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

歐陽炳昌(Bing-Chang Ouyang) ； 饒忻(Hsin Rau)

《工業工程學刊》 25卷3期 (2008/05) Pp. 229-236

https://doi.org/10.29977/JCIIE.200805.0005

摘要

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。

關鍵字

線性需求 ； 經濟生產批量 ； 無限制條件非線性規劃

並列摘要

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.

並列關鍵字

linear trend in demand ； economic production quantity ； unconstraint nonlinear programming

參考文獻

Donaldson, W. A.(1977).Inventory replenishment policy for a linear trend in demand-an analytical solution.Operational Research Quarterly.28,663-670.

Hariga, M.(1993).The inventory replenishment problem with a linear trend in demand.Computer and Industrial Engineering.24,143-150.

Henery, R. J.(1979).Inventory replenishment policy for increasing demand.Journal of the Operational Research Society.30,611-617.

Hill, R. M.(1996).Batching policies for linearly increasing demand with a finite input rate.International Journal of Production Economics.43,149-154.

Lo, W. Y.,C. H. Tsai,R. K. Li(2002).Exact solution of inventory replenishment policy for a linear trend in demand-two-equation model.International Journal of Production Economics.76,111-120.