Abstract: This paper investigates inventory control strategies and the importance of production coordination in supply chains. We apply the two-stage tandem production mode of make-to-stock (MTS) and make-to-order (MTO) to the joint production and inventory control in efficient and responsive supply chains. Also, the optimal strategy is characterized. In cases where order arrivals follow a Poisson distribution and production time follows an exponential distribution, through the technique of rate uniformization for Markov process transitions, we formulate a Markov decision process (MDP) model and derive the corresponding Bellman optimality equation. Then, based on the structural properties of the optimal cost function, we characterize the optimal production and inventory control strategies as a basic inventory strategy dependent on system states. Subsequently, the model is extended for cases of batch production. Numerical examples verify the monotone structural property of the optimal strategy and further provide the system performance using the optimal strategy. In addition, we compare the optimal strategy with two other commonly used ones. In the baseline scenario, the capacity limit strategy deviates from the optimal one by 7.36%, while the myopic strategy deviates from the optimal one by 25.73%. In other scenarios, the optimal strategy remarkably outperforms the other two strategies.

Key words: supply chain, tandem production system, inventory control, Markov decision process, optimal policy