An asymptotic approximation scheme for the concave cost bin packing problem

Department of Logistics2008-2009 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

The Generalized Bin Packing Problem

In the Generalized Bin Packing Problem a set of items characterized by volume and profit and a set of bins of different types characterized by volume and cost are given. The goal consists in selecting those items and bins which optimize an objective function which combines the cost of the used bins and the profit of the selected items. We propose two methods to tackle the problem: branch-and-price as an exact method and beam search as a heuristics, derived from the branch-and-price. Our branch-and-price method is characterized by a two level branching strategy. At the first level the branching is performed on the number of available bins for each bin type. At the second level it consists on pairs of items which can or cannot be loaded together. Exploiting the branch-and-price skeleton, we then present a variegated beam search heuristics, characterized by different beam sizes. We finally present extensive computational results which show a high accuracy of the exact method and a very good efficiency of the proposed heuristics

Flexible Stock Allocation and Trim Loss Control for Cutting Problem in the Industrial-Use Paper Production

We consider a one-dimensional cutting stock problem (CSP) in which the stock widths are not used to fulfill the order but kept for use in the future for the industrial-use paper production. We present a new model based on the flexible stock allocation and trim loss control to determine the production quantity. We evaluate our approach using a real data and show that we are able to solve industrial-size problems, while also addressing common cutting considerations such as aggregation of orders, multiple stock widths, and cutting different patterns on the same machine. In addition, we compare our model with others, including trim loss minimization problem (TLMP) and cutting stock problem (CSP). The results show that the proposed model outperforms the other two models regarding total flexibility and trim loss ratio

Desenvolvimento de protótipo de consolidação bidimensional de carga

O setor dos transportes e logística onde os transitários se inserem, constitui uma vasta rede de indivíduos fulcral para um bom desempenho nos serviços prestados. Com a pandemia da COVID-19 e os seus efeitos a assolar a economia global, verificouse uma enorme escassez no número de contentores disponíveis face à procura do mercado, surgindo assim a necessidade de otimizar o carregamento dos equipamentos disponíveis como forma de evitar desperdícios e maximizar os proveitos em cada exportação. O presente trabalho visa o desenvolvimento de um protótipo com recurso a heurísticas já abordadas para problemas semelhantes e assim aumentar os lucros na Justlog. Para isso, foram criadas um conjunto de restrições que aplicadas em sinergia com o algoritmo GRG Não Linear, visam alocar as caixas em diferentes linhas consecutivas até formar uma parede, e, por conseguinte, essas paredes completarem o contentor. No final, foram apresentados 3 casos distintos nos quais o protótipo foi colocado em prática como forma de testar a sua utilidade, entre os quais foram criadas soluções de parede cujas ocupações rondam os 80% a 90% em situações reais ou de grande heterogeneidade entre caixas. Assim, podemos perspetivar uma grande utilidade futura deste protótipo nas tomadas de decisão relativas a serviços de consolidação de contentores, prestados pela Justlog.The transport and logistics sector, where freight forwarders are inserted, constitutes a vast network of individuals that is central to a good performance in the services provided. With the COVID-19 pandemic and its effects ravaging the global economy, there was a huge shortage in the number of containers available in the face of market demand, thus creating the need to optimize the loading of available equipment to avoid waste and maximize profits from each export. The present work aims to develop a prototype using heuristics already addressed for similar problems and thus increase profits at Justlog. For this, a set of restrictions were created that, applied in synergy with the Non-Linear GRG algorithm, aim to allocate the boxes in different consecutive lines until forming a wall, and, therefore, the walls complete the container. In the end, 3 different cases were presented in which the prototype was put into practice as a way of testing its usefulness, among which wall solutions were created whose occupations are around 80% to 90% in real situations or with great heterogeneity between boxes. Thus, we can foresee a great future use of this prototype in decision-making regarding container consolidation services provided by Justlog

Optimal Shipping Decisions in an Airfreight Forwarding Network

This thesis explores three consolidation problems derived from the daily operations of major international airfreight forwarders. First, we study the freight forwarder's unsplittable shipment planning problem in an airfreight forwarding network where a set of cargo shipments have to be transported to given destinations. We provide mixed integer programming formulations that use piecewise-linear cargo rates and account for volume and weight constraints, flight departure/arrival times, as well as shipment-ready times. After exploring the solution of such models using CPLEX, we devise two solution methodologies to handle large problem sizes. The first is based on Lagrangian relaxation, where the problems decompose into a set of knapsack problems and a set of network flow problems. The second is a local branching heuristic that combines branching ideas and local search. The two approaches show promising results in providing good quality heuristic solutions within reasonable computational times, for difficult and large shipment consolidation problems. Second, we further explore the freight forwarder's shipment planning problem with a different type of discount structure - the system-wide discount. The forwarder's cost associated with one flight depends not only on the quantity of freight assigned to that flight, but also on the total freight assigned to other flights operated by the same carrier. We propose a multi-commodity flow formulation that takes shipment volume and over-declaration into account, and solve it through a Lagrangian relaxation approach. We also model the "double-discount" scheme that incorporates both the common flight-leg discount (the one used in the unsplittable shipment problem) and the system-wide discount offered by cargo airlines. Finally, we focus on palletized loading using unit loading devices (ULDs) with pivots, which is different from what we assumed in the previous two research problems. In the international air cargo business, shipments are usually consolidated into containers; those are the ULDs. A ULD is charged depending on whether the total weight exceeds a certain threshold, called the pivot weight. Shipments are charged the under-pivot rate up to the pivot weight. Additional weight is charged at the over-pivot rate. This scheme is adopted for safety reasons to avoid the ULD overloading. We propose three solution methodologies for the air-cargo consolidation problem under the pivot-weight (ACPW), namely: an exact solution approach based on branch-and-price, a best fit decreasing loading heuristic, and an extended local branching. We found superior computational performance with a combination of the multi-level variables and a relaxation-induced neighborhood search for local branching