Abstract:
This paper is going to present two different methods of solving the multi item single source (MISS) problem considering two different sets of assumptions and treatments. So the paper consists of two parts, the first part is going to derive the probabilistic continuous review inventory, with mixture shortage, when the holding cost is a function of the ordered quantity. The objective is to minimize the expected total cost using Lagrange multipliers. The mathematical optimal solutions for the order quantity, Q^*, and the reorder point, r^*, can be obtained when the lead time is a constant and the demand is a random variable (when demand follows Normal, Exponential and Chi-Square distributions). The second part is devoted to study the same model when the demand, the order and the holding unit costs are triangular fuzzy numbers. An actual application is added to illustrate the models.