A Simple Algorithm for Production Policies with a Linear Trend in Demand

線性需求下經濟生產批量演算法的改進

10.29977/JCIIE.200805.0005

歐陽炳昌(Bing-Chang Ouyang)；饒忻(Hsin Rau)

線性需求 ； 經濟生產批量 ； 無限制條件非線性規劃 ； linear trend in demand ； economic production quantity ； unconstraint nonlinear programming

工業工程學刊

25卷3期（2008 / 05 / 01）

229 - 236

英文

在有限的時間週期與生產率，Hill [4]是第一位研究線性需求下經濟生產批量演算法，其演算法是遵循Donaldson [1]的解析表列式演算法，Omar等人[6]假設需求爲線性遞減函數，又提出一種動態規劃演算法，此兩種法爲許多文獻認定爲計算繁瑣且複雜度高的演算法。除此以外，上述兩篇研究無法證明經濟生產批量的總成本爲一凸函數，而保留了此項的推測。本篇研究針對線性需求下經濟生產批量提出一簡單演算法，簡化上述兩篇研究的複雜運算，並使用一個公式涵蓋線性遞增與遞減的問題，更提供完整理論證明經濟生產批量的總成本爲一凸函數。此外，本研究亦提出此問題的數值驗證，由結果證實我們的演算法也可以得到最佳解。

Under a fixed time horizon and a finite production rate, Hill [4] was the first to study the optimal production policy for a linearly increasing demand, but his approach followed Donaldson's analytic approach [1] with a complicated computation using tabular and interpolation. In addition, Omar et al. [6] presented a dynamic programming approach for the same problem with a linearly decreasing demand. Unfortunately, both studies failed to demonstrate the total cost is a convex function in number of production cycles and only provided a conjecture. In this paper, we provide theorems to fill the theoretical gap. Moreover, considering both linearly increasing and decreasing demands, we present a general and simple algorithm to solve this problem for simplifying computation. A general procedure to derive the optimal solution is presented and validations are performed as well. According to our validations, this proposed algorithm can also obtain optimal solutions.

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