Efficiency in shortage reduction when using a more expensive common component

The paper considers the contribution of a common component in minimizing the expected units shortage subject to a budget constraint. A two-level product structure in an assemble-to-order system, where demands for two end products follow independent Erlang distributions, is assumed. We present closed form expressions for the objective function under various scenarios and provide efficient algorithms to compute the corresponding optimal inventory stock levels. It is found that, for all demand patterns considered, the relative reduction in the expected units shortage can be substantial when the inventory budget is large unless the cost of the common component is very high. When the budget is small, any potential benefit from employing commonality can be insignificant even if the premium for the common component is tiny. Using common components in different products is an appealing idea. However, if a common component is more expensive than the unique components that it replaces, then it will require careful analysis to decide whether it is beneficial to employ the common component. Here we consider the contribution of a more expensive common component in minimizing the expected units shortage for meeting demands of two end products, subject to a budget constraint. Under a general cost structure, for models with or without commonality, we show that the objective function is convex for any unbounded continuous demand distributions. Applying this result and assuming Erlang demand distributions, we show that a more expensive common component can be beneficial when the inventory budget is large but commonality will not be helpful if the budget is small.