Alexandros Diamantidis

Exact analysis of a discrete material three-station one-buffer merge system with unreliable machines

In this paper, a model of a discrete material flow line consisting of three unreliable machines and one buffer of limited capacity is analysed. A similar system, but with continuous flow of material was examined by Helber and Mehrtens (2001) and Tan (2001). In our system it is assumed that the buffer has two immediate preceding machines, performing the same operations and one immediate succeeding machine that receives material from the buffer. For the case where the buffer reaches its own capacity, one of the two preceding machines has priority over the other to dispose its processed part into the buffer. Processing times are assumed to be deterministic and identical for all machines and are taken as the time unit. Geometrically distributed operation dependent failures at the machines are assumed. All possible transition equations for the examined model are derived and a recursive algorithm that generates the transition matrix for any value N of the storage level is developed. Once the transition matrix is known the performance measures of the model under consideration can be easily evaluated. This model may be used as a building block in a decomposition method to evaluate large production systems with split/merge operations (for example, flow lines with quality inspections and rework loops).

A dynamic programming algorithm for the buffer allocation problem in homogeneous asymptotically reliable serial production lines

In this study, the buffer allocation problem (BAP) in homogeneous, asymptotically reliable serial production lines is considered. A known aggregation method, given by Lim, Meerkov, and Top (1990), for the performance evaluation (i.e., estimation of throughput) of this type of production lines when the buffer allocation is known, is used as an evaluative method in conjunction with a newly developed dynamic programming (DP) algorithm for the BAP. The proposed algorithm is applied to production lines where the number of machines is varying from four up to a hundred machines. The proposed algorithm is fast because it reduces the volume of computations by rejecting allocations that do not lead to maximization of the lines throughput. Numerical results are also given for large production lines.

Approximate analysis of serial flow lines with multiple parallel-machine stations

This paper studies serial flow lines, in which each station consists of multiple identical reliable parallel machines. The parallel machines of different work stations are not necessarily identical, viz., station processing times are assumed to be exponentially distributed with non-identical mean service rates. Initially, a model consisting of two stations with multiple parallel machines and an intermediate buffer is solved analytically, by developing a recursive algorithm that generates the transition matrix for any value of the intermediate buffer capacity. This model is used as a decomposition block for solving larger lines. More specifically, the decomposition block is solved via exact Markovian analysis and then the decomposition equations and an algorithm that simultaneously solves them are derived in order to evaluate the performance measures of large production systems with multiple parallel-machine stations. Numerical results are provided for large production lines with up to 1000 workstations. These results are compared against simulation and the average percentage error is found to be very small.

Markovian analysis of a discrete material manufacturing system with merge operations, operation-dependent and idleness failures

This paper examines a discrete material manufacturing system consisting of three machines that are subject to breakdown and one buffer of finite capacity. It is assumed that the buffer has two immediate preceding machines performing the same operations and one immediate succeeding machine receiving material from the buffer. When the buffer reaches its own capacity, one of the two preceding machines has priority over the other to dispose its processed part into the buffer.It is also assumed that there is a new way of the machines reaching failure, by allowing the machines to fail not only when they are operational but also when are either blocked or starved. The latter gives rise to the possibility of modeling the production of more than one part types. The model is solved analytically by developing a recursive algorithm that generates the transition matrix for any value C of the intermediate buffer capacity. Then various performance measures of the system (e.g., throughput) can be easily evaluated. Numerical results for the throughput are also given and these are compared against simulation. The proposed model may be used as a decomposition block to solve large flow lines with merge/ split operations (for example, flow lines with quality inspections and rework loops) and multiple part types.

Markovian Analysis of a Push-Pull Merge System with Two Suppliers, An Intermediate Buffer, and Two Retailers

This paper examines a push-pull merge system with two suppliers, two retailers and an intermediate buffer distribution centre. Two reliable non identical suppliers performing merge operations feed a buffer that is located immediately upstream of two non-identical reliable retailers. External customers arrive to each retailer with non-identical inter-arrival times that are exponentially distributed. The amount ordered from each retailer by a customer is exactly one unit. The material flows between upstream stages suppliers is push type, while between downstream stages retailers it is driven by continuous review, reorder point/order quantity inventory control policy s,S. Both suppliers and retailers have exponential service rates. The considered system is modelled as a continuous time Markov process with discrete states. An algorithm that generates the transition matrix for any value of the parameters of the system is developed. Once the transition matrix is known the stationary probabilities can be computed and therefore the performance measures of the model under consideration can be easily evaluated.

Performance evaluation of a push–pull merge system with multiple suppliers, an intermediate buffer and a distribution centre with parallel machines/channels

This paper examines a push–pull merge system with external demand. Multiple reliable non-identical suppliers feed a buffer that is located immediately upstream a distribution centre (DC) with parallel identical reliable machines. The DC performs another operation on the items stored in the preceding buffer and the finished products are stored in another buffer (the finished products buffer) immediately downstream the DC. Customers arrive to the system according to a Poisson process with given intensity λ and remove a finished product from the buffer of finished products. The size of a customer demand is equal to one. Both suppliers and the identical machines at DC have exponential service rates. The considered system is modelled as a continuous-time Markov process with discrete states. An algorithm that generates the transition matrix for any value of the parameters of the system is developed and all possible transition equations are derived and solved analytically. Once the transition matrix is known the performance measures of the model under consideration can be easily evaluated.

Performance Evaluation of a Push Merge System with Multiple Suppliers, an Intermediate Buffer and a Distribution Center with Parallel Channels: The Erlang Case

In this paper, the most important performance measures of a two stage, push merge system are estimated. More specifically, S non identical and reliable suppliers send material to a distribution center (DC) of one product type. The DC has N possible parallel identical reliable machines. Between the suppliers and the DC a buffer with unlimited capacity, is located in order the material flow to be controlled. All stations processing and replenishment times are assumed stochastic and follow the Erlang distribution. The considered model is developed as Markov Process with discrete states where the Matrix Analytic method is used to calculate the system stationary probabilities and performance measures.

A Comparison of Three Search Algorithms for Solving the Buffer Allocation Problem in Reliable Production Lines

This paper investigates the performance of three search algorithms: Myopic Algorithm, Adaptive Tabu Search and Degraded Ceiling to solve the buffer allocation problem in reliable production lines. DECO algorithm is used to calculate throughput. This algorithm is a variant of a decomposition algorithm specifically developed to solve large reliable production lines with parallel machines at each workstation and exponentially distributed service times. The measures of performance used are the CPU time required and closeness to the maximum throughput achieved. The three search algorithms are ranked in respect to these two measures and certain findings regarding their performances over the experimental set are given.

Analysis of a three machine-one buffer merge system with quality and operational failures

Abstract This paper examines a three machine- one buffer merge system with quality and operational failures. It is assumed that the buffer has two immediate preceding machines, performing the same operations and one immediate succeeding machine that receive material from the buffer. For the case where the buffer reaches its own capacity, one of the two preceding machines has priority over the other to dispose its processed part into the buffer. Processing times are assumed to be deterministic and identical for all machines and are taken as the time unit. Operational, quality failures and repair probabilities are geometrically distributed. All possible transition equations for the examined model are derived and a recursive algorithm that generates the transition matrix for any value N of the storage level is developed. Such a model can be used as a building block in a decomposition method for the performance evaluation of large production systems with split/merge operations (for example, flow lines with rework loops).