多服務者存貨排隊系統之最佳補貨策略研究

Research on the Optimal Replenishment Strategy of Multi-server Inventory Queue

蘇賢欽(Hsien-Chin Su)

指導教授 ： 巫佳煌

國立交通大學/管理學院/工業工程與管理系所/碩士(2020年)

摘要

近年來，電子商務和在線購物是人類生活中非常重要的一部分，可以節省商店租金和商店人員的運營成本，同時，這也意味著公司運營結構中的庫存成本佔了更大比例。對於企業而言，使用良好的補貨策略可以節省庫存成本並提高企業的營收。本文考慮M/M/c的存貨排隊，並以最小的期望成本制定了一種最優的補貨策略。為了要建立模型的穩態分析，必須先得到該系統的穩態條件，之後利用幾何矩陣法得到近似的機率矩陣，透過機率矩陣得到穩態機率。除此之外，我們也針對系統中重要系統特徵做了敏感度分析，再建立了成本函數來得到在不同情況下包含補貨率以及訂貨點的最佳補貨策略。最後，我們使用黃金切割法來針對一個最小化的成本函數計算進而得到一個啟發式的解決方法，同時針對系統參數做了敏感度分析，也提供數據化的表格方便讀者使用。

關鍵字

黃金切割法 ； 存貨排隊 ； 幾何矩陣法 ； 最佳化補貨策略

並列摘要

Nowadays, e-commerce and online shopping are an important part of human life, which can save store rental costs and store personnel operating costs. At the same time, this also means that inventory costs in the company's operating structure account for a larger proportion. For the enterprise, a good replenishment strategy is essential to save the inventory cost and enhance the operating profit. This thesis considers a multi-server inventory queue and develops an optimal replenishment strategy with minimum expected cost. An M/M/c inventory queue is established to perform a steady-state analysis. First, the sufficient and necessary condition for system stability is deduced. Next, the matrix-geometric method is employed with an approximate rate matrix and the steady-state probabilities of the system are calculated recursively. In addition, closed-form expressions of critical system characteristics are derived explicitly. The cost function is then constructed to obtain the optimal replenishment strategy including the optimal replenishment rate and the optimal order points under different conditions. Finally, we implement the golden section method to obtain a heuristic solution to minimize the cost function. The sensitivity analysis of this model is also performed to examine the effects of system parameters on the optimal replenishment strategy. Numerical results are tabulated for the practitioner’s convenience.

並列關鍵字

Golden section method ； Inventory queue ； Matrix-geometric method ； Optimal replenishment strategy

參考文獻

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