Débora P. Ronconi

A NOTE ON CONSTRUCTIVE HEURISTICS FOR THE FLOWSHOP PROBLEM WITH BLOCKING

Abstract This paper analyzes the minimization of the makespan criterion for the flowshop problem with blocking. In this environment, there are no buffers between successive machines, and therefore intermediate queues of jobs waiting in the system for their next operations are not allowed. As the problem is NP-hard, a constructive heuristic that explores specific characteristics of the problem is developed. The small computational effort of such strategy, which is valuable in practical applications, is one of the reasons that motivated this study. The performance of a combination of the proposed method with existing ones is examined through a comparative study. The new methods outperform the NEH algorithm, currently the best constructive heuristic for this problem, in problems with up to 500 jobs and 20 machines.

Optimizing the packing of cylinders into a rectangular container: A nonlinear approach

Abstract The container loading problem has important industrial and commercial applications. An increase in the number of items in a container leads to a decrease in cost. For this reason the related optimization problem is of economic importance. In this work, a procedure based on a nonlinear decision problem to solve the cylinder packing problem with identical diameters is presented. This formulation is based on the fact that the centers of the cylinders have to be inside the rectangular box defined by the base of the container (a radius far from the frontier) and far from each other at least one diameter. With this basic premise the procedure tries to find the maximum number of cylinder centers that satisfy these restrictions. The continuous nature of the problem is one of the reasons that motivated this study. A comparative study with other methods of the literature is presented and better results are achieved.

Tabu search for total tardiness minimization in flowshop scheduling problems

This work addresses the permutation flowshop scheduling problem with the objective of minimizing total tardiness. First, the behavior of solutions for small problems is analyzed for different due date scenarios. Then a tabu search-based heuristic is proposed as a method to explore the solution space. Diversification, intensification, and neighborhood restriction strategies are evaluated. Computational tests are presented and comparisons with the NEH algorithm and with a Branch-and-Bound algorithm are made. Scope and purpose Surveys of production scheduling show that meeting customer due dates is a critical concern for many manufacturing systems. While there is considerable research to minimize the makespan, very little work is reported on minimizing the total tardiness for scheduling jobs on a permutation flowshop. In this paper, we investigate the application of tabu search to this problem in order to obtain better solutions in a reasonable time. Special strategies are included to improve the performance of the method.

Minimizing earliness and tardiness penalties in a single-machine problem with a common due date

Abstract Scheduling problems involving both earliness and tardiness costs have received significant attention in recent years. This type of problem became important with the advent of the just-in-time (JIT) concept, where early or tardy deliveries are highly discouraged. In this paper we examine the single-machine scheduling problem with a common due date. Performance is measured by the minimization of the sum of earliness and tardiness penalties of the jobs. Since this problem is NP-hard, we propose a tabu search-based heuristic and a genetic algorithm which exploit specific properties of the optimal solution. Hybrid strategies are also analyzed to improve the performance of these methods. The proposed approaches are examined through a computational comparative study with 280 benchmark problems with up to 1000 jobs.

A Branch-and-Bound Algorithm to Minimize the Makespan in a Flowshop with Blocking

This work addresses the minimization of the makespan criterion for the flowshop problem with blocking. In this environment there are no buffers between successive machines, and therefore intermediate queues of jobs waiting in the system for their next operations are not allowed. We propose a lower bound which exploits the occurrence of blocking. A branch-and-bound algorithm that uses this lower bound is described and its efficiency is evaluated on several problems. Results of computational experiments are reported.

Lower bounding schemes for flowshops with blocking in-process

While there is a considerable amount of research that deals with a flowshop with no storage constraints, few works have addressed the flowshop with blocking in-process. Scheduling problems with blocking arise in serial manufacturing processes where no intermediate buffer storage is available. This paper proposes a lower bound, which exploits the occurrence of blocking, on the total tardiness of the jobs. Its efficiency is evaluated using a branch-and-bound algorithm on several problems. A lower bound on the makespan is also derived and computational tests are presented.

Orthogonal packing of rectangular items within arbitrary convex regions by nonlinear optimization

The orthogonal packing of rectangular items in an arbitrary convex region is considered in this work. The packing problem is modeled as the problem of deciding for the feasibility or infeasibility of a set of nonlinear equality and inequality constraints. A procedure based on nonlinear programming is introduced and numerical experiments which show that the new procedure is reliable are exhibited.Scope and purpose We address the problem of packing orthogonal rectangles within an arbitrary convex region. We aim to show that smooth nonlinear programming models are a reliable alternative for packing problems and that well-known general-purpose methods based on continuous optimization can be used to solve the models. Numerical experiments illustrate the capabilities and limitations of the approach.

Method of sentinels for packing items within arbitrary convex regions

A new method is introduced for packing items in convex regions of the Euclidian n-dimensional space. By means of this approach the packing problem becomes a global finite-dimensional continuous optimization problem. The strategy is based on the new concept of sentinels. Sentinels sets are finite subsets of the items to be packed such that, when two items are superposed, at least one sentinel of one item is in the interior of the other. Minimal sets of sentinels are found in simple two-dimensional cases. Numerical experiments and pictures showing the potentiality of the new technique are presented.

Scheduling in a two-machine flowshop for the minimization of the mean absolute deviation from a common due date

This paper addresses the minimization of the mean absolute deviation from a common due date in a two-machine flowshop scheduling problem. We present heuristics that use an algorithm, based on proposed properties, which obtains an optimal schedule for a given job sequence. A new set of benchmark problems is presented with the purpose of evaluating the heuristics. Computational experiments show that the developed heuristics outperform results found in the literature for problems up to 500 jobs.

The single machine earliness and tardiness scheduling problem: lower bounds and a branch-and-bound algorithm*

This paper addresses the single machine scheduling problem with a common due date aiming to minimize earliness and tardiness penalties. Due to its complexity, most of the previous studies in the literature deal with this problem using heuristics and metaheuristics approaches. With the intention of contributing to the study of this problem, a branch-and-bound algorithm is proposed. Lower bounds and pruning rules that exploit properties of the problem are introduced. The proposed approach is examined through a computational comparative study with 280 problems involving different due date scenarios. In addition, the values of optimal solutions for small problems from a known benchmark are provided. Mathematical subject classification: 90C11, 62P30, 90B35.