Dynamic material handling for a class of flexible manufacturing systems

A real-time hierarchical routing control scheme for a large class of material handling systems is presented. The higher level (coordinator) performs resource allocation tasks and supplies parameter values to the lower (local control) level. The lower level operates in an autonomous (without continuous supervision) and distributed fashion. If state information is made available to the coordinator, the routing strategy can furthermore be adaptively adjusted.     

The part families problem in flexible manufacturing systems

Parts grouping into families can be performed in flexible manufacturing systems (FMSs) to simplify two classes of problems: long horizon planning and short horizon planning. In this paper the emphasis is on the part families problem applicable to the short horizon planning. Traditionally, parts grouping was based on classification and coding systems, some of which are reviewed in this paper. To overcome the drawbacks of the classical approach to parts grouping, two new methodologies are developed. The methodologies presented are very easy to implement because they take advantage of the information already stored in the CAD system. One of the basic elements of this system is the algorithm for solving the part families problem. Some of the existing clustering algorithms for solving this problem are discussed. A new clustering algorithm has been developed. The computational complexity and some of the computational results of solving the part families problem are also discussed.     

Impact of flexible machines on automated manufacturing systems

Although the problem of scheduling dynamic job shops is well studied, setup and changeover times are often assumed to be negligibly small and therefore ignored. In cases where the product mix changes occur frequently, setup and changeover times are of critical importance. This paper applies some known results from the study of multi-class single-server queues with setup and changeover times to develop an approximation for evaluating the performance of job shops. It is found that the product mix, setup and changeover times, and scheduling rules affect the performance significantly, in particular at high levels of machine utilisation. This approach could be used to determine the required level of flexibility of machines and to choose an appropriate scheduling policy such that production rates remain within acceptable limits for foreseeable changes in the product mix.     

Piecewise deterministic Markov process model for flexible manufacturing systems with preventive maintenance

In this paper, we consider a maintenance and production model of a flexible manufacturing system. The maintenance activity involves lubrication, routine adjustments, etc., which reduce the machine failure rates and therefore reduce the aging of the machines. The objective of the problem is to choose the rate of maintenance and the rate of production that minimize the overall costs of inventory/shortage, production, and maintenance. It is shown that the value function is locally Lipschitz. Then, the existence of the optimal control policy is shown, and necessary and sufficient conditions for optimality are obtained.This research has been supported by NSERC-Canada, Grant OGP-003644 and FCAR-NC0271F.     

Numerical performance of approximate queuing formulae with application to flexible manufacturing systems

This paper calls attention to two of the more successful queuing approximation formulae — one by Kramer and one by Marchal. The analytic solution of a range of single server Erlang cases is compared to the two approximation formulae. Then a family of H₂/M/1 cases is similarly considered. Maximum errors are seen to be about three percent. The Kramer formula seems to be better when the interarrival coefficient of variation is less than 0.66 and the Marchal formula is better for larger interarrival coefficients of variation. Finally, a multiserver refinement function (the ratio of G/G/1 results to M/M/1 results) is proposed to scale M/M/s as an approximation for G/G/s. In most of these multiple channel cases, the maximum error is less than six percent. The last section of this paper presents a simple, representative FMS. It is modelled as an open queuing network. Then the approximation procedure is applied node by node to illustrate the estimation of system performance measures such as machine utilizations and throughput.     

An efficient method to determine the optimal configuration of a flexible manufacturing system

A frequently encountered design issue for a flexible manufacturing system (FMS) is to find the lowest cost configuration, i.e. the number of resources of each type (machines, pallets, ...), which achieves a given production rate. In this paper, an efficient method to determine this optimal configuration is presented. The FMS is modelled as a closed queueing network. The proposed procedure first derives a heuristic solution and then the optimal solution. The computational complexity for finding the optimal solution is very reasonable even for large systems, except in some extreme cases. Moreover, the heuristic solution can always be determined and is very close (and often equal) to the optimal solution. A comparison with the previous method of Vinod and Solberg shows that our method performs very well.     

State-Dependent Coupling in General Networks

In this paper we extend a result which holds for the class of networks of quasireversible nodes to a class of networks constructed by coupling Markov chains. We begin with a network in which the transition rates governing the stochastic behaviour of the individual nodes depend only on the state of the node. Assuming that the network has an invariant measure, we construct another network with transition rates at each node depending on the state of the entire network, and obtain its invariant measure.     

