Solve Manufacturer's Pallet Loading Problem (MPLP) with Practical Warehouse Constraints

Neste artigo apresentamos métodos exatos, baseados em relaxações Lagrangiana e surrogate, com bom desempenho para resolver o problema de carregamento de paletes do produtor. Este problema consiste em arranjar ortogonalmente e sem sobreposição o máximo número de retângulos de dimensões (l,w) ou (l,w) sobre um retângulo maior (L,W). Os métodos propostos são procedimentos de busca em árvore do tipo branch and bound que, em cada nó, utilizam limitantes derivados de relaxações Lagrangiana e/ou surrogate de uma formulação de programação linear 0-1. Algoritmos de otimização do subgradiente são usados para otimizar estes limitantes. São aplicados ainda testes de redução do problema e heurísticas Lagrangiana e surrogate para se obter boas soluções factíveis na otimização do subgradiente. Testes computacionais foram realizados utilizando exemplos da literatura e exemplos reais de uma transportadora. Os resultados mostram que um dos métodos propostos é competitivo com outros métodos da literatura, incluindo o software GAMS/CPLEX.

Higher order block heuristics for 2D pallet loading problems with multiple box inputs

Enhancing pallet load stability: A MILP model for the Manufacturer’s Pallet Loading Problem with interlocking constraints

This paper introduces the three‐dimensional case picking problem (3D‐CPP) and proposes a multistart biased‐randomized algorithm (BRA) to solve it. The 3D‐CPP combines two important topics in modern warehouse logistics: the pallet loading problem and the routing of pickers in manual warehouses. The proposed optimization procedure aims at minimizing the overall distance traveled by the pickers, and is achieved by combining a routing problem (i.e., the order in which picking positions are visited) with a loading problem (i.e., the way in which cases are placed onto the pallet). We also consider additional constraints regarding the weight, vertical support, and strength of the cases. In order to solve this problem, we first propose a constructive heuristic which combines routing and packing procedures. This initial heuristic is then extended into a multistart BRA by employing a skewed probability distribution to introduce a certain degree of randomness during the solution‐construction process. A series of computational experiments allow us to assess the quality of the proposed approach, through a comparison with other algorithms as well as using real‐life data provided by an industrial partner.

Many cutting problems on two- or three-dimensional objects require that the cuts be orthogonal and of guillotine type. However, there are applications in which the cuts must be orthogonal but need not be of guillotine type. In this paper we focus on the latter type of cuts on rectangular bins. We investigate the so-called \(L\)-approach, introduced by Lins et al. (J Oper Res Soc 54:777–789, 2003), which has been used to tackle, among others, the pallet loading problem and the two-dimensional unconstrained knapsack problem. This approach concerns a method to generate two \(L\)-shaped pieces from an \(L\)-shaped piece. More recently, Birgin et al. (J Oper Res Soc 63(2):183–200, 2012), raised two questions concerning this approach. The first question is whether one may restrict only to cuts on raster points (rather than on all discretization points), without loss in the quality of the solution. We prove that the answer to this question is positive. The second question is whether the \(L\)-approach is an optimal method to solve the unconstrained knapsack problem. We show an instance of the problem for which this approach fails to find an optimum solution.

This paper concerns the use of strategic oscillation (SO) for packing problems. The SO algorithm spends a certain time exploring infeasible solutions rather than restricting the search to feasible solutions only. The main features of the algorithm are explained and suggestions on different implementations are given. The pallet-loading problem is probably the simplest form of packing problem and is thus suitable for initial experiments with SO. The results obtained suggest that SO is successful for this problem and that it will probably be fruitful to extend the use of SO to other, harder, packing problems.

A two-step evolutionary algorithm for the distributor’s pallet loading problem with multi-size pallets

The pallet-loading problem, in which a number of identical boxes are to be packed orthogonally onto a rectangular pallet, has been the subject of several algorithms in recent years. These algorithms are concerned with maximizing the number of boxes fitted. In this paper, consideration is given to the development of loading patterns into pallet stacks, and criteria which might be applied to determine the suitability of these stacks for storage and transportation. A technique is developed which allows the stability and clampability of stacks to be tested, and this is applied to layouts produced by the recent algorithm of Bischoff and Dowsland. The relative importance of different criteria is illustrated and shown to have implications for the structure of algorithms that are to provide acceptable pallet stacks.

