An approximate dynamic programming approach for production‐delivery scheduling under non‐stationary demand

We consider an integrated production and delivery scheduling problem with non‐stationary demand in a two‐stage supply chain, where orders arrive dynamically and the demand is time‐varying. Orders should be first processed on identical machines and then delivered to a single next‐stage destination by the transporters with fixed departure times. The objective is to minimize the order waiting time via production‐delivery scheduling. We formulate the problem into a Markov decision process model and develop an approximate dynamic programming (ADP) method. To shrink action (decision) space, we propose the shorter processing time first and first completion first delivery (SPTm/FCFD) principle to determine order processing sequences and order delivery, and then we establish two constraints to eliminate a fraction of inferior actions. Based on the SPTm/FCFD principle, we propose the SPT/FCFD rule, and show its optimality for two scenarios. In addition, we deploy five basis functions to approximate the value function. The superior performance of ADP policy is validated via numerical experiments, compared with four benchmark policies. We also empirically study the impact of demand features on the waiting time, and results show that these features significantly affect the performances of all polices. In practice, it is suggested to postpone the peak demand, when total demand exceeds the available production capacity.