Denise Sato Yamashita

Three-dimensional container loading models with cargo stability and load bearing constraints

Mathematical models for the problem of loading rectangular boxes into containers, trucks or railway cars have been proposed in the literature, however, there is a lack of studies which consider realistic constraints that often arise in practice. In this paper, we present mixed integer linear programming models for the container loading problem that consider the vertical and horizontal stability of the cargo and the load bearing strength of the cargo (including fragility). The models can also be used for loading rectangular boxes on pallets where the boxes do not need to be arranged in horizontal layers on the pallet. A comprehensive performance analysis using optimization software with 100s of randomly generated instances is presented. The computational results validate the models and show that they are able to handle only problems of a moderate size. However, these models might be useful to motivate future research exploring other solution approaches to solve this problem, such as decomposition methods, relaxation methods, heuristics, among others.

An exact algorithm for minimizing resource availability costs in project scheduling

A new exact algorithm that solves the Resource Availability Cost Problem (RACP) in project scheduling is shown to yield a significant improvement over the existing algorithm in the literature. The new algorithm consists of a hybrid method where an initial feasible solution is found heuristically. The branching scheme solves a Resource-Constrained Project Scheduling Problem (RCPSP) at each node where the resources of the RACP are fixed. The knowledge of previously solved RCPSPs is used to produce cuts in the search tree. A worst-case-performance theorem is established for this new algorithm. Experiments are performed on instances adapted from the PSPLIB database. The new algorithm can be used to minimize any resource availability cost problem once a procedure for the underlying resource-constrained problem is available.

A note on time/cost tradeoff curve generation for project scheduling with multi-mode resource availability costs

In this note we combine two known algorithms and show how they can be used in order to generate tradeoff curves between time and cost for deterministic project scheduling problems with multiple modes and resource availability costs. The approach can handle linear and non-linear non-decreasing cost functions and it is based on the exact algorithm presented in Demeulemeester (1995) for the resource availability cost problem without multiple modes. As the problem is NP-hard, the method is computationally viable to solve only problems of a moderate size. The performance of the combined algorithm is compared to solutions generated by GAMS/CPLEX.

Um algoritmo exato para o problema de programação de projetos com custo de disponibilidade de recursos e múltiplos modos

In this paper we propose an exact algorithm to generate tradeoff curves between cost and time of a project, based on the multi-mode resource availability cost problem. Two versions of the algorithm are proposed, the first is an adaptation of an exact algorithm proposed in the literature, where there is only a single mode to execute the activities, and the second incorporates strategies in order to improve the performance of the solution method, resulting in a significant decrease in the computational time. It is worth noting that the proposed algorithm is computationally viable to solve only problems of moderate size. Both versions of the algorithm were tested solving different instances generated by the software Progen. Tradeoff curves are presented and analyzed, illustrating how the method can be used in situations where the decision maker is confronted with the difficult task of balancing costs and deadlines of a project.

Optimization Models for the Three-Dimensional Container Loading Problem with Practical Constraints

The last decades have seen an increasing emergence of solution approaches to three-dimensional container loading problems. Starting from simple constructive algorithms and passing through sophisticated metaheuristics, the container loading literature offers a range of solving options. However, few authors have engaged themselves in proposing optimization models to deal with container loading problems that aim to pack the largest volume (or value) of rectangular boxes orthogonally inside a single container. In this sense, studies are even scarcer when practical constraints are considered. Cargo stability, load bearing strength of the boxes, and multi-drop situations, among others, are constraints that have important practical claim and should be considered in order to model more realistic situations. In this chapter we are concerned with presenting mixed integer linear programming models for container loading problems that consider vertical and horizontal stability of the cargo, load bearing strength of the boxes, and multi-drop situations, besides the non-overlapping of boxes. Computational results achieved with a modeling language and an optimization solver, comparing the performance of the models on instances from the literature, are also presented and discussed. Finally, we discuss some potential directions for future works in this area.

