H.T. Papadopoulos

Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines

Abstract Queueing network modeling of manufacturing systems has been addressed by a large number of researchers. The purpose of this paper is to provide a bibliography of material concerned with modeling of production and transfer lines using queueing networks. Both production and transfer lines have a product-flow layout and are used in mass manufacturing. We denote production lines as flow lines with asynchronous part transfer, while transfer lines have synchronous part transfer. As well as providing a bibliography of material, a contribution of this paper is also the systematic categorization of the queueing network models based on their assumptions. This, it is hoped, will be of use to researchers of queueing networks and also manufacturing system designers. A number of suggestions are also given for further research. The basic source for this work is the book by Papadopoulos, Heavey and Browne, with the addition of the newly published papers and books (from 1992 to early 1995).

The throughput rate of multistation unreliable production lines

Abstract This paper is concerned with unreliable multistation series production lines. The first station is never starved and the last station is never blocked. The processing times at each station i is Erlang type P i distributed with P i , the number of phases, allowed to vary for each station. Buffers of nonidentical capacities are allowed between successive stations. A station maybe reliable or unreliable. Time to failure is exponentially distributed and repair times are Erlang type R i distributed with R i allowed to vary, at each station. In this paper a methodology for generating the associated set of linear equations is presented. These set of linear equations are solved via the use of the Successive Over-Relaxation (SOR) method with a dynamically adjusted relaxation factor as used by Seelen [25]. Referring to the throughput rate of the production lines, many numerical cases are solved and documented. These exact results are of use for comparison purposes against approximate results which exist in the literature. Although many new results are obtained, the size of the system which can be solved is inherently limited by the technique being used. This is due to the curse of dimensionality.

A heuristic algorithm for the buffer allocation in unreliable unbalanced production lines

Abstract In this work we investigate the buffer allocation problem (BAP) in short unbalanced production lines consisting of up to six machines that are subject to breakdowns. Times to failure are assumed exponential whereas service and repair times are allowed to follow any Erlang- k distribution (with k ≥1). An algorithm that is based on the sectioning (segmentation) approach was developed which solves the BAP. This, in conjunction with a method not previously reported that determines a “good” initial solution for the buffer allocation constitutes the main contribution of the present work. The accuracy of the proposed heuristic algorithm is remarkably good and its convergence is fast making it a promising tool that can be implemented in conjunction with a fast decomposition method to solve the BAP in large production lines.

Throughput rate of multistation reliable production lines with inter station buffers. (I) Exponential case

Abstract This paper is concerned with reliable multistation series production lines. Items arrive at the first station according to a Poisson distribution with an operation performed on each item by the single machine at each station. The processing times at each station i is Erlang type P i distributed with P i , the number of phases, allowed to vary for each station. Buffers of non-identical capacities are allowed between successive stations. The structure of the transition matrices of these specific type of production lines is examined and a recursive algorithm is developed for generating them. The transition matrices are block-structured and very sparse and by applying the proposed algorithm, one can create the transition matrix of a K- station line for any K . This process allows one to obtain the exact solution of the large sparse linear systems via the use of the Successive Overrelaxation (SOR) method with a dynamically adjusted factor. Referring to the throughput rate of the production lines, new numerical results are given.

A field service support system using a queueing network model and the priority MVA algorithm

In many companies, the field service (FS) department plays an important role, contributing up to 40% to the companys total revenue. FS managers have to cope with conflicting objectives: (a) to maintain a high level of customer service and (b) to keep the spares inventory level as low as possible. Therefore, they need tools to analyse the impact of their decisions on customer service and inventory cost. Such a tool is presented in this paper. We have developed a closed queueing network model, similar to one due to Waller, incorporating priority classes of customers via the application of the priority mean value analysis (PMVA) algorithm, developed by Shalev-Oren et al. This model has been applied to the FS organization of the Greek subsidiary of a multinational computer company, and it has proved to be very efficient from the computational point of view, thus constituting a powerful tool for the FS managers.

Optimal buffer allocation in short m -balanced unreliable production lines

Abstract In this work, we investigate the optimal buffer allocation in short μ -balanced production lines consisting of machines that are subject to breakdown. Repair times and times to failure are assumed exponential, whereas service times are allowed to follow the Erlang- k distribution (with k =1, 2, 4 and 8). By an improved enumeration procedure and applying the evaluative algorithm of Heavey et al. (European Journal of Operational Research 1993;68:69–89) for the calculation of throughput, we have examined in a systematic way several systems with 3, 4, 5, 6 and 7 stations and with a different total number of buffer slots. We have been able to give answers to some critical questions. These include the effect of the distribution of the service and repair times, the availability of the stations and the repair rates on the optimal buffer allocation and the throughput of the lines.

An analytic formula for the mean throughput of K-station production lines with no intermediate buffers

Abstract Using the holding time model (HTM) method, an approximate analytic formula is derived for calculating the average throughput of a K -station production line with exponential service times, manufacturing blocking and no intermediate buffers between adjacent stations. The usefulness of the proposed analytical formula relies on the fact that it can handle the (general) case of workstations with different mean processing times — this being the contribution of this work compared against that of Alkaff and Muth — provided a good estimation of some coefficients involved is being made. By doing this for the balanced lines case, a simple formula is proposed with very good numerical results.

A recursive algorithm for generating the transition matrices of multistation series production lines

Abstract This paper is concerned with reliable multistation series production lines, where an operation is performed on each job by the single machine at each station and jobs for the first station arrive according to a Poisson distribution. The processing times of all the stations are exponentially distributed and no buffers are allowed between successive stations. The structure of the transition matrices of these specific types of production lines is examined and a one-stage recursive algorithm is provided for generating them. The transition matrices are block-structured and sparse and by applying the proposed algorithm, one can create the transition matrix of a K- station line from the ( K−1)- station transition matrix. This process avoids the necessity of writing down explicitly all the feasible states and transitions of the model, which is tedious and time-consuming especially for long production lines (i.e. for K=12 stations, the number of states is 46, 368.

The Throughput of Multistation Production Lines with No Intermediate Buffers

This paper concerns the throughput rate of multistation reliable production lines with no intermediate buffers. Processing times at the service stations are independent, exponential random variables, possibly with different means. We extend the work started in E. J. Muth (Muth, E. J. 1984. Stochastic processes and their network representations associated with production line queueing model. Eur. J. Opnl. Res. 15 63–83.) to provide an algorithm that allows for the efficient computation of longer lines and to provide results for the nonidentical server case. A result is presented which provides the distribution function of the holding time at the stations.

A model management system (MMS) for the design and operation of production lines

This work presents a prototype model management system (MMS) for the design and operation of manufacturing systems. The model management system classifies different models according to the type of the manufacturing system to which they apply and according to the particular technique employed. In its present state, the system comprises three different techniques, namely, analytical, simulation and artificial intelligence (AI) based techniques for production lines. The first two are evaluative methods, whereas the last one is a generative (optimization) method that solves the well-known buffer allocation problem in a production line. The contribution of this work is twofold. First, the development of an architecture of a MMS which provides a simple and intelligible framework for classifying different modelling techniques, enables the interaction among these models and does not restrict developers to follow a particular model development task. Second, the development of a knowledge based system, called ASBA,...