The optimal production cycle time in an integrated production-inventory model for decaying raw materials

In 1983, Park presented an integrated production-inventory model for decaying raw materials. This paper discusses the same model as that of Park. The main purpose is threefold:(1)This paper shows that the total cost function per unit time is convex by a rigorous proof.(2)This paper derives the closed forms for the upper and lower bounds on the optimal cycle time of the total cost function per unit time, thereby enabling straightforward application of the standard bisection algorithm to numerically compute the optimal cycle time.(3)This paper compares optimal solutions obtained by using our approach (the bisection algorithm) and Park’s approach. Numerical examples show that our approach is better.