MRTA reveals that it is no longer a sufficient taxonomy, due to the increasing importance of interrelated utilities and constraints in realistic MRTA problems under consideration. Thus, in this paper, we present a new, comprehensive taxonomy, iTax, that explicitly takes into consideration the issues of interrelated utilities and constraints. Our taxonomy maps categories of MRTA problems to existing mathematical models from combinatorial optimization and operations research, and hence draws important parallels between robotics and these fields.