A line-balancing strategy for designing flexible assembly systems

We present a rough-cut analysis tool that quickly determines a few potential cost-effective designs at the initial design stage of flexible assembly systems (FASs) prior to a detailed analysis such as simulation. It uses quantitative methods for selecting and configuring the components of an FAS suitable for medium to high volumes of several similar products. The system is organized as a series of assembly stations linked with an automated material-handling system moving parts in a unidirectional flow. Each station consists of a single machine or of identical parallel machines. The methods exploit the ability of flexible hardware to switch almost instantaneously from product to product. Our approach is particularly suitable where the product mix is expected to be stable, since we combine the hardware-configuration phase with the task-allocation phase.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45513/1/10696_2004_Article_BF00167513.pd

Manufacturing flow line systems: a review of models and analytical results

The most important models and results of the manufacturing flow line literature are described. These include the major classes of models (asynchronous, synchronous, and continuous); the major features (blocking, processing times, failures and repairs); the major properties (conservation of flow, flow rate-idle time, reversibility, and others); and the relationships among different models. Exact and approximate methods for obtaining quantitative measures of performance are also reviewed. The exact methods are appropriate for small systems. The approximate methods, which are the only means available for large systems, are generally based on decomposition, and make use of the exact methods for small systems. Extensions are briefly discussed. Directions for future research are suggested.National Science Foundation (U.S.) (Grant DDM-8914277

Stochastic programming approaches to stochastic scheduling

Practical scheduling problems typically require decisions without full information about the outcomes of those decisions. Yields, resource availability, performance, demand, costs, and revenues may all vary. Incorporating these quantities into stochastic scheduling models often produces diffculties in analysis that may be addressed in a variety of ways. In this paper, we present results based on stochastic programming approaches to the hierarchy of decisions in typical stochastic scheduling situations. Our unifying framework allows us to treat all aspects of a decision in a similar framework. We show how views from different levels enable approximations that can overcome nonconvexities and duality gaps that appear in deterministic formulations. In particular, we show that the stochastic program structure leads to a vanishing Lagrangian duality gap in stochastic integer programs as the number of scenarios increases.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44935/1/10898_2004_Article_BF00121682.pd

Bounding a Probability Measure over a Polymatroid with an Application to Transportation Problems

We are given a set of supply nodes, a set of demand nodes and a set of arcs between certain supply/demand pairs, which indicate if the supply node can serve as a source for the demand node. The level of the supply available at each supply node and the amount demanded by each demand node are independent random variables. We derive an upper bound on the probability that the random demand can be met by the random supply under the assumption that the supply levels have new better than used (NBU) distribution functions. The functional form of the bound is the product of the probabilities that each demand node, viewed independently, can be feasibly satisfied. In order to prove this result we first prove another result concerning polymatroids. This result gives a lower bound on the probability that a random vector is the member of the polymatroid