O planejamento da produção é uma atividade que avalia decisões para um melhor uso dos recursos disponíveis, visando satisfazer aos objetivos produtivos da empresa ao longo de um horizonte de planejamento. Este trabalho enfoca o problema de dimensionamento de lotes com restrições de capacidade (PDLC), que é uma das tarefas centrais envolvidas no planejamento da produção. O PDLC visa determinar o tamanho dos lotes a serem produzidos em períodos de tempo de um horizonte de planejamento. Os PDLC estudados neste trabalho contemplam duas características importantes: a presença de múltiplos itens e a existência de tempos de preparação para as máquinas. Além disso, são consideradas restrições de capacidade e situações onde o atraso para atender a demanda é permitido (backlogging). Alguns dos modelos estudados permitem que a preparação do ambiente de produção para um dado item possa ser mantida de um período para o seguinte, o que propiciaria a economia de até uma preparação a cada período. Esta característica é chamada de preservação de preparação (carry-over). Também existem situações onde a preparação de uma máquina começa em um período e termina no período seguinte. Na literatura, esta característica é chamada de set-up crossover. Este trabalho tem três metas centrais: a) avaliar diferentes configurações do software comercial ILOG CPLEX 11 para a solução dos PDLC estudados; b) estudar a influência na solução dos PDLC quando se acrescenta a possibilidade de atraso na demanda, de preservação de preparação e de set-up crossover; c) aplicar local branching para resolver os problemas estudados. Para resolver as instâncias propostas, foram utilizados o software comercial ILOG CPLEX 11 e um programa em C++ que foi desenvolvido neste trabalho. Foram utilizados exemplos encontrados na literatura para avaliar as propostas, e bons resultados foram obtidos / The production planning is an activity that evaluates the decision for a better use of the available resources, in order to satisfy the productive objectives of the company over a planning horizon. This work focuses on the capacitated lot-sizing problem (CLSP), which is one of the central tasks involved in production planning. The CLSP means to determine the size of the lots to be produced in time periods of a planning horizon. The CLSP studied in this work contemplate two complicating characteristics: the presence of multiple items and the existence of set-up times for the machines. Besides that, capacity constraints and situations where backlog of the demand is allowed are also considered (backlogging). Some of the studied models allow the set-up of the production environment for a given item to be carried over to the next period, which could result in economy of a set-up in each period (carry-over). There are situations where the set-up of a machine starts in one period and crosses over to the next period (set-up crossover). This work has three main goals: a) evaluate different configurations of the commercial software ILOG CPLEX 11 to solve the different kinds of CLSP studied; b) study the influence of the solution of the CLSP when you consider the possibility of backlogging, set-up carry-over and set-up crossover; c) apply local branching to solve the studied problems. To solve the proposed instances, we used the commercial solver ILOG CPLEX 11 and the program in C++ developed in this work. The examples used to test both programs are found in the literature, and good results were obtained

O planejamento da produção é uma atividade que avalia decisões para um melhor uso dos recursos disponíveis, visando satisfazer aos objetivos produtivos da empresa ao longo de um horizonte de planejamento. Este trabalho enfoca o problema de dimensionamento de lotes com restrições de capacidade (PDLC), que é uma das tarefas centrais envolvidas no planejamento da produção. O PDLC visa determinar o tamanho dos lotes a serem produzidos em períodos de tempo de um horizonte de planejamento. Os PDLC estudados neste trabalho contemplam duas características importantes: a presença de múltiplos itens e a existência de tempos de preparação para as máquinas. Além disso, são consideradas restrições de capacidade e situações onde o atraso para atender a demanda é permitido (backlogging). Alguns dos modelos estudados permitem que a preparação do ambiente de produção para um dado item possa ser mantida de um período para o seguinte, o que propiciaria a economia de até uma preparação a cada período. Esta característica é chamada de preservação de preparação (carry-over). Também existem situações onde a preparação de uma máquina começa em um período e termina no período seguinte. Na literatura, esta característica é chamada de set-up crossover. Este trabalho tem três metas centrais: a) avaliar diferentes configurações do software comercial ILOG CPLEX 11 para a solução dos PDLC estudados; b) estudar a influência na solução dos PDLC quando se acrescenta a possibilidade de atraso na demanda, de preservação de preparação e de set-up crossover; c) aplicar local branching para resolver os problemas estudados. Para resolver as instâncias propostas, foram utilizados o software comercial ILOG CPLEX 11 e um programa em C++ que foi desenvolvido neste trabalho. Foram utilizados exemplos encontrados na literatura para avaliar as propostas, e bons resultados foram obtidos / The production planning is an activity that evaluates the decision for a better use of the available resources, in order to satisfy the productive objectives of the company over a planning horizon. This work focuses on the capacitated lot-sizing problem (CLSP), which is one of the central tasks involved in production planning. The CLSP means to determine the size of the lots to be produced in time periods of a planning horizon. The CLSP studied in this work contemplate two complicating characteristics: the presence of multiple items and the existence of set-up times for the machines. Besides that, capacity constraints and situations where backlog of the demand is allowed are also considered (backlogging). Some of the studied models allow the set-up of the production environment for a given item to be carried over to the next period, which could result in economy of a set-up in each period (carry-over). There are situations where the set-up of a machine starts in one period and crosses over to the next period (set-up crossover). This work has three main goals: a) evaluate different configurations of the commercial software ILOG CPLEX 11 to solve the different kinds of CLSP studied; b) study the influence of the solution of the CLSP when you consider the possibility of backlogging, set-up carry-over and set-up crossover; c) apply local branching to solve the studied problems. To solve the proposed instances, we used the commercial solver ILOG CPLEX 11 and the program in C++ developed in this work. The examples used to test both programs are found in the literature, and good results were obtained

