1,606 research outputs found
The Pyramidal Capacitated Vehicle Routing Problem
No full textThis paper introduces the Pyramidal Capacitated Vehicle Routing Problem (PCVRP) as a restricted version of the Capacitated Vehicle Routing Problem (CVRP). In the PCVRP each route is required to be pyramidal in a sense generalized from the Pyramidal Traveling Salesman Problem (PTSP). A pyramidal route is de ned as a route on which the vehicle rst visits customers in increasing order of customer index, and on the remaining part of the route visits customers in decreasing order of customer index. Provided that customers are indexed in nondecreasing order of distance from the depot, the shape of a pyramidal route is such that its traversal can be divided in two parts, where on the rst part of the route, customers are visited in nondecreasing distance from the depot, and on the remaining part of the route, customers are visited in nonincreasing distance from the depot. Such a route shape is indeed found in many optimal solutions to CVRP instances. An optimal solution to the PCVRP may therefore be useful in itself as a heuristic solution to the CVRP. Further, an attempt can be made to nd an even better CVRP solution by solving a TSP, possibly leading to a non-pyramidal route, for each of the routes in the PCVRP solution. This paper develops an exact branch-and-cut-and-price (BCP) algorithm for the PCVRP. At the pricing stage, elementary routes can be computed in pseudo-polynomial time in the PCVRP, unlike in the CVRP. We have therefore implemented pricing algorithms that generate only elementary routes. Computational results suggest that PCVRP solutions are highly useful for obtaining near-optimal solutions to the CVRP. Moreover, pricing of pyramidal routes may due to its eciency prove to be very useful in column generation for the CVRP.vehicle routing; pyramidal traveling salesman; branch-and-cut-and-price
Scheduling participants of Assessment Centres
No full textAssessment 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;
Column generation approaches to ship scheduling with flexible cargo sizes
No full textWe 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
A note on “Multicriteria adaptive paths in stochastic, time-varying networks”
No full textIn a recent paper, Opasanon and Miller-Hooks study multicriteria adaptive paths in stochastic time-varying networks. They propose a label correcting algorithm for finding the full set of efficient strategies. In this note we show that their algorithm is not correct, since it is based on a property that does not hold in general. Opasanon and Miller-Hooks also propose an algorithm for solving a parametric problem. We give a simplified algorithm which is linear in the input size.Multiple objective programming; shortest paths; stochastic time-dependent networks; time-adaptive strategies
Optimal vehicle routing with lower and upper bounds on route durations
No full textThis article is concerned with the problem of finding optimal vehicle routes to minimize the overall travel time, with constraints on the minimum and maximum amount of time spent on each route. The problem extends previous work on the distance-constrained vehicle routing problem by introducing lower bounds on route durations to ensure that the resulting routes are balanced. The article also explicitly addresses the situation where a solution is artificially balanced as a result of inoptimal orders of visits. The article describes alternative ways in which the restrictions on route connectivity, duration, and artificial balancing can be formulated, and introduces an exact algorithm based on cutting planes and mixed-integer linear programming. To the best of our knowledge, this is the first exact algorithm proposed for such a problem that explicitly addresses artificially balanced routes. Computational results are presented for three versions of the exact algorithm using TSPLIB instance
Reachability cuts for the vehicle routing problem with time windows
No full textThis paper introduces a class of cuts, called reachability cuts, for the Vehicle Routing Problem with Time Windows (VRPTW). Reachability cuts are closely related to cuts derived from precedence constraints in the Asymmetric Traveling Salesman Problem with Time Windows and to k-path cuts for the VRPTW. In particular, any reachability cut dominates one or more k-path cuts. The paper presents separation procedures for reachability cuts and reports computational experiments on well-known VRPTW instances. The computational results suggest that reachability cuts can be highly useful as cutting planes for certain VRPTW instances.Routing; time windows; precedence constraints
Robust Branch-Cut-and-Price for the Capacitated Minimum Spanning Tree Problem over a Large Extended Formulation
No full textThis paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The variables are associated to q-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arbores- cence problem in order to make it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used. Moreover, a novel feature is introduced in such kind of algorithms. Powerful new cuts expressed over a very large set of variables could be added, without increasing the complexity of the pricing subproblem or the size of the LPs that are actually solved. Computational results on benchmark instances from the OR-Library show very signi¯cant improvements over previous algorithms. Several open instances could be solved to optimalityNo keywords;
Jens Christian Grøndahl
No full textThis is a short presentation of the main works of the Danish author Jens Christian Grøndahl
Jens August Schade
No full textShort presentation of Danish author Jens August Schade and his main work
Interview with Jens Zimmermann: Author of ‘Hermeneutics: A Very Short Introduction’
No full textDr. Jens Zimmermann is a German-Canadian philosopher and J.I. Packer Professor of Theology at Regent College. As the author of Hermeneutics: A Very Short Introduction, he held a lecture titled “Gadamer, Ricoeur and the Future of Philosophical Hermeneutics” at SFU. Hosted by the Department of World Languages and Literatures, the lecture focused on how we can use the art of hermeneutics to interpret literature and our identities of being human
- …
