Optimal use and replenishment of two substitutable raw materials in a stochastic capacitated make-to-order production system


Management Science and Operations

Publishing details

Social Sciences Research Network

Authors / Editors

Chen Q; Duenyas I; Jasin S


Publication Year



We consider a joint production and replenishment problem in a make-to-order setting where the firm can use either of two kinds of raw materials (or their mixture) to produce an end product using a shared production line with stochastic capacity. The two types of raw materials are substitutable but one is operationally more efficient (i.e. it has a higher conversion rate) whereas the other is cheaper, and their availability is stochastic due to, for example, delivery uncertainty. We show that a Use-down-to/Balancing Production Policy and modified Order-up-to Ordering Policy is optimal. Our sensitivity analysis of the optimal policy reveals some counter intuitive results when the availability of the raw materials is stochastic. For example, it may be optimal for the firm to use strictly less of the operationally more efficient material when the demand for the end product stochastically increases. Since using a brute-force approach to compute the optimal policy is time-consuming due to the curse of dimensionality of the dynamic program, we use the structural properties of the optimal policy to develop an efficient algorithm to compute the optimal policy. Although the optimal policy is complex, our numerical study shows that solving for it using the algorithm we develop is feasible, and it significantly outperforms two straw heuristic policies that could be used in practice.


Social Sciences Research Network