abstract: In this thesis, a single-level, multi-item capacitated lot sizing problem with setup carryover, setup splitting and backlogging is investigated. This problem is typically used in the tactical and operational planning stage, determining the optimal production quantities and sequencing for all the products in the planning horizon. Although the capacitated lot sizing problems have been investigated with many different features from researchers, the simultaneous consideration of setup carryover and setup splitting is relatively new. This consideration is beneficial to reduce costs and produce feasible production schedule. Setup carryover allows the production setup to be continued between two adjacent periods without incurring extra setup costs and setup times. Setup splitting permits the setup to be partially finished in one period and continued in the next period, utilizing the capacity more efficiently and remove infeasibility of production schedule. The main approaches are that first the simple plant location formulation is adopted to reformulate the original model. Furthermore, an extended formulation by redefining the idle period constraints is developed to make the formulation tighter. Then for the purpose of evaluating the solution quality from heuristic, three types of valid inequalities are added to the model. A fix-and-optimize heuristic with two-stage product decomposition and period decomposition strategies is proposed to solve the formulation. This generic heuristic solves a small portion of binary variables and all the continuous variables rapidly in each subproblem. In addition, the case with demand backlogging is also incorporated to demonstrate that making additional assumptions to the basic formulation does not require to completely altering the heuristic. The contribution of this thesis includes several aspects: the computational results show the capability, flexibility and effectiveness of the approaches. The average optimality gap is 6% for data without backlogging and 8% for data with backlogging, respectively. In addition, when backlogging is not allowed, the performance of fix-and-optimize heuristic is stable regardless of period length. This gives advantage of using such approach to plan longer production schedule. Furthermore, the performance of the proposed solution approaches is analyzed so that later research on similar topics could compare the result with different solution strategies. / Dissertation/Thesis / Masters Thesis Industrial Engineering 2015

Simultaneous lot-sizing and scheduling problem is the problem to decide what products to be produced on which machine and in which order, as well as the quantity of each product. Problems of this type are hard to solve. Therefore, they were studied for years, and a considerable number of papers is published to solve different lotsizing and scheduling problems, specifically real-case problems. This work proposes a Real-Coded Genetic Algorithm (RCGA) with a new chromosome representation to solve a non-identical parallel machine capacitated lot-sizing and scheduling problem with sequence dependent setup times and costs, machine cost and backlogging. Such a problem can be found in real world production line at furniture manufacturer in Sweden. Backlogging is an important concept in this problem, and it is often ignored in the literature. This study implements three different types of crossover; one of them has been chosen based on numerical experiments. Four mutation operators have been combined together to allow the genetic algorithm to scan the search area and maintain genetic diversity. Other steps like initializing of the population and a reinitializing process have been designed carefully to achieve the best performance and to prevent the algorithm from trapped into the local optimum. The proposed algorithm is implemented and coded in MATLAB and tested for a set of standard medium to large-size problems taken from the literature. A variety of problems were solved to measure the impact of different characteristics of problems such as the number of periods, machines, and products on the quality of the solution provided by the proposed RCGA. To evaluate the performance of the proposed algorithm, the average deviation from the lower bound and runtime for the proposed RCGA are compared with three other algorithms from the literature. The results show that, in addition to its high computational speed, the proposed RCGA outperforms the other algorithms for non-identical parallel machine problems, while it is outperformed by the other algorithms for problems with the more identical parallel machine. The results show that the different characteristics of problem instances, like increasing setup cost, and size of the problem influence the quality of the solutions provided by the proposed RCGA negatively.