The liner-shipping network design problem is to create a set of nonsimple cyclic sailing routes for a designated fleet of container vessels that jointly transports multiple commodities. The objective is to maximize the revenue of cargo transport while minimizing the costs of operation. The potential for making cost-effective and energy-efficient liner-shipping networks using operations research (OR) is huge and neglected. The implementation of logistic planning tools based upon OR has enhanced performance of airlines, railways, and general transportation companies, but within the field of liner shipping, applications of OR are scarce. We believe that access to domain knowledge and data is a barrier for researchers to approach the important liner-shipping network design problem. The purpose of the benchmark suite and the paper at hand is to provide easy access to the domain and the data sources of liner shipping for OR researchers in general. We describe and analyze the liner-shipping domain applied to network design and present a rich integer programming model based on services that constitute the fixed schedule of a liner shipping company. We prove the liner-shipping network design problem to be strongly NP-hard. A benchmark suite of data instances to reflect the business structure of a global liner shipping network is presented. The design of the benchmark suite is discussed in relation to industry standards, business rules, and mathematical programming. The data are based on real-life data from the largest global liner-shipping company, Maersk Line, and supplemented by data from several industry and public stakeholders. Computational results yielding the first best known solutions for six of the seven benchmark instances is provided using a heuristic combining tabu search and heuristic column generation.

The two-dimensional bin-packing problem is the problem of orthogonally packing a given set of rectangles into a minimum number of two-dimensional rectangular bins. The problem is 𝒩𝒫-hard and very difficult to solve in practice as no good mixed integer programming (MIP) formulation has been found for the packing problem. We propose an algorithm based on the well-known Dantzig-Wolfe decomposition where the master problem deals with the production constraints on the rectangles while the subproblem deals with the packing of rectangles into a single bin. The latter problem is solved as a constraint-satisfaction problem (CSP), which makes it possible to formulate a number of additional constraints that may be difficult to formulate as MIP models. This includes guillotine-cutting requirements, relative positions, fixed positions and irregular bins. The CSP approach uses forward propagation to prune inferior arrangements of rectangles. Unsuccessful attempts to pack rectangles into a bin are brought back to the master model as valid inequalities. Hence, CSP is used not only to solve the pricing problem but also to generate valid inequalities in a branch-and-cut system. Using delayed column-generation, we obtain lower bounds of very good quality in reasonable time. In all instances considered, we obtain similar or better bounds than previously published. Several instances with up to n = 100 rectangles are solved to optimality through the developed branch-and-price-and-cut algorithm.

No abstract

 Users may download and print one copy of any publication from the public portal for the purpose of private study or research.  You may not further distribute the material or use it for any profit-making activity or commercial gain  You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.

I n the classical vehicle-routing problem (VRP) the objective is to service some geographically scattered customers with a given number of vehicles at the minimal cost. In the present paper, we consider a variant of the VRP where the vehicles should deliver some goods between groups of customers. The customers have an associated time window, a precedence number, and a quantity. Each vehicle should visit the customers within their time windows, in nondecreasing order of precedence respecting the capacity of the vehicle. The problem will be denoted the pickup-and-delivery problem with time windows and precedence constraints (PDPTWP). The PDPTWP has applications in the transportation of live animals where veterinary rules demand that the livestocks are visited in a given sequence in order not to spread specific diseases. We propose a tighter formulation of the PDPTWP based on Dantzig-Wolfe decomposition. The formulation splits the problem into a master problem, which is a kind of set-covering problem, and a subproblem that generates legal routes for a single vehicle. The LP-relaxation of the decomposed problem is solved through delayed column generation. Computational experiments show that the obtained bounds are less than 0.24% from optimum for the considered problems. As solving the pricing problems takes up the majority of the solution time, a reformulation of the problem is proposed that makes use of the precedence constraints. By merging customers having the same precedence number into "super nodes," the pricing problem may be reformulated as a shortest-path problem defined on an acyclic layered graph. This makes it possible to solve the pricing problem in pseudopolynomial time through dynamic programming. The paper concludes with a comprehensive computational study involving real-life instances from the transportation of live pigs. It is demonstrated that instances with up to 580 nodes can be solved to optimality.