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. (C) 2010 Elsevier Ltd. All rights reserved.

Bootstrap confidence intervals for industrial recurrent event data

Industrial recurrent event data where an event of interest can be observed more than once in a single sample unit are presented in several areas, such as engineering, manufacturing and industrial reliability. Such type of data provide information about the number of events, time to their occurrence and also their costs. Nelson (1995) presents a methodology to obtain asymptotic confidence intervals for the cost and the number of cumulative recurrent events. Although this is a standard procedure, it can not perform well in some situations, in particular when the sample size available is small. In this context, computer-intensive methods such as bootstrap can be used to construct confidence intervals. In this paper, we propose a technique based on the bootstrap method to have interval estimates for the cost and the number of cumulative events. One of the advantages of the proposed methodology is the possibility for its application in several areas and its easy computational implementation. In addition, it can be a better alternative than asymptotic-based methods to calculate confidence intervals, according to some Monte Carlo simulations. An example from the engineering area illustrates the methodology.