Due-date assignment for multi-server multi-stage assembly systems

Abstract

In this paper, we attempt to present a constant due-date assignment policy in a multi-server multi-stage assembly system. This system is modelled as a queuing network, where new product orders are entered into the system according to a Poisson process. It is assumed that only one type of product is produced by the production system and multi-servers can be settled in each service station. Each operation of every work is operated at a devoted service station with only one of the servers located at a node of the network based on first come, first served (FCFS) discipline, while the processing times are independent random variables with exponential distributions. It is also assumed that the transport times between each pair of service stations are independent random variables with generalised Erlang distributions. Each product's end result has a penalty cost that is some linear function of its due date and its actual lead time. The due date is calculated by adding a constant to the time that the order enters into the system. Indeed, this constant value is decided at the beginning of the time horizon and is the constant lead time that a product might expect between the time of placing the order and the time of delivery. For computing the due date, we first convert the queuing network into a stochastic network with exponentially distributed arc lengths. Then, by constructing an appropriate finite-state continuous-time Markov model, a system of differential equations is created to find the manufacturing lead-time distribution for any particular product, analytically. Finally, the constant due date for delivery time is obtained by using a linear function of its due date and minimising the expected aggregate cost per product.

Keywords:

• assembly system
• due-date assignment
• Markov processes
• queuing

Additional information

Notes on contributors

Saeed Yaghoubi

Saeed Yaghoubi is an assistant professor of industrial engineering at Iran University of Science and Technology, Tehran, Iran. He obtained his PhD degree in 2012 from the Iran University of Science and Technology in industrial engineering. His current research interests include stochastic processes and their applications, supply chains and project scheduling. He has contributed articles to different international journals such as European Journal of Operational Research, Iranian Journal of Science & Technology, International Journal of Advanced Manufacturing Technology, Journal of Industrial Engineering International, etc.