Modelos de otimização para problemas de carregamento de contêineres com considerações de estabilidade e de empilhamento

In this paper we present 0-1 integer linear programming models for problems of loading rectangular boxes into containers, trucks or railway cars, considering the practical constraints of stability and load bearing strength of the cargo. The models can also be applied to three-dimensional problems of loading rectangular boxes on pallets, in which the boxes do not need to be arranged in horizontal layers on the pallet. We are not aware of other studies in the literature that present mathematical formulations to these problems considering these constraints explicitly. Computational experiments with the proposed models were performed with the software GAMS/CPLEX and randomly generated instances. The results showed that the models are consistent and they properly represent the situations treated, although this approach (in its current version) is limited to optimally solve only problems of moderate size. However, the models can be useful to motivate future research exploring decomposition methods, relaxations, heuristics, among others, to solve these problems.

Production scheduling of assembly fixtures in the aeronautical industry

In this work, we study the production scheduling of a real world assembly problem present in the aeronautical industry. Parts of aircrafts should be produced on fixtures, which are commonly used in aircraft manufacturing and consist of several workstations. Due to a lack of physical space in the fixture, when a workstation is in use, other workers cannot use adjacent workstations in this fixture. These constraints are called here adjacency constraints. This assembly fixture scheduling problem is studied in the context of a workforce learning process including four main qualification stages (or epochs). Mathematical models are developed and implemented for each stage using a modeling language and an optimization solver. Computational experiments with this approach were performed in a case study of a Brazilian aeronautical company and they resulted in better solutions than those currently practiced in the company.

Ship Routing with Pickup and Delivery for a Maritime Oil Transportation System: MIP Model and Heuristics

This paper examines a ship routing problem with pickup and delivery and time windows for maritime oil transportation, motivated by the production and logistics activities of an oil company operating in the Brazilian coast. The transportation costs from offshore platforms to coastal terminals are an important issue in the search for operational excellence in the oil industry, involving operations that demand agile and effective decision support systems. This paper presents an optimization approach to address this problem, based on a mixed integer programming (MIP) model and a novel and exploratory application of two tailor-made MIP heuristics, based on relax-and-fix and time decomposition procedures. The model minimizes fuel costs of a heterogeneous fleet of oil tankers and costs related to freighting contracts. The model also considers company-specific constraints for offshore oil transportation. Computational experiments based on the mathematical models and the related MIP heuristics are presented for a set of real data provided by the company, which confirm the potential of optimization-based methods to find good solutions for problems of moderate sizes.

Um algoritmo branch-and-bound para o problema de programação de projetos com custo de disponibilidade de recursos e múltiplos modos

In a recent study (YAMASHITA; MORABITO, 2007a), it was proposed an exact algorithm to solve problems of resource-constrained project scheduling with resource availability costs under multiple modes of execution. That algorithm is an adaptation of another exact algorithm recorded in the literature for the particular case where there is only a single mode for executing the tasks. In the present study, we propose a new exact algorithm based on the branch and bound method to deal with multiple performing modes problem. Since the problem is NP-hard, the algorithm is computationally viable only for problems of moderate size. Numerous computational tests using the generator ProGen were run to compare the performance of the proposed algorithm with the former algorithm and with the CPLEX software. The results show that the proposed version of the algorithm is competitive with the other methods and encourage further research for the development of more elaborate versions of this algorithm.

Otimização na programação de montagens na indústria aeronáutica

This paper presents a case study of production scheduling in the aeronautical industry. Tasks must be scheduled in assembly fixtures with several adjacent workstations, taking into account special constraints where simultaneous processing of the tasks is allowed (adjacency constraints). Such constraints arise due to a space limitation in the fixture. This paper is a continuation of a previous work published in Silva, Morabito and Yanasse (2011), where the objective of the problem was to minimize the makespan. Here, the problem is studied more broadly, where the workforce qualification is represented in four stages, with the objective of minimizing the total amount of workforce needed in each stage, and each stage is modeled as an integer linear programming problem. These models were implemented using an optimization software, and several computational experiments were performed in order to validate the proposed models. The results suggest that productivity gains can be achieved with the models developed in this work.