Department of Industrial Management, Vanung University
Chungli, Taiwan 320, R.O.C.
Department of Industrial Engineering, Chung Yuan Christian University
Chungli, Taiwan 320, R.O.C.
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.
Keywords: linear trend in demand, economic production quantity, unconstraint nonlinear programming
(*Contact: E-mail hsinrau@cycu.edu.tw )
Cite this article as: Bing-Chang OuYang and Hsin Rau, "A Simple Algorithm for Production Policies with Linear Trend in Demand," Journal of the Chinese Institute of Industrial Engineers, 25, 229-236 (2008).