Infinitesimal perturbation analysis based optimization for a manufacturing system with delivery time

In this paper, a manufacturing system composed by a single-product machine, a manufacturing stock, a purchase warehouse and a constant demand is considered. A stochastic fluid model is adopted to describe the system and to take into account delivery times. The goal of this paper is to evaluate the two optimal inventory levels: that of the manufacturing stock and that of the warehouse. Those optimal levels allow minimizing the total cost which is the sum of inventory, transportation and backlog costs. Infinitesimal perturbation analysis is used for optimisation of the failure-prone manufacturing system. The trajectories of the inventory levels are studied and the infinitesimal perturbation analysis estimates are evaluated. These estimates are shown to be unbiased and then they are implemented in an optimisation algorithm which determines the optimal inventory levels in the presence of constant delivery time.

[1]  Xi-Ren Cao,et al.  Perturbation analysis and optimization of queueing networks , 1983 .

[2]  Christos G. Cassandras,et al.  Perturbation analysis for online control and optimization of stochastic fluid models , 2002, IEEE Trans. Autom. Control..

[3]  B. Porter,et al.  Evolutionary optimisation of hedging points for unreliable manufacturing systems , 2006 .

[4]  Stanley B. Gershwin,et al.  Modeling and Analysis of Markovian Continuous Flow Production Systems with a Finite Buffer: A General Methodology and Applications , 2007 .

[5]  Jason D. Papastavrou,et al.  A stochastic and dynamic model for the single-vehicle pick-up and delivery problem , 1999, Eur. J. Oper. Res..

[6]  Michael Manitz,et al.  Queueing-model based analysis of assembly lines with finite buffers and general service times , 2008, Comput. Oper. Res..

[7]  Christos G. Cassandras,et al.  Perturbation analysis and control of two-class stochastic fluid models for communication networks , 2003, IEEE Trans. Autom. Control..

[8]  Y. Wardi,et al.  Multi-process control using queuing theory , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[9]  Xiaolan Xie,et al.  Simulation-based optimization of a single-stage failure-prone manufacturing system with transportation delay , 2008 .

[10]  Yorai Wardi,et al.  Continuous flow models: modeling, simulation and continuity properties , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[11]  R. Akella,et al.  Optimal control of production rate in a failure prone manufacturing system , 1985, 1985 24th IEEE Conference on Decision and Control.

[12]  Weibo Gong,et al.  Ill-conditioned performance functions of queueing systems , 1995 .

[13]  Nathalie Sauer,et al.  Perturbation analysis based-optimization for a failure-prone manufacturing system with constant delivery time and stochastic demand , 2009 .

[14]  Nathalie Sauer,et al.  Perturbation analysis for Continuous and discrete flow models: a failure-prone manufacturing system study , 2010 .

[15]  Christos G. Cassandras,et al.  Infinitesimal Perturbation Analysis and Optimization for Make-to-Stock Manufacturing Systems Based on Stochastic Fluid Models , 2006, Discret. Event Dyn. Syst..

[16]  Christos G. Cassandras,et al.  Perturbation analysis for production control and optimization of manufacturing systems , 2004, Autom..

[17]  Christoforos Panayiotou,et al.  Optimization of discrete event system parameters using SFM-based infinitesimal perturbation analysis estimates , 2007, 2007 46th IEEE Conference on Decision and Control.

[18]  Weibo Gong,et al.  Ill-conditioned performance functions of queueing systems , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[19]  Turki Sadok,et al.  INFINITESIMAL PERTURBATION ANALYSIS FOR OPTIMIZATION OF TWO-PRODUCT-MANUFACTURING SYSTEM , 2011 .

[20]  Nathalie Sauer,et al.  Perturbation analysis based-optimization for a failure-prone manufacturing system with constant delivery time and stochastic demand , 2009, 2009 International Conference on Computers & Industrial Engineering.