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標題: 以馬可夫決策過程探討最適物料存貨政策
Using Markov Decision Process Investigate the Optimal Material Inventory Policy
作者: Jia-Chen Yu
關鍵字: Inventory Control;Markov Decision Process;Optimization;存貨管理;馬可夫決策過程;最佳化
引用: 中文部分: 台經院產業資料庫(TIE, 2014)。 英文部分: Ahiska, S. S., Appaji, S. R., King, R. E., and Warsing Jr, D. P. (2013). A Markov decision process-based policy characterization approach for a stochastic inventory control problem with unreliable sourcing. International Journal of Production Economics, 144(2), 485-496. Akar, N., and Sohraby, K. (2009). System-theoretical algorithmic solution to waiting times in semi-Markov queues. Performance Evaluation, 66(11), 587-606. Arıkan, E., Fichtinger, J., & Ries, J. M. (2013). Impact of transportation lead-time variability on the economic and environmental performance of inventory systems. International Journal of Production Economics. Arreola-Risa, A., Giménez-García, V. M., & Martínez-Parra, J. L. (2011). Optimizing stochastic production-inventory systems: A heuristic based on simulation and regression analysis. European Journal of Operational Research, 213(1), 107-118. Awate, P. G. (1989). Inventories as work backlogs—Three case studies in diagnostic analyses using regressions, moving-averages and cum-sum charts. Engineering Costs and Production Economics, 15, 151-156. Bellman, R. (1954). The theory of dynamic programming (No. P-550). RAND CORP SANTA MONICA CALIF. Bellman, R. (1957). A Markovian Decision Process. (No. P-1066). Journal of Mathematics and Mechanics . Harris, F. W. (1990). How Many Parts to Make at Once. Operations Research, 38(6), 947–950. Harvey, A., & Snyder, R. D. (1990). Structural time series models in inventory control. International Journal of Forecasting, 6(2), 187-198. Hoque, M. A. (2013). A vendor–buyer integrated production–inventory model with normal distribution of lead time. International Journal of Production Economics, 144(2), 409-417. Jacobs, F. R., & Whybark, D. C. (1992). A Comparison of Reorder Point and Material Requirements Planning Inventory Control Logic*. Decision Sciences, 23(2), 332-342. Liu, M., Feng, M., & Wong, C. Y. (2013). Flexible service policies for a Markov inventory system with two demand classes. International Journal of Production Economics. Puterman, M. L. (2009). Markov decision processes: discrete stochastic dynamic programming (Vol. 414). Wiley. Render, B., & Heizer, J. H. (1997). Principles of Operations Management: With Tutorials. Prentice Hall. Rossi, R., Tarim, S. A., Hnich, B., & Prestwich, S. (2010). Computing the non-stationary replenishment cycle inventory policy under stochastic supplier lead-times. International Journal of Production Economics, 127(1), 180-189. Sajadieh, M. S., Jokar, M. R. A., & Modarres, M. (2009). Developing a coordinated vendor–buyer model in two-stage supply chains with stochastic lead-times. Computers & Operations Research, 36(8), 2484-2489. Sterman, J. D. (1989). Modeling managerial behavior: Misperceptions of feedback in a dynamic decision making experiment. Management science, 35(3), 321-339. Vollmann, T. E., Berry, W. L., & Whybark, C. D. (1997). Manufacturing planning and control systems. Irwin Professional Publishing. Warren Liao, T., & Chang, P. C. (2010). Impacts of forecast, inventory policy, and lead time on supply chain inventory—a numerical study. International Journal of Production Economics, 128(2), 527-537. Wild, T. (2002). Best practice in inventory management. Routledge. Yelland, P. M. (2009). Bayesian forecasting for low-count time series using state-space models: An empirical evaluation for inventory management. International Journal of Production Economics, 118(1), 95-103. Zhang, X., and Gao, H. (2012). Road maintenance optimization through a discrete-time semi-Markov decision process. Reliability Engineering & System Safety, 103, 110-119. Jacobs, F. R., & Whybark, D. C. (1992). A Comparison of Reorder Point and Material Requirements Planning Inventory Control Logic. Decision Sciences, 23(2), 332-342. Bobko, P. B., & Whybark, D. C. (1985). The coefficient of variation as a factor in MRP research. Decision Sciences, 16(4), 420-427.
This paper discusses the selection of three kinds of reorder level from the perspective of a cost seeking corporate and a cumulative grade minimizing. Specifically, we consider a Markov Decision Process model for selecting the best inventory policy for improving the performance of steel Industry.
In practical application, information about the inventory between probability distribution assumptions may be ambiguous to the experimenter and difficult to determine. To address this problem, our results are based on real data including sales and inventory quantity from an owner of the steel corporate. The whole data set covered the period from January, 2010 to February, 2014, a total of 216 data points. We also consider lead time, hold inventory and in-transit inventory constraints in ours system.
First, we use the information before 164 periods (1~164periods) to build the transition probability matrix of each action for all states in system. And through the conditions to calculus the optimal decision by MDP. Then, we use the optimal decision to test last 52 periods (165~216periods). The results show that, from the perspective of cost minimization, the best inventory policy would assign lower reorder quantity and the level of safety stock and also can meet demand for each period.

本研究旨在探討鋼鐵業的最佳物料存貨政策,試圖降低企業目前所面臨到的龐大庫存壓力,以提升企業的競爭力。本研究運用馬可夫決策過程(Markov Decision Process; MDP)分析存貨管理議題,使用某鋼鐵公司的其三品項之實際資料,包含實際銷售量與實際庫存量,年度期間為2010年1月至2014年2月共216周之資料,並同時考慮前置時間(lead time)、持有存貨(stock in hand)與在途存貨(in-transit stock)的限制,因此有別於以往分析的過程中制訂許多假設,能在排除更多不確定因素的情況下,更近一步探討合適的再訂購點與再訂購量問題。
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