Abstract

After studying the maximization of the profit of an inventory model where the selling rate is dependent on stock, we generalized the demand from a ramp type demand to an arbitrary positive demand and then examined the solution structure to locate the optimal solution. Our findings are an extension of several previous papers. Consequently, we can provide a reasonable explanation for the unsolved phenomenon that appears in the solution structure in several previous papers. Furthermore, we have also provided an intuitive derivation for the optimal solution that will illustrate why the optimal solution is independent of the demand. The paper of Wu et al. (2008) published on International Journal of Information and Management Sciences were discussed to demonstrate how our findings have significantly simplified the solution process.

Key words: Inventory models, stock dependent selling rate, ramp type demand.