Supply System Design under Uncertainty Constraint by Using Markov Modulated Poisson Process Modeling

應用馬可夫調整卜瓦松過程於不確定因素下供應系統設計

王風帆(Fong-Fan Wang) ； 蘇朝墩(Chao-Ton Su)

《工業工程學刊》 23卷1期 (2006/01) Pp. 20-33

https://doi.org/10.29977/JCIIE.200601.0003

摘要

本研究假設供應鏈各站台為多機系統且配置維修人員，探討供應及需求不確定因素對供應鏈最適資源配置的影響。本文除考慮機器可能無法正常營運外，另亦考慮維修人員可能無法正常工作及市場需求可能為非穩定隨機過程，目標是使得等候、延期交貨量、營運及修護等成本最低。本研究針對所假設不確定因素建立馬可夫調整卜瓦松過程模式，運用擬生死過程求解程序以獲得主要系統績效，進而分析各種不確定因素對系統績效及總成本的影響，結果可供決策者在作實際產能設計或資源配置時參考。

關鍵字

馬可夫調整卜瓦松過程 ； 擬生死過程 ； 供應系統

並列摘要

This study used Markov modulated Poisson process (MMPP) to model supply systems under various uncertainty constraints. First the uncertainty factors embedded in a supply system were assumed to be unreliable server with or without unreliable repairman. The market demand may be non-stationary random process. Steady state performance measures under different uncertainty scenarios were investigated by using an algorithmic procedure to solve the underlying quasi-birth-and-death (QBD) process. The optimal resource design of the supply systems under various uncertainty constraints was then solved as the trade-off among costs of inventory holding, customer waiting, server repair and normal operation. Numerical studies of the proposed models investigated the impact of uncertainties on the performance of a multi-echelon supply system under a make-to-order (MTO) supply policy. The results are satisfactory and provide managerial insights on strategic supply decision.

並列關鍵字

Markov modulated Poisson process ； quasi-birth-and-death ； supply system

參考文獻

Chen H., D. D. Yao(2001).(Fundamentals of Queueing Networkr: Performance, Asymptotics, and Optimization, Springer).

Ching, W. K.(2001).Markovian Approximation for Manufacturing Systems of Unreliable Machines in Tandem.Naval Research Logistics.(Naval Research Logistics).

Dun C., Y Frein,M. Di Mascolo(2000).Performance evaluation and design of base stock systems.(European Journal of Operational Research).

Latouche G,V. Ramaswami(1999).(Introduction to Matrix Analytic Methods in Stochastic Modeling).

Lee, Y. J.,P. H. Zipkin(1992).Tandem queues with planned inventories.(Operations Research).