當產品進入生命週期末端時，需求顯著下降，即將退出市場，此時製造商或經銷商必須決定在此期間之生產或訂購決策，此即為產品在生命末期之生產或訂購問題。由於理論模式發展之困難度甚高，現有文獻上所發展之決策模式其基本假設與實務上仍有落差，本論文建立單位時間期望總成本模式，以決定產品在生命末期之最終一次或多次生產、訂購批量。研究中考慮產品之末期規劃時程為連續且有限，此期間之需求為一非齊次卜瓦松隨機過程，且需求速率為隨時間下降之線性函數。期望總成本包含整備或訂購成本、存貨成本、缺貨與存貨過剩之相關處理成本，以最小化單位時間期望總成本為目標，求得最佳一次或多次生產或訂購量。
本論文應用隨機過程與存貨理論，首先建立單次生產或訂購政策之單位時間期望總成本模式，進而建立總利潤模式，經由數學分析發現，在總成本模式之期望存貨成本部分，雖可求得存貨成本之理論期望值，但其數學式並非閉合型式，故難以發現其函數特性。為快速求得最佳批量，本研究發展一搜尋演算法，可求得在給定參數下之最佳生產或訂購量，以最小化期望總成本或最大化期望總利潤。延伸上述之單次生產或訂購決策模式，本論文並發展一多次決策模式，可決定最後規劃期間之最佳訂購次數及相對之訂購時間點與訂購量，以最小化整個規劃期之總成本。
經由演算實驗分析可發現，在單次決策模式上，需求速率初始值對總成本之影響為最大，其次為存貨持有成本與缺貨成本。相對地，銷售價格與需求速率初始值對期望總利潤之影響最大，其次為存貨持有成本與缺貨成本，就整體來看，過剩存貨之處理成本對決策模式之影響較微。在多次決策模式上，其發現與前者雷同，由求解結果可發現當需求初始值較大且其它參數不變下，其多次決策可以大幅降低相關總成本，故顯示當規劃期較長時，應採用多次生產或訂購決策。

In this thesis, inventory replenishment models under stochastic declining demand process is investigated. When an item enters the terminating phase of its product life cycle, the mean demand rate decreases over time, where a non-homogeneous Poisson process with a linear declining mean is used to model this demand. The replenishment policies to meet the demand in the future are to be determined so as to optimize the total expected cost or the total expected profit. The expected cost model includes: setup or ordering cost, inventory carrying cost, lost sale cost of unsatisfied demand, and overstock cost at the end of planning horizon. The expected total cost and total profit models for the single stage procurement policy are developed. Using cost model as a basis, a multi-stage procurement model is also analyzed. Two efficient solution procedures are developed and tested to find the optimal replenishment policies. Extensive computational test has demonstrated the effectiveness of the approaches. When planning horizon is sufficiently long and multi-stage procurement policy is implemented, the average cost reduction is 38%, if compared with that of the single-stage procurement policy.

中文參考文獻
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