Lead time control in multi-server multi-stage assembly system

Abstract

In this paper, two multi-objective models to optimally control the lead time in multi-server multi-stage assembly system by considering server allocation problem (SAP) and also service rate control problem (SCP) are presented, where new product orders, including all their operations, are entered to the system according to a Poisson process, only one type of products also is produced by the production system, and multi-servers can be settled in each service station. Each operation of any work is operated at a devoted service station with only one of the servers located at a node of the network based on a first-come-first-serve discipline, while the processing times are independent random variables with exponential distributions. Furthermore, it is also assumed that the transport times between each pair of service stations are independent random variable with generalized Erlang distributions. Such system can be modeled as a queueing network, where the system is in the steady state and the lead time is controllable. For modeling of multi-server multi-stage assembly system, initially the network of queues is transformed into an appropriate stochastic network with exponentially distributed arc lengths. A differential equations system is organized to solve and obtain approximate lead time distribution for any particular wok by applying a proper finite-state continuous-time Markov model. Then, two multi-objective models including four conflicted objectives are presented to optimally control the servers allocated to the service stations in SAP and also service rate of service stations in SCP. For solving a discrete-time approximation of the primary multi-objective problems, the goal attainment technique is employed. In this research, reactive controlling in a multi-server multi-stage assembly system also is discussed.