Experimental investigation of real-time scheduling in flexible manufacturing systems

This paper presents a new two-phase (TP) approximate method for real-time scheduling in a flexible manufacturing system (FMS). This method combines a reduced enumeration schedule generation algorithm with a 0–1 optimization algorithm. In order to make the combined algorithm practicable, heuristic rules are introduced for the selection of jobs to be scheduled. The relative performance of the TP method vis-a-vis conventional heuristic dispatching rules such as SPT, LPT, FCFS, MWKR, and LWKR is investigated using combined process-interaction/discrete-event simulation models. An efficient experimental procedure is designed and implemented using these models, and the statistical analysis of the results is presented. For the particular case investigated, the conclusions are very encouraging. In terms of mean flow time, the TP method performs significantly better than any other tested heuristic dispatching rules. Also, the experimental results show that using global information significantly improves the FMS performance.     

Sojourn and waiting times in a single-server system with state-dependent mean service rate

A birth-death queueing system with asingle server, first-come first-served discipline, Poisson arrivals and state-dependent mean service rate is considered. The problem of determining the equilibrium densities of the sojourn and waiting times is formulated, in general. The particular case in which the mean service rate has one of two values, depending on whether or not the number of customers in the system exceeds a prescribed threshold, is then investigated. A generating function is derived for the Laplace transforms of the densities of the sojourn and waiting times, leading to explicit expressions for these quantities. Explicit expressions for the second moments of the sojourn and waiting times are also obtained.     

A supervisory control paradigm for real-time control of flexible manufacturing systems

Most of the current academic flexible manufacturing system (FMS) scheduling research has focused on the derivation of algorithms or knowledge-based techniques for efficient FMS real-time control. Here, the limitations of this view are outlined with respect to effective control of actual real-time FMS operation. A more realistic paradigm for real-time FMS control is presented, based on explicit engineering of human and automated control functions and system interfaces. To illustrate design principles within the conceptual model, an example of algorithmic and operator function models for a specific real-time FMS control problem are developed.Portions of this paper have appeared in: Proc. 2nd ORSA/TIMS Conf. on Flexible Manufacturing Systems: Operations Research Models and Applications, Ann Arbor, Michigan, August 12–15, 1986, and Proc. 1986 Int. Conf. on Systems, Man, and Cybernetics, Atlanta, Georgia, October 14–17, 1986.This research was supported in part by the New Faculty Research Program of the Georgia Institute of Technology.     

Structure-reversibility and departure functions of queueing networks with batch movements and state dependent routing

We consider characterizations of departure functions in Markovian queueing networks with batch movements and state-dependent routing in discrete-time and in continuous-time. For this purpose, the notion of structure-reversibility is introduced, which means that the time-reversed dynamics of a queueing network corresponds with the same type of queueing network. The notion is useful to derive a traffic equation. We also introduce a multi-source model, which means that there are different types of outside sources, to capture a wider range of applications. Characterizations of the departure functions are obtained for any routing mechanism of customers satisfying a recurrent condition. These results give a unified view to queueing network models with linear traffic equations. Furthermore, they enable us to consider new examples as well as show limited usages of this kind of queueing networks. This revised version was published online in June 2006 with corrections to the Cover Date.     

Measurement of loading and operations flexibility in flexible manufacturing systems: An information-theoretic approach

An information-theoretic approach is applied for measuring the flexibility in flexible manufacturing systems (FMSs). The general relation between flexibility and entropy is discussed. The entropy for a Markovian process is obtained and then applied to closed queueing network models of FMSs to discuss loading flexibility which arises from the power to regulate the frequency of the visit of a part to different work stations. The concept of operations entropy as a measure of operations flexibility, which arises from the power to choose the work station and the corresponding operations, is introduced. The operations entropy has been decomposed into entropies within and between operations and entropies within and between groups of operations. This measure has been used to determine the next operation to be performed on a part by using the principle of least reduction of flexibility.The present paper is an improved version of the paper On measurement of flexibility in flexible manufacturing systems: An information-theoretic approach, presented at the II ORSA/TIMS Special Conference on Flexible Manufacturing Systems, held at Ann Arbor in August 1986.     

