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

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

Alexandros Diamantidis (Department of Economics, Aristotle University of Thessaloniki Thessaloniki, Greece), Stylianos Koukoumialos (Department of Business Administration, Technological Educational Institute of Thessaly, Larissa, Greece), and Michael Vidalis (Department of Business Administration, University of the Aegean, Chios, Greece)
DOI: 10.4018/IJORIS.2017040101
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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.
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Literature Review

There is a rich body of literature on the analysis of push serial flow lines with linear flow of material (Gershwin, 1994; Papadopoulos, Heavey, & Browne, 1993). The amount of research devoted to the analysis of push-pull systems is relatively small. Moreover, the number of papers in the literature addressing the analysis of push-pull systems with merge operations is really small.

Considering the literature of push merge systems, a push model with two merging stations and two buffers, which was analysed through decomposition using as a decomposition block virtual two-machine one buffer lines was presented by (Helber, 1999). Three machine one buffer systems with machine specific processing times, exponentially distributed failure and repair times examined by (Helber & Mehrtens, 2003). Additionally, continuous flow of material was assumed. An exact analysis of this model was presented using differential equations to derive the transition probabilities. An exact algorithm to compute the throughput of a more general system that allows arbitrary deterministic processing times and exponentially distributed failure and repair times was developed by (Helber & Jusic, 2004). A discrete material push merge system with three unreliable machines and one buffer of limited capacity was examined by (Diamantidis, Papadopoulos, & Vidalis, 2004). Processing times were assumed to be deterministic and identical for all machines and were taken as the time unit. The operation dependent failures at the machines were also assumed to be Geometrically distributed.

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