Alysson M. Costa

A survey on benders decomposition applied to fixed-charge network design problems

Network design problems concern the selection of arcs in a graph in order to satisfy, at minimum cost, some flow requirements, usually expressed in the form of origin-destination pair demands. Benders decomposition methods, based on the idea of partition and delayed constraint generation, have been successfully applied to many of these problems. This article presents a review of these applications.

Benders, metric and cutset inequalities for multicommodity capacitated network design

Abstract Solving multicommodity capacitated network design problems is a hard task that requires the use of several strategies like relaxing some constraints and strengthening the model with valid inequalities. In this paper, we compare three sets of inequalities that have been widely used in this context: Benders, metric and cutset inequalities. We show that Benders inequalities associated to extreme rays are metric inequalities. We also show how to strengthen Benders inequalities associated to non-extreme rays to obtain metric inequalities. We show that cutset inequalities are Benders inequalities, but not necessarily metric inequalities. We give a necessary and sufficient condition for a cutset inequality to be a metric inequality. Computational experiments show the effectiveness of strengthening Benders and cutset inequalities to obtain metric inequalities.

Simple heuristics for the assembly line worker assignment and balancing problem

We propose simple heuristics for the assembly line worker assignment and balancing problem. This problem typically occurs in assembly lines in sheltered work centers for the disabled. Different from the well-known simple assembly line balancing problem, the task execution times vary according to the assigned worker. We develop a constructive heuristic framework based on task and worker priority rules defining the order in which the tasks and workers should be assigned to the workstations. We present a number of such rules and compare their performance across three possible uses: as a stand-alone method, as an initial solution generator for meta-heuristics, and as a decoder for a hybrid genetic algorithm. Our results show that the heuristics are fast, they obtain good results as a stand-alone method and are efficient when used as a initial solution generator or as a solution decoder within more elaborate approaches.

Fast heuristics for the Steiner tree problem with revenues, budget and hop constraints

This article describes and compares three heuristics for a variant of the Steiner tree problem with revenues, which includes budget and hop constraints. First, a greedy method which obtains good approximations in short computational times is proposed. This initial solution is then improved by means of a destroy-and-repair method or a tabu search algorithm. Computational results compare the three methods in terms of accuracy and speed.

Influence of consumer purchasing behaviour on the production planning of perishable food

This paper addresses the impact of consumer purchasing behaviour on the production planning of perishable food products for companies operating in the fast moving consumer goods using direct store delivery. The research presented here builds on previous marketing studies related to the effects of expiry dates in order to derive mathematical formulae, which express the age dependent demand for different categories of perishable products. These demand expressions take into account both customer willingness to pay and product quality risk. The paper presents deterministic and stochastic production planning models, which incorporate the customer’s eagerness to pick up the fresher products available. Results indicate that model approximations neglecting the fact that customers pick up the fresher products or considering that all products have the same product quality risk have a reduced impact on profit losses. On the other hand, not considering the decreasing customer willingness to pay has an important impact both on the profit losses and on the amount of spoiled products.

Model and heuristics for the Assembly Line Worker Integration and Balancing Problem

We propose the Assembly Line Worker Integration and Balancing Problem (ALWIBP), a new assembly line balancing problem arising in lines with conventional and disabled workers. The goal of this problem is to maintain high productivity levels by minimizing the number of workstations needed to reach a given output, while integrating in the assembly line a number of disabled workers. Being able to efficiently manage a heterogeneous workforce is especially important in the current social context where companies are urged to integrate workers with different profiles. In this paper we present mathematical models and heuristic methodologies that can help assembly line managers to cope with this additional complexity. We demonstrate by means of a robust benchmark how this integration can be done with losses of productivity that are much lower than expected.

Sustainable vegetable crop supply problem

We consider an agricultural production problem, in which one must meet a known demand of crops while respecting ecologically-based production constraints. The problem is twofold: in order to meet the demand, one must determine the division of the available heterogeneous arable areas in plots and, for each plot, obtain an appropriate crop rotation schedule. Rotation plans must respect ecologically-based constraints such as the interdiction of certain crop successions, and the regular insertion of fallows and green manures. We propose a linear formulation for this problem, in which each variable is associated with a crop rotation schedule. The model may include a large number of variables and it is, therefore, solved by means of a column-generation approach. We also discuss some extensions to the model, in order to incorporate additional characteristics found in field conditions. A set of computational tests using instances based on real-world data confirms the efficacy of the proposed methodology.

Makespan minimization on parallel processors: an immune-based approach

This work deals with the problem of scheduling jobs to identical parallel processors with the goal of minimizing the completion time of the last processor to finish its execution (makespan). This problem is known to be NP-Hard. The algorithm proposed here is inspired by the immune systems of vertebrate animals. The advantage of combinatorial optimization algorithms based on artificial immune systems is the inherent ability to preserve a diverse set of near-optimal solutions along the search. The results produced by the method are compared with results of classical heuristics.

Balancing parallel assembly lines with disabled workers

We study an assembly line balancing problem that occurs in sheltered worker centers for the disabled, where workers with very different characteristics are present. We are interested in the situation in which parallel assembly lines are allowed and name the resulting problem as parallel assembly line worker assignment and balancing problem. We present a linear mixed-integer formulation and a four-stage heuristic algorithm. Computational results with a large set of instances recently proposed in the literature show the advantages of allowing alternative line layouts.

Robust assembly line balancing with heterogeneous workers

We describe an assembly line problem with worker heterogeneity and uncertainty.Two mixed-integer formulations and one heuristic method are proposed.Extensive numerical results show the importance of considering uncertainty.Computational experiments also show that the proposed heuristic is fast and accurate. Assembly lines are manufacturing systems in which a product is assembled progressively in workstations by different workers or machines, each executing a subset of the needed assembly operations (or tasks). We consider the case in which task execution times are worker-dependent and uncertain, being expressed as intervals of possible values. Our goal is to find an assignment of tasks and workers to a minimal number of stations such that the resulting productivity level respects a desired robust measure. We propose two mixed-integer programming formulations for this problem and explain how these formulations can be adapted to handle the special case in which one must integrate a particular set of workers in the assembly line. We also present a fast construction heuristic that yields high quality solutions in just a fraction of the time needed to solve the problem to optimality. Computational results show the benefits of solving the robust optimization problem instead of its deterministic counterpart.