Scheduling methods for a class of flexible manufacturing systems

Scheduling methods are proposed for a class of flexible manufacturing systems consisting of machine centers served by a cyclic conveyor. The minimization of finish time is considered as the optimization criterion. An optimal algorithm is proposed for the minimum conveyor speed (S=1) for a particular system in the class under consideration. Scheduling algorithms based on a job matching principle, that are developed for the general systems, yield good results particularly for low conveyor speeds.This research is supported in part by NSERC Grant A4619 and Manufacturing Research Corporation of Ontario.     

Markovian network processes: Congestion-dependent routing and processing

A Markovian network process describes the movement of discrete units among a set of nodes that process the units. There is considerable knowledge of such networks, often called queueing networks, in which the nodes operate independently and the routes of the units are independent. The focus of this study, in contrast, is on networks with dependent nodes and routings. Examples of dependencies are parallel processing across several nodes, blocking of transitions because of capacity constraints on nodes, alternate routing of units to avoid congestion, and accelerating or decelerating the processing rate at a node depending on downstream congestion. We introduce a general network process representing the numbers of units at the nodes and derive its equilibrium distribution. This distribution takes the form of a product of functions of vectors in which the arguments of the functions satisfy an interchangeability property. This new type of distribution may apply to other multi-variate processes as well. A basic idea in our approach is a linking of certain micro-level balance properties of the network routing to the processing rates at the nodes. The link is via routing-balance partitions of nodes that are inherent in any network. A byproduct of this approach is a general characterization of blocking of transitions without the restriction that the process is reversible, which had been a standard assumption. We also give necessary and sufficient conditions under which a unit moving in the network sees a time average for the unmoved units (called the MUSTA property). Finally, we discuss when certain flows between nodes in an open network are Poisson processes.This research was sponsored in part by Air Force Office of Scientific Research contract 84-0367.     

Evaluation of entropy-based dispatching in flexible manufacturing systems

Traditionally, part dispatching has been done using static rules, rules that fail to take advantage of the dynamic nature of today’s manufacturing systems. In modern manufacturing systems, machines carry multiple tools so parts have the option of being machined at more than one machine. This flexibility, termed routing flexibility in the literature, opens up new possibilities for shop floor planners for the scheduling and dispatching of parts.     

Robust stabilization of a class of state-dependent jump linear systems

In this article, we consider a continuous-time state-dependent jump linear system (SDJLS), a kind of stochastic hybrid system, with the presence of uncertainties in system parameters. In SDJLS, we consider that the transition rates of the underlying random jump process depend on the state variable. In particular, we assume the transition rates to have different values across suitably defined sets to which the state of the system belongs, and address a problem of robust stability and stabilization analysis. We obtain sufficient conditions for robust stability and state-feedback stabilization in terms of linear matrix inequalities (LMIs). We validate the obtained sufficient robust stability and stabilization conditions with numerical examples.     

Analysis of flexible manufacturing systems with priority scheduling: PMVA

A new methodology for performance analysis of flexible manufacturing systems (FMSs) with priority scheduling is presented. The analytic model developed extends the mean value analysis of closed networks of queues with multiple product types, various non-preemptive priority service disciplines, and with parallel machine stations. Performance measures derived include the expected throughput per product and per station, utilization of machines and transporters, queuing times and queue length measures for various configurations. Extensive numerical calculations have shown that the algorithm used for solving the problem converges rapidly and retains numerical stability for large models. The paper also illustrates the application of the model to a system with a mixture of FCFS and HOL disciplines which gives insights into various priority assignment policies in FMSs. Special attention was given to the problem of scheduling the robot carriers (transporters).     

Integrated production scheduling in large-scale flexible electronic parts manufacturing

This study reports the development of a production scheduling system for the integrated management of production in large-scale, high-volume electronic assembly lines. The development of the system incorporates control and planning considerations by addressing the interaction of various subsystems. Stochastic and deterministic aspects of the problem environment are appropriately handled via relevant simulation and analytic models. By effecting a hierarchical breakdown of the problem environment, the system produces information used in practical decision making for production planning and scheduling. Procedures used encompass and address considerations for management of work-in-process, optimization of the various subsystems' performance, minimization of setup time effect, and inventory carrying costs.