A relax-and-fix with fix-and-optimize heuristic applied to multi-level lot-sizing problems

Abstract

In this paper, we propose a simple but efficient heuristic that combines construction and improvement heuristic ideas to solve multi-level lot-sizing problems. A relax-and-fix heuristic is firstly used to build an initial solution, and this is further improved by applying a fix-and-optimize heuristic. We also introduce a novel way to define the mixed-integer subproblems solved by both heuristics. The efficiency of the approach is evaluated solving two different classes of multi-level lot-sizing problems: the multi-level capacitated lot-sizing problem with backlogging and the two-stage glass container production scheduling problem (TGCPSP). We present extensive computational results including four test sets of the Multi-item Lot-Sizing with Backlogging library, and real-world test problems defined for the TGCPSP, where we benchmark against state-of-the-art methods from the recent literature. The computational results show that our combined heuristic approach is very efficient and competitive, outperforming benchmark methods for most of the test problems

Integrated Production and Imperfect Preventive Maintenance Planning - An Effective MILP-based Relax-and-Fix/Fix-and-Optimize Method

“…The RFFO method is a framework designed to combine the Relax-and-fix (RF) and fix-and-optimize (FO) heuristics. In (Toledo et al, 2015), the authors propose an approach in which most binary variables are fixed or relaxed and only few of them are forced to be integer and are optimized. They named this small set of integer variables a "window" and suggested three window type strategies: row-wise, in which the window moves along rows; column-wise, in which the window moves along columns; and value-wise, in which the window selects the variables with relaxed values closest to 0.5.…”

“…They named this small set of integer variables a "window" and suggested three window type strategies: row-wise, in which the window moves along rows; column-wise, in which the window moves along columns; and value-wise, in which the window selects the variables with relaxed values closest to 0.5. As in (Toledo et al, 2015), For both heuristics applied to the Re IPImPMP model, we consider a matrix Y where each of its entries is the binary varaible y t . The inputs of the RF are the set of binary variables (sol.y), the number of binary variables (windowSize) to be chosen, the selection criteria to choose variables (windowType), the overlap rate of binary variables to be re-optimized (overlap) and the execution time limit (timeLimit).…”

Fix-and-Optimize and Variable Neighborhood Search Approaches for Stochastic Multi-Item Capacitated Lot-Sizing Problems

“…The authors presented three types of decomposition method: product decomposition, resource decomposition, and time periods decomposition. Based on the work of [17], variants of FO are developed by [18][19][20]. However, all of the variants follow the decomposition framework of [17].…”

Métodos de solução para o problema de escalonamento de médicos

“…E caso em alguma iteração não se obtenha solução factível, o processo é abortado e desse modo não se encontra solução para o problema original usando a estratégia de particionamento selecionado. Toledo et al (2015) propõem a heurística relax-and-fix e a heurística fix-and-optimize para tratar do problema de dimensionamento de lote multi-estágios com backlogging e o problema de dimensionamento de lotes de dois estágios numa indústria de garrafas (recipientes) de vidro. A heurística relax-and-fix foi usada para a construção de solução inicial que posteriormente foi melhorada através da fix-and-optimize.…”