John A. Buzacott

Models of automatic transfer lines with inventory banks a review and comparison

Abstract The purpose of this paper is to evaluate and compare past models of transfer lines. After a discussion of the nature of transfer lines and their stoppages, the assumptions and derivations of seven analytical models are compared. The major discrepancies in assumptions concern whether failures are time dependent or operation dependent. The comparison of derivations includes a translation of all results to a common set of symbols. The predictions of the models at various banking levels are observed to vary significantly. Model validation is discussed in two phases. First the validity of the assumptions is tested by real data from a transfer line. The major problem is the failure of the real data to satisfy the assumptions of the model. Finally, the predictions of the analytical models are compared with a simulation model which uses the actual data. The difference between analytical and simulation models was found to be significant.

Models for Understanding Flexible Manufacturing Systems

Abstract The basic features of flexible manufacturing systems are reviewed and models for determining the production capacity of such systems are developed. These models show the desirability of a balanced work load, the benefit of diversity in job routing if there is adequate control of the release of jobs (a job shop can be better than a flow shop), and the superiority of common storage for the system over local storage at machines. The models are extended to allow for material handling delays between machines and for unreliable machines. It is also shown that production capacity models can be used to develop good approximations to the mean number of jobs in the system for given job arrival rates and machine utilizations.

Open queueing network models of dynamic job shops

An open queueing network model of dynamic job shops with general service times and first come first served or shortest processing time service discipline is considered here. An approximate decomposition approach is proposed to analyse this queueing network model and its accuracy is compared to simulation results of some symmetric and flow shops.

Flexibility and decision making

Abstract This paper presents a formal treatment of flexibility by using decision theory in a two-period decision problem. It is supposed that each action at the first period has a flexibility measure the number of options open at the second period. The model presented assumes that uncertainty exists in the loss functions of the decision problem and shows how this uncertainty gives rise to a consideration of flexibility as a criterion in the decision process. The tradeoff of flexibility against an expected loss calculated using a preliminary model is shown. A simple manufacturing example is used to illustrate the ideas.

The role of inventory banks in flow-line production systems

Many production managers of flow-line systems, such as in the steel and metal processing industries, observe the high levels of in-process inventories. They feel that it should be possible to reduce these inventories; however, before doing so it is necessary for them to understand their function. Although the general rule that inventories exist because of imbalance in supply and demand at a point within the system is true, it is necessary to show more precisely how such an imbalance might arise in single-product systems due to variability in processing times at the stations, or interruptions in production due to breakdown and subsequent repair of stations. Quantitative results have been obtained which indicate how such factors as the number, location and capacity of inventory bank, affect the system production rate. These results enable system designers and operators to check whether their systems could be improved.

On queueing network models of flexible manufacturing systems

This paper outlines the state-of-the-art in studying flexible manufacturing systems (FMSs) using analytical queueing network models. These include Jackson networks, reversible networks and approximate models of non-product-form networks. The focus is on identifying the major features of the models as they relate to the operational characteristics of FMSs. Prescriptive models concerning the optimal design and/or operational control of FMS networks are also discussed.

Modelling the performance of flexible manufacturing systems

An open-queueing network model with general service times and limited local buffers is developed to evaluate the performance of the flexible manufacturing system (FMS). The model accommodates two major characteristics of the FMS, namely, improving machine utilization and reducing work-in-process storage. A ‘flow equivalent’ decomposition approach is developed to derive approximate solutions to the model. Numerical examples are studied to illustrate the accuracy of the approximations.

The Effect of Station Breakdowns and Random Processing Times on the Capacity of Flow Lines with In-Process Storage

Abstract In-process inventory banks are considered for a flow-line producing a single product. Models are developed which enable the increase in production capacity to be calculated if both sources of station production rate variability are present. An exact Markov model of a two station system gives complicated results. However, a simple method of combining the results of the previous work on random processing times and on breakdowns in a fixed-cycle system gives very good approximations to the results of the exact model. The approximate approach can be extended to three or more stations.

Models of flexible manufacturing systems with limited local buffers

SUMMARY Local buffers at the work stations in moat flexible manufacturing systems have very limited storage capacity and, consequently, parts attempting to enter the work stations may be blocked. Parts routing that follows a dynamic scheme adapted to the state of the system is also desirable. A set of models has been developed to accommodate these features of real systems. The models have easily computable solutions, and with small local buffers are robust to various processing-time distributions. For systems with large local buffers, they can readily incorporate the exponentialization approach to yield accurate results.

On the approximations to the single server queue

In this article some approximations for the mean number in the single server queueing system are presented and compared. Based on numerical comparison a guide is provided to select the appropriate approximation(s) for different ranges, of the squared coefficient of variation of the inter-arrival and service time distributions. Two approximations for the distribution of the number in the system are given and the better is chosen.