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TITLE: Lattice-Dependent Base-Stock and Rationing Policies for Assemble-to-Order Systems
SPEAKER: Mustafa Akan
ABSTRACT:
We consider an assemble-to-order generalized M-system with multiple components and products, batch ordering of components, random lead times, and lost sales. We model the system as an infinite-horizon Markov decision process and seek an optimal control policy, which specifies when a batch of components should be produced and whether an arriving demand for each product should be satisfied. To facilitate our analysis, we introduce new functional characterizations for convexity and submodularity with respect to certain non-unitary directions. These help us characterize optimal inventory replenishment and allocation policies under a mild condition on component batch sizes: lattice-dependent base-stock and lattice-dependent rationing (LBLR). We conduct numerical experiments to evaluate the use of an LBLR policy for general ATO systems (which violate the M-system product structure) as a heuristic, comparing it to two other heuristics from the literature: a state-dependent base-stock and state-dependent rationing (SBSR) policy, and a fixed base-stock and fixed rationing (FBFR) policy. Remarkably, LBLR yields the globally optimal cost in every experiment. LBLR and SBSR perform significantly better than FBFR when replenishment batch sizes imperfectly match the component requirements of the most valuable or most highly demanded product. In addition, LBLR substantially outperforms SBSR if a significant amount of inventory must be held for rationing. Finally, we approximate the optimal cost function by reducing the state space of the original problem through a novel hard aggregation technique. We establish that LBLR is the optimal policy obtained by solving the aggregate problem. We derive error bounds for this approximation and present preliminary computational results.
