Communications in Mathematical Sciences

Volume 14 (2016)

Number 7

Routing strategies in production networks with random breakdowns

Pages: 1799 – 1820



Simone Göttlich (Department of Mathematics, University of Mannheim, Germany)

Sebastian Kühn (Department of Mathematics, University of Mannheim, Germany)


Routing strategies in unreliable production networks are an essential tool to meet given demands and to avoid high inventory levels. Therefore, we are interested in studying stateindependent and state-dependent control policies to maximize the total throughput of the production network. Different from M/M/1 queuing theory, the underlying model is based on partial and ordinary differential equations with random breakdowns capturing the time-varying behavior of the system. The key idea is to numerically compare suitable routing strategies with results computed by nonlinear optimization techniques. We comment on the efficiency of the proposed methods and their qualitative behavior as well.


production networks, differential equations, random breakdowns, routing strategies, optimal control

2010 Mathematics Subject Classification

65Mxx, 90B15, 90C30

Published 14 September 2016