Compensating for part arrival uncertainties in two-processing-machine, one-buffer flow lines: Inventory flexibility design based on the system transient performances

Abstract

• A structured Markov process model for the proposed flow lines;. • Transition equation derivation for the flow lines;. • The algorithms for factoring a class of states to derive closed-form expressions;. • System transient performance analysis of the flow lines system;. • Discrete event dynamic system simulation and verification. In one-of-a-kind production (OKP), a flow line with two distinct deterministic processing time machines and one “flexible” storage buffer is studied from the perspective of manufacturing system design and transient behaviour analysis. This manufacturing process is disrupted by part arrival uncertainties and is considered a discrete dynamic stochastic system. The dynamic behaviour of the flow line is structured as a transfer line with multi-state machines and finite-storage buffers by a discrete-time, discrete-state Markov chain for the transient performance analysis, optimal design and efficient production operation. To assess the dynamic disruptions and further limit the cascading effects on the flow line, in the presented analytical model, the studies quantify the evolution of a basic serial production process over time; and meanwhile, we evaluate and optimize the manufacturing system transient performance to determine the optimal design of inventory flexibility as a function of the time and states. By factoring out a class of appropriate transient states associated with an initial state at a certain time slot and deriving closed-form expressions using the transition equations, we sought to determine the transient probabilities of the manufacturing system states to establish relationships between the variable system parameters and the performance measures. By embedding these practical results with quantitative precision in an optimal design process of inventory flexibility, we consider setting the storage buffer level between two processing machines for refined production optimization and control when the part arrival uncertainties and lack of synchronization constantly occur in this serial manufacturing system.