This paper presents mixed-integer programming models to hybrid manufacturing and remanufacturing lotsizing problems in which remanufactured products are treated as new ones, so that both manufactured and remanufactured products compete to meet the demands. Differently from previous studies, we consider an environment with multiple products, both manufacturing and remanufacturing costs, disposal, backlogging, and the inherent uncertainties of demands, return rates of usable products, and setup costs. In order to deal with these uncertainties, we propose a scenario-based two-stage stochastic programming model that assumes production and setup as first-stage decision variables, whereas inventory, disposal, and backlogging are defined as second-stage decision variables.We also analyze a risk-averse model in an attempt to reduce the dispersion of the second-stage costs. The main results of the present study indicate that setup costs for remanufacturing can be decisive in choosing between manufacturing or remanufacturing. Even though remanufacturing costs are lower, the process is still largely dependent on return rates and low storage costs for returned products.
ResumoO problema estudado neste trabalho visa minimizar o custo de energia elétrica necessário para a operação de bombas hidráulicas, que captam água de poços artesianos para os reservatórios distribuídos em bairros da cidade, de onde a população é atendida. Como o custo da energia elétrica varia ao longo do dia, se faz necessário um planejamento da operação das bombas e armazenamento de água no sistema. Um modelo de otimização linear inteira é proposto para o problema, considerando um custo de partida das bombas. Desconsiderando esse custo, as variáveis binárias do modelo são eliminadas e um segundo modelo de otimização linear é também analisado. Algumas instâncias geradas aleatoriamente são resolvidas e suas soluções analisadas, demonstrando que os modelos propostos oferecem suporte gerencial consistente para seu uso no problema real.Palavras-chave: logística de distribuição; otimização inteiro-mista; otimização linear.
AbstractThe aim of the problem studied in this paper is to minimize the electrical energy cost necessary to manage water distribution networks. We consider water distribution systems that are designed to deliver water from pump stations suitably distributed in a city, to the final water consumers. Since the cost of the electrical energy varies during the day, it is necessary to plan the operation of the pumps and water inventory in the system. An integer linear optimization model is proposed for the problem, when considering a fixed cost for the starting of the pumps. On the other hand, when we do not consider this cost, the binary variables are eliminated and the problem can be formulated as a linear optimization model. Some randomly generated instances are solved and corresponding solutions evaluated. The examples show that the proposed models offer consistent managerial support for their use in the real problem.
The aim of this work was to study a distribution and lot-sizing problem that considers costs with transportation to a company warehouse as well as, inventory, production and setup costs. The logistic costs are associated with necessary containers to pack produced items. The company negotiates a long-term contract in which a fixed cost per period is associated with the transportation of the items. On the other hand, a limited number of containers are available with a lower cost than the average cost. If an occasional demand increase occurs, other containers can be utilized; however, their costs are higher. A mathematical model was proposed in the literature and solved using the Lagrangian heuristic. Here, the use of the Lagrangian/ surrogate heuristic to solve the problem is evaluated. Moreover, an extension of the literature model is considered adding capacity constraints and allowing backlogging. Computational tests show that Lagrangian/ surrogate heuristics are competitive, especially when the capacity constraints are tight.Keywords: lot-sizing; transportation costs; Lagrangian/surrogate relaxation.
ResumoNeste trabalho estuda-se um problema de dimensionamento de lotes e distribuição que envolve além de custos de estoques, produção e preparação, custos de transportes para o armazém da empresa. Os custos logísticos estão associados aos contêineres necessários para empacotar os produtos produzidos. A empresa negocia um contrato de longo prazo onde um custo fixo por período é associado ao transporte dos itens, em contrapartida um limite de contêineres é disponibilizado com custo mais baixo que o custo padrão. Caso ocorra um aumento ocasional de demanda, novos contêineres podem ser utilizados, no entanto, seu custo é mais elevado. Um modelo matemático foi proposto na literatura e resolvido utilizando uma heurística Lagrangiana. No presente trabalho a resolução do problema por uma heurística Lagrangiana/surrogate é avaliada. Além disso, é considerada uma extensão do modelo da literatura adicionando restrições de capacidade e permitindo atraso no atendimento a demanda. Testes computacionais mostraram que a heurística Lagrangiana/surrogate é competitiva especialmente quando se têm restrições de capacidade apertada.Palavras-chave: dimensionamento de lotes; custos de transporte; relaxação Lagrangiana/surrogate.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.