Franklina Maria Bragion Toledo

A Lagrangian-based heuristic for the capacitated lot-sizing problem in parallel machines

This paper addresses the capacitated lot-sizing problem involving the production of multiple items on unrelated parallel machines. A production plan should be determined in order to meet the forecast demand for the items, without exceeding the capacity of the machines and minimize the sum of production, setup and inventory costs. A heuristic based on the Lagrangian relaxation of the capacity constraints and subgradient optimization is proposed. Initially, the heuristic is tested on instances of the single machine problem and results are compared with heuristics from the literature. For parallel machines and small problems the heuristic performance is tested against optimal solutions, and for larger problems it is compared with the lower bound provided by the Lagrangian relaxation.

GRASP heuristic with path-relinking for the multi-plant capacitated lot sizing problem ☆

This paper addresses the independent multi-plant, multi-period, and multi-item capacitated lot sizing problem where transfers between the plants are allowed. This is an NP-hard combinatorial optimization problem and few solution methods have been proposed to solve it. We develop a GRASP (Greedy Randomized Adaptive Search Procedure) heuristic as well as a path-relinking intensification procedure to find cost-effective solutions for this problem. In addition, the proposed heuristics is used to solve some instances of the capacitated lot sizing problem with parallel machines. The results of the computational tests show that the proposed heuristics outperform other heuristics previously described in the literature. The results are confirmed by statistical tests.

A coupling cutting stock-lot sizing problem in the paper industry

Abstract An important production programming problem arises in paper industries coupling multiple machine scheduling with cutting stocks. Concerning machine scheduling: how can the production of the quantity of large rolls of paper of different types be determined. These rolls are cut to meet demand of items. Scheduling that minimizes setups and production costs may produce rolls which may increase waste in the cutting process. On the other hand, the best number of rolls in the point of view of minimizing waste may lead to high setup costs. In this paper, coupled modeling and heuristic methods are proposed. Computational experiments are presented.

A network flow model for the capacitated lot-sizing problem

The lot-sizing problem considered in this paper consists in planning the production of multiple items on a single machine over a finite planning horizon divided into time periods. The objective of the problem is to determine a minimum cost production plan that meets the forecast demand for the items. The mathematical model considers setup time and setup cost, and is represented as a minimum cost network flow problem. A branch-and-bound method is proposed for solving the model. The performance of the method is evaluated by using numerical experiments for various demand patterns and values of cost parameters.

A knapsack problem as a tool to solve the production planning problem in small foundries

According to recent research carried out in the foundry sector, one of the most important concerns of the industries is to improve their production planning. A foundry production plan involves two dependent stages: (1) determining the alloys to be merged and (2) determining the lots that will be produced. The purpose of this study is to draw up plans of minimum production cost for the lot-sizing problem for small foundries. As suggested in the literature, the proposed heuristic addresses the problem stages in a hierarchical way. Firstly, the alloys are determined and, subsequently, the items that are produced from them. In this study, a knapsack problem as a tool to determine the items to be produced from furnace loading was proposed. Moreover, we proposed a genetic algorithm to explore some possible sets of alloys and to determine the production planning for a small foundry. Our method attempts to overcome the difficulties in finding good production planning presented by the method proposed in the literature. The computational experiments show that the proposed methods presented better results than the literature. Furthermore, the proposed methods do not need commercial software, which is favorable for small foundries.

Investigation of a new GRASP-based clustering algorithm applied to biological data

A large amount of biological data has been produced in the last years. Important knowledge can be extracted from these data by the use of data analysis techniques. Clustering plays an important role in data analysis, by organizing similar objects from a dataset into meaningful groups. Several clustering algorithms have been proposed in the literature. However, each algorithm has its bias, being more adequate for particular datasets. This paper presents a mathematical formulation to support the creation of consistent clusters for biological data. Moreover, it shows a clustering algorithm to solve this formulation that uses GRASP (Greedy Randomized Adaptive Search Procedure). We compared the proposed algorithm with three known other algorithms. The proposed algorithm presented the best clustering results confirmed statistically.

Three time-based scale formulations for the two-stage lot sizing and scheduling in process industries

In this paper, we propose three novel mathematical models for the two-stage lot-sizing and scheduling problems present in many process industries. The problem shares a continuous or quasi-continuous production feature upstream and a discrete manufacturing feature downstream, which must be synchronized. Different time-based scale representations are discussed. The first formulation encompasses a discrete-time representation. The second one is a hybrid continuous-discrete model. The last formulation is based on a continuous-time model representation. Computational tests with state-of-the-art MIP solver show that the discrete-time representation provides better feasible solutions in short running time. On the other hand, the hybrid model achieves better solutions for longer computational times and was able to prove optimality more often. The continuous-type model is the most flexible of the three for incorporating additional operational requirements, at a cost of having the worst computational performance.

HOPS – Hamming-Oriented Partition Search for production planning in the spinning industry

In this paper, we investigate a two-stage lot-sizing and scheduling problem in a spinning industry. A new hybrid method called HOPS (Hamming-Oriented Partition Search), which is a branch-and-bound based procedure that incorporates a fix-and-optimize improvement method is proposed to solve the problem. An innovative partition choice for the fix-and-optimize is developed. The computational tests with generated instances based on real data show that HOPS is a good alternative for solving mixed integer problems with recognized partitions such as the lot-sizing and scheduling problem.

Robust mixed-integer linear programming models for the irregular strip packing problem

Two-dimensional irregular strip packing problems are cutting and packing problems where small pieces have to be cut from a larger object, involving a non-trivial handling of geometry. Increasingly sophisticated and complex heuristic approaches have been developed to address these problems but, despite the apparently good quality of the solutions, there is no guarantee of optimality. Therefore, mixed-integer linear programming (MIP) models started to be developed. However, these models are heavily limited by the complexity of the geometry handling algorithms needed for the piece non-overlapping constraints. This led to pieces simplifications to specialize the developed mathematical models. In this paper, to overcome these limitations, two robust MIP models are proposed. In the first model (DTM) the non-overlapping constraints are stated based on direct trigonometry, while in the second model (NFP−CM) pieces are first decomposed into convex parts and then the non-overlapping constraints are written based on nofit polygons of the convex parts. Both approaches are robust in terms of the type of geometries they can address, considering any kind of non-convex polygon with or without holes. They are also simpler to implement than previous models. This simplicity allowed to consider, for the first time, a variant of the models that deals with piece rotations. Computational experiments with benchmark instances show that NFP−CM outperforms both DTM and the best exact model published in the literature. New real-world based instances with more complex geometries are proposed and used to verify the robustness of the new models.

A relax-and-fix-based algorithm for the vehicle-reservation assignment problem in a car rental company

Empty repositions are a major problem for car rental companies that deal with special types of vehicles whose number of units is small. In order to meet reservation requirements concerning time and location, companies are forced to transfer cars between rental stations, bearing significant costs and increasing the environmental impact of their activity due to the fuel consumption and CO2 emission. In this paper, this problem is tackled under a vehicle-reservation assignment framework as a network-flow model in which the profit is maximized. The reservations are allocated considering the initial and future availability of each car, interdependencies between rental groups, and different reservation priorities. To solve this model, a relax-and-fix heuristic procedure is proposed, including a constraint based on local branching that enables and controls modifications between iterations. Using real instances, the value of this approach is established and an improvement of 33% was achieved when compared to the company’s current practices.