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Dual-index Policies for Serial Systems with Dual Delivery Modes and Batch Orders

In this paper, we consider a stochastic serial inventory system with dual delivery/supply modes for each echelon stage. The two modes in each stage take different lead times, incur different ordering costs and require different base order batch sizes. We study a class of dual-index echelon-(R,nQ) policies which is a nature extension of the well-studied dual-index policies (Veeraraghavan and Scheller-Wolf 2008, Zhou and Yang 2016) and echelon-(R,nQ) policy (Chen 2000) that have been proved to be near-optimal/optimal for the single-echelon dual-sourcing system and the batch-ordering serial system, respectively. Based on the concept of strong Q-jump-convexity, we prove that this policy is indeed optimal for the case in which the lead time difference between the two delivery modes in each stage is one period and the order batch sizes satisfy an integer-ratio constraint. For the general case, we analyze the system dynamics under this policy and show separability results for the policy parameters. Based on these properties, we provide a simulation-based optimization procedure for policy parameters. Three simple heuristics are then provided to find the near-optimal policy parameters, which are shown to be very efficient by the numerical studies.We also numerically investigate the value of the dual delivery modes and observe that as long as the regular delivery mode of the upstream echelon is only marginally less favorable than the regular delivery mode of the downstream echelon, the downstream echelon should be given priority by firms thinking of adding an expedited mode to the system.