An assemble-to-order system with product and components demand with lost sales

This paper studies a single end product assemble-to-order system serving both the demand of the end product and the individual components. Demands are assumed to form independent Poisson streams with different rates. Unsatisfied demand, both for the end product and for components, is assumed lost and thus incurs a per unit lost sale penalty. The end product is assembled from K distinct components each produced on a different production facility (or procured from independent suppliers). Production lead times are non-identical and are assumed to be independent and exponentially distributed. Produced components are held in stock in anticipation of future demands. The goal is to determine the optimal component production and inventory allocation policy. The optimal policy is characterised using a Markov Decision Process model. It is shown that, in addition to the state-dependent threshold type, the optimal policy exhibits counter-intuitive features which have not been observed in systems without components demand. In particular, for certain combinations of system parameters, the optimal inventory allocation policy switches priority as the inventory level of components changes. Furthermore, for a particular component k, as the inventory level of other components increases, the desirability of satisfying Component k demand decreases. Finally, because in general the optimal policy is fairly complicated and is difficult to obtain numerically, due to the curse of dimensionality of dynamic programming, three heuristic policies are proposed. Extensive numerical experiments indicate that the three heuristics perform very well compared to the optimal policy.