Constrained Single Period Stochastic Uniform Inventory Model With Continuous Distributions of Demand and Varying Holding Cost

This paper derives the single period stochastic inventory model with continuous distributions of demand and the holding unit cost is a function of the purchased (ordered) quantity. The objective is to find the optimal purchased quantity which minimizes the expected total cost for the period under a restriction on the expected varying holding cost when the demand during the period follows the uniform, the exponential and the Laplace distributions, using the Lagrange multiplier approach. Some special cases are deduced and illustrative numerical examples with some graphs are added.