Knowledge that Transforms

We address a medium‐ to short‐term production planning problem in a flexible manufacturing environment. First we present a single‐machine, mixed integer programming model for part type selection and lot‐sizing problems over a T‐period planning horizon. Demand for part types changes dynamically through the periods. The objective is to meet the demand for part types during the periods they are demanded. Available machine time and tool magazine capacities are the system constraints in our models. We next extend on the single‐ machine model to include multiple machines. In addition to part type selection and lotsizing decisions, the extended model also addresses the machine‐loading decision. We present exact branch and bound procedures based on linear programming relaxations for the two models. We also report the results of our computational experiments.

In assembly plants, random line stoppages cause production variability. For analytic tractability and data availability, researchers commonly assume that the production process possesses the independent increments property (necessary for a process to be Poisson). If the production process has independent increments, then the production in any interval is independent of the production in any other nonoverlapping interval. This property means, for one thing, that the current period's production is never influenced by previous production periods. Intuition, however, suggests that current production could be correlated to past production‐violating this assumption of independence. If production problems persist from one period to the next, then one would expect the production in adjacent time periods to be correlated. Although the independent increments property is oflen assumed, its validity has not been demonstrated in practice. We analyze data from an automotive assembly plant to assess the validity of the independent increments assumption for its production.

To design (or redesign) a competitive product, it is imperative that both the sales and manufacturing cost implications are assessed in a structured way. That is, the interactive (multidimensional) aspects of manufacturing and marketing variables need to be positioned in a proper perspective so that the system impact of variation in one or more variables may be ascertained quickly. In this paper we show how some of the system‐related paradigms can be used as foundations for developing quantitative and qualitative models for tracking such interactive ímpacts. The emphasis is not on building complex mathematical models to solve specific problems but on providing a framework where system properties expressed as simple postulates can be used in an intelligent way to assess the impact of improvements in specific product‐process scenarios.

The early/tardy problem is one of the most vexing pieces of the complex production scheduling decision process. So far most of the research has been on single‐machine environments. Hence, we considered the weighted early/tardy scheduling problem in a simulated dynamic multimachine job shop. We analyzed controlled job‐release and dispatch rules using time and cost information at a variety of stationary and nonstationary utilization rates, due‐date allowances, and early/tardy cost levels. We found a newly developed method for controlling the release for all job operations using early/tardy cost information, superior to other release mechanisms overall in both our stationary and nonstationary analyses. We found immediate release useful at many high utilization conditions and a gateway‐only release method best in many low utilization conditions. A modified version of a single‐machine early/tardy dispatch method was clearly superior to the dispatch rules for almost all the simulated shop conditions.

We developed a framework for analyzing semiconductor fabrication facilities where each processing step of each product can use a collection of resources. The interaction of these resources is not prespecified by the analysis system but is described by the modeler. Our framework includes three types of modeling approaches: analytic approximation, simulation, and a hybrid analytic/simulation technique. All models are automatically generated from a data description of the facility and the products produced, along with the resource interaction models provided by the user. The novel feature of our approach is that the data description language includes a simple but quite flexible simulation‐like modeling language for expressing resource interactions. Our analytic modeling approach is an extension of the standard decomposition method used for studying networks of queues. In our hybrid analytic/simulation technique we use simulation to estimate processing step flow times to improve the performance of the analytic model.

The allocation and weekly scheduling of mobile magnetic resonance imaging (MRI) units leased to a group of hospitals that share the equipment can be a complex problem. Similar problems occur in other domains where expensive equipment or facilities such as video conference facilities, aircraft, and supercomputers are leased. The crux of the problem was determining the number of days and which days of the week various types of equipment types should be leased to hospitals, so as to maximize the rental revenues and satisfy client preferences for days of the week and equipment types. We found rental revenues were a decreasing function of the number of days allocated to a hospital. We considered two sub‐problems linked by a set of variables to model the problem. We show that one of these subproblems is a minimum cost network flow problem and the other is an integer multi‐commodity transportation problem. We developed a procedure for solving the latter problem by exploiting earlier results for specialized networks. We conducted a computational study to evaluate the performance of this procedure and showed that it generally provides near‐optimal integer solutions. We describe the development and implementation of a spreadsheet‐based decision support system based on this model. This system was successfully implemented by a small firm with no expertise or prior experience using models.