Stanley B. Gershwin

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.

An Algorithm for the Computer Control of a Flexible Manufacturing System

Abstract The problem of production management for an automated manufacturing system is described. The system consists of machines that can perform a variety of tasks on a family of parts. The machines are unreliable, and the main difficulty the control system faces is to meet production requirements while the machines fail and are repaired at random times. A multilevel hierarchical control algorithm is proposed which involves a stochastic optimal control problem at the first level. Optimal production policies are characterized, and a computational scheme is described.

An efficient decomposition method for the approximate evaluation of tandem queues with finite storage space and blocking

This paper presents an efficient method for evaluating performance measures for a class of tandem queueing systems with finite buffers in which blocking and starvation are important. These systems are difficult to evaluate because they have large state spaces and because they cannot be decomposed exactly. The approximate decomposition approach we describe is based on system characteristics such as conservation of flow. Comparisons with exact and simulation results indicate that the approach is very accurate.

Hierarchical flow control: a framework for scheduling and planning discrete events in manufacturing systems

The synthesis of operating policies for manufacturing systems is discussed. These are feedback laws that respond to potentially disruptive events. Laws are developed that are based on realistic dynamic programming models that account for the discrete nature of manufacturing and are computationally tractable. These scheduling and planning policies have a hierarchical structure which is systematically based on the production process. The levels of the hierarchy correspond to classes of events that occur with distinct frequencies. At each level, feedback laws select times for the controllable events whose frequency class is treated at that level and frequency targets for much higher-frequency controllable events. >

An algorithm for the computer control of production in a flexible manufacturing system

The problem of management of production for an automated manufacturing system is described. The system consists of machines which can perform a variety of operations on a family of parts. The machines are unreliable, and the chief difficulty the control system faces is to meet production requirements while the machines fail and become repaired at random times. A three-level hierarchical control algorithm is proposed which involves stochastic optimal control, network optimization, and scheduling. An example is presented.

Information inaccuracy in inventory systems: stock loss and stockout

Many companies have automated their inventory management processes and now rely on information systems when making critical decisions. However, if the information is inaccurate, the ability of the system to provide a high availability of products at the minimal operating cost can be compromised. In this paper, analytical and simulation modelling demonstrate that even a small rate of stock loss undetected by the information system can lead to inventory inaccuracy that disrupts the replenishment process and creates severe out-of-stock situations. In fact, revenue losses due to out-of-stock situations can far outweigh the stock losses themselves. This sensitivity of the performance to the inventory inaccuracy becomes even greater in systems operating in lean environments. Motivated by an automatic product identification technology under development at the Auto-ID Center at MIT, various methods of compensating for the inventory inaccuracy are presented and evaluated. Comparisons of the methods reveal that the inventory inaccuracy problem can be effectively treated even without automatic product identification technologies in some situations.

A comparison of production-line control mechanisms

We study the performance of the kanban, minimal blocking, basestock, CONWIP, and hybrid kanban-CONWIP control policies in a four-machine tandem production line making parts for an automobile assembly line. Cases with both constant and changing demand rates are studied. The main performance measures are the service level and the amount of work-in-progress. We also consider other performance measures such as variability amplification along the line. The results are obtained by extensive simulations. We find that the best parameter choices for the hybrid policy decrease inventories by 10% to 20% over the best kanban policy while maintaining the same service levels. The inventory difference grows as the demands on service level increase. The performance of basestock and CONWIP policies falls between those of the kanban and hybrid policies. The CONWIP and hybrid policies also give significantly better response to changes in the demand rate.

Efficient algorithms for buffer space allocation

This paper describes efficient algorithms for determining how buffer space should be allocated in a flow line. We analyze two problems: a primal problem, which minimizes total buffer space subject to a production rate constraint; and a dual problem, which maximizes production rate subject to a total buffer space constraint. The dual problem is solved by means of a gradient method, and the primal problem is solved using the dual solution. Numerical results are presented. Profit optimization problems are natural generalizations of the primal and dual problems, and we show how they can be solved using essentially the same algorithms.

Short-term production scheduling of an automated manufacturing facility

We describe extensions to the on-line hierarchical scheduling scheme for flexible manufacturing systems of Kimemia and Gershwin. Major improvements to all levels of the algorithm are reported, including algorithm simplification, substantial reductions of off-line and on-line computation time, and improvement of performance. Simulation results based on a detailed model of an IBM printed circuit card assembly facility are summarized.

Modeling and Analysis of Three-Stage Transfer Lines with Unreliable Machines and Finite Buffers

In an important class of systems, which arises in manufacturing, chemical process, and computer contexts, objects move sequentially from one work station to another, and rest between stations in buffers. In the manufacturing context, such systems are called transfer lines. The dynamic behavior of a buffered transfer line with unreliable work stations is modeled as a Markov chain. The system states consist of the operational conditions of the work stations and the levels of material in the buffers. The steady-state probabilities of these states are sought in order to establish relationships between system parameters and performance measures such as production rate (efficiency), forced-down times, and expected in-process inventory. The steady state probabilities are found by choosing a sum-of-products form solution for a class of states, and deriving the remaining expressions by using the transition equations. In this way, the order of the system of equations to be solved is drastically reduced. This algorithm suggests a general approach for solving large scale structured Markov chain problems.