Optimal Use and Replenishment of Two Substitutable Raw Materials in a Stochastic Capacitated Make-to-Order Production System

Problem definition : We study a multiperiod, nonstationary, make-to-order, joint production and inventory model where two kinds of input raw materials with availability uncertainties and different output conversion rates can be blended and then processed in a production line with stochastic capacity to produce the output product. Academic/practical relevance : The problem is motivated by the practice in coal-fired power plants, an important part of the energy sector, where two types of coal with different energy content per unit mass are blended for electrical power generation. Our model is the first to capture the key operational features in this context. Methodology : We model the problem as a Markov decision process and develop a novel approximate optimization approach to analyze and characterize the structure of the optimal policy. Results : We show that a use-down-to/balancing production policy and modified order-up-to ordering policy is optimal. We also propose a heuristic policy based on piece-wise linear value function approximation. Whereas computing the value function approximation via brute-force is time-consuming because of the curse of dimensionality, we leverage the structure of the optimal policy to develop an algorithm that greatly improves the computational time of the value function approximation. Our numerical studies on both a synthetic data set and real-world data show that the proposed heuristic provides significant profit improvement over three simpler straw policies, some of which are used in practice. Managerial implications : Our paper suggests the significant profit improvement opportunity of using our proposed policy and demonstrates how one can develop computationally more efficient heuristic policies by leveraging the structure of the optimal policy.