Exact analysis of a push–pull system with multiple non identical retailers, a distribution center and multiple non identical unreliable suppliers with supply disruptions

Abstract

In this paper, a push–pull system with K (K≥ 1) non identical suppliers with disruptions that send products to an intermediate distribution center which in turn serves M (M≥ 1) non identical retailers is analyzed. Each retailer satisfies a Poisson distributed external demand of one product unit.The flow of material at the upstream stages (suppliers) is push type. The flow of material at the downstream stages (retailers) is driven by a continuous review inventory control policy (s, S). The replenishment rate of suppliers and retailers is exponentially distributed. More over it is assumed that the suppliers may not be always operational. This is modelled using exponentially distributed failure and repair rates of the suppliers. The considered system is modelled as a continuous time Markov process with discrete states. The derivation of the transition probabilities among the various states of the system is given. Solving the corresponding transition equations system, the stationary probabilities of the system's states are computed and therefore using the stationary probabilities, performance measures of the considered system such as the Fill Rate and WIP are evaluated. Moreover the effect of the system parameters on its performance measures is thoroughly explored. Finally the proposed model is examined from an economic point of view, where the optimal parameter values for the (s, S) type policy are detected to minimize a total inventory cost function. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.