The paper discusses the complexities of the air cargo loading problem and provides an effective approach based on the proposed heuristic to tackle the problem. The primitive class of problems like general bin packing, cutting stock and knapsack problems can be taken as the basic step towards the air-cargo loading problem. The discussed problem is very different in its nature in respect to the general pallet, container or truck loading problem. Generally, the container loading problems consider only the rectangular type of containers to load the items whereas in case of air-cargos, the shape of containers are very different such as irregular pentagon, hexagon etc. Apart from this, the objective of air cargo loading problem discussed in this paper is based on the minimization of the shipping cost of the container keeping in mind the number of constraints involved in loading. In past research literatures, most of the container loading problems are aimed to pack the container in such a way so that either the number of containers is minimized or the volume of the packed items are maximized. In this paper the objective function includes the shipment cost as the primary goal and the volume and weight of the containers are taken as constraints. A very interesting finding can be noticed in this paper which states that even if the container's volume is properly utilized the cost of shipment may be increased.

The problem of designing finite precision one-dimensional infinite impulse response (IIR) filters with prescribed magnitude, phase, and stability constraints is studied. The design problem is formulated as the minimization of a cost function incorporating these conflicting requirements. The first two elements of the cost function express magnitude and group delay errors between the desired and the actual frequency responses of a filter, while the third one is related to its stability margin. This cost function is minimized using simulated annealing based on the Metropolis (1953) algorithm. Examples of several finite wordlength filters designed by the above method are presented and compared with Chebyshev and elliptic filters with rounded coefficients. >

The paper presents a genetic algorithm (GA) for the container loading problem. The main ideas of the approach are first to generate a set of disjunctive box towers and second to arrange the box towers on the floor of the container according to a given optimization criterion. The loading problem may include different practical constraints. The performance of the GA is demonstrated by a numerical test comparing the GA and several other procedures for the container loading problem.

This article presents a metaheuristic algorithm to solve the pallet-building problem and the loading of these in trucks. This approach is used to solve a real application of a Colombian logistics company. Several practical requirements of goods loading and unloading operations were modeled, such as the boxes’ orientation, weight support limits associated with boxes, pallets and vehicles, and static stability constraints. The optimization algorithm consists of a two-phase approach, the first is responsible for the construction of pallets, and the second considers the optimal location of the pallets into the selected vehicles. Both phases present a search strategy type of GRASP. The proposed methodology was validated through the comparison of the performance of the solutions obtained for deliveries of the logistics company with the solutions obtained using a highly accepted commercial packing tool that uses two different algorithms. The proposed methodology was compared in similar conditions with the previous works that considered the same constraints of the entire problem or at least one of the phases separately. We used the sets of instances published in the literature for each of the previous works. The results allow concluding that the proposed algorithm has a better performance than the most known commercial tool for real cases. The proposed algorithm managed to match most of the test instances and outperformed some previous works that only involve decisions of one of the two problems. As future work, it is proposed to adapt this work to the legal restrictions of the European community.

The incorporation of renewable energy sources (RES) such as wind and solar power plants into traditional power systems offers numerous technical and environmental benefits. However, improper operation of power grids with RES may lead to high operating costs and higher system losses, as well as voltage fluctuations. To solve these problems, in this paper a formulation of the dynamic optimal power flow (DOPF) problem has been proposed with the integration of RES in the grid. The maximum allowable number of switching operations in a day for on-load tap-changer (OLTC) of transformers is taken into consideration as practical constraint. For 24 hours, the objective functions were to minimize the total operating cost (including fuel cost and cost of power loss), minimize power loss and the daily number of tap operations for transformer's OLTC. The minimization of the daily number of operations for transformers was taken as the goal to preserve the service life of transformers, reduce maintenance and depreciation. The objectives were minimized by coordination between control variables such as the output power of generators, the voltage of generators, transformer tap changer, and shunt capacitor. The improved practical swarm optimization (PSO) algorithm has been employed successfully to solve DOPF with discrete and continuous decision variables in the electric power system.

Active and reactive dispatch with minimum control movements

The main idea is good 1. The literature is not strong enough and outdated. There are plenty of studies about pallet loading problem and a detailed comparison should be done to show the necessity of the proposed loading approach. 2. The problem with characteristics can be described in a more understandable way. 3. Clarify if there is difference between the brach and bound method used in this article and those used for solving the pallet loading problem in literature. 4. The language can be improved for more readable manuscript.