Using Markov Chain to Analyze Production Lines Systems with Layout Constraints

There are some problems with estimating the time required for the manufacturing process of products, especially when there is a variable serving time, like control stage. These problems will cause overestimation of process time. Layout constraints, reworking constraints and inflexible product schedule in multi product lines need a precise planning to reduce volume in particular situation of line stock. In this article, a hybrid model has been presented by analyzing real queue systems with layout constraints as well as by using concepts and principles of Markov chain in queue theory. This model can serve as benchmark to assess queue systems with probable parameters of service. Here, the proposed model will be described drawing on the findings of a case study. Thus, production lines of a home application manufacturer will be analyzed

A two-station queue with dependent preparation and service times

We discuss a single-server multi-station alternating queue where the preparation times and the service times are auto- and cross-correlated. We examine two cases. In the first case, preparation and service times depend on a common discrete time Markov chain. In the second case, we assume that the service times depend on the previous preparation time through their joint Laplace transform. The waiting time process is directly analysed by solving a Lindley-type equation via transform methods. Numerical examples are included to demonstrate the effect of the auto-correlation of and the cross-correlation between the preparation and service times

A two-station queue with dependent preparation and service times

We discuss a single-server multi-station alternating queue where the preparation times and the service times are auto- and cross-correlated. We examine two cases. In the first case, preparation and service times depend on a common discrete time Markov chain. In the second case, we assume that the service times depend on the previous preparation time through their joint Laplace transform. The waiting time process is directly analysed by solving a Lindley-type equation via transform methods. Numerical examples are included to demonstrate the effect of the auto-correlation of and the cross-correlation between the preparation and service times.Alternating service Lindley-type equation Markov-modulation Wiener-Hopf decomposition