| In the Assemble-To-Order environment, where lead times for components are long and assembly times are short, inventory is held at the component or sub-assembly level awaiting the realization of unique stochastic customer orders. In this scenario it is not unusual for one component to stock out. On average it may still be more profitable to fill demand for the end product using a more capable and usually more expensive component normally used for another end product. Like commonality, substitutability may have a significant effect on optimum inventory levels for all components.; Given problem parameters, this research determines the optimum inventory levels for all components to obtain maximum profitability for a problem with two simple end products, each assembled from two components. A general profit equation is first developed. Proof that the optimal component inventory levels for the substitutable component and its mate are equivalent, thereby reducing the search space to three variables, is presented next. Concavity of the expected profit equations is proven. These equations are then differentiated with respect to the three component inventory levels. Five of six bounds are then developed which limit the search for optimum to a finite and reasonable space. This research also shows that the profitability of the end product substitution problem is an upper bound to the component substitution problem. Finally, the effects of changing problem parameters are investigated.; This research presents cases where component substitution can (1) increase expected profitability, (2) increase the expected average number of cycles where all demand for both end products is met, (3) increase the expected percentage of demand met for both end products with the same or less dollar amount of component inventory, and (4) decrease the dollar amount of component inventory at maximum expected profit. |
