Performance analysis and optimisation of stochastic flow lines with limited material supply

ABSTRACT

We consider stochastic flow lines with limited buffer sizes and limited material supply. In these systems, the configuration of the flow line parameters and the configuration of the material supply determine the system output. Shortages of material supply can limit the performance of the production system. We use flexible (mixed-integer) linear programming approaches to evaluate and optimise the performance of long stochastic flow lines with limited material supply in discrete and continuous time. The approaches are used to quantify the impact of material shortages on the system output. Further, they are applied to determine the minimum material levels that are required to prevent material shortages of a given flow line configuration. The results of the numerical study reveal insights on the approximation accuracy of the linear programs as well as on the dependence of optimal material levels on flow line characteristics such as the presence of bottleneck machines and the system variability. The contribution of this paper consists of both, integrated models for stochastic flow lines with limited material supply and new insights on the optimal material supply of stochastic flow lines.

KEYWORDS:

• Limited material supply
• milkrun system
• stochastic flow line
• linear programming
• manufacturing system design

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 $p_i=0.9$, $b_i=3$, $r=30$, $S_i=24\mathrm{\forall }i$.

2 $p_i=0.9$, $b_1=3$, $r=60$, $S_1=60\mathrm{\forall }i$.

3 $p_i=0.9$, $b_1=3$, $S_i=60\mathrm{\forall }i$.

Additional information

Notes on contributors

Julia Mindlina

Julia Mindlina works as a research assistant at the University of Cologne. She was awarded a Ph.D. from the University of Cologne in 2019. Her main research interest lies in the analysis and optimisation of stochastic manufacturing systems.

Horst Tempelmeier

Horst Tempelmeier has been Full Professor for Supply Chain Management and Production at the University of Cologne from 1993 to 2020. He has published articles in the International Journal of Production Research, European Journal of Operational Research and Management Science, among others. He is the (co-)author of textbooks on Flexible Manufacturing Systems and on Inventory Analytics. His research interests are Production Management, Inventory Management, and Stochastic Models in Supply Chains Management.