This paper derives the optimal simultaneous capacity and production plan for a shortlife-cycle, produce-to-stock good under stochastic demand. Capacity can be reduced as well as added, at exogenously set unit prices. In both cases studied, with and without carryover of unsold units, a target interval policy is optimal: There is a (usually different) target interval for each period such that capacity should be changed as little as possible to bring the level available into that interval. Our contribution in the case of no carry-over, is a detailed characterization of the target intervals, assuming demands increase stochastically at the beginning of the life cycle and decrease thereafter. In the case of carry-over, we establish the general result and show that capacity and inventory are economic substitutes: The target intervals decrease in the initial stock level and the optimal unconstrained base stock level decreases in the capacity level. In both cases, optimal service rates are not necessarily constant over time. A numerical example illustrates the results.Capacity management, Production management, Capacity expansion, Capacity contraction, Finite lifetime, Stochastic demand, Nonstationary

Our Bayesian dynamic programming model builds on existing models to account for inspection delay, choice of keeping production going during inspection and/or restoration, and lot sizing. We focus on describing how dynamic statistical process control (DSPC) rules can improve on traditional, static ones. We explore numerical examples and identify nine opportunities for improvement. Some of these ideas are well known and strongly supported in the literature. Other ideas may be less well understood. Our list includes the following: Cancel some of the inspections called for by an (economically) optimal static rule when starting in control (such as at the beginning of a production run and following a restoration). Inspect more frequently than called for by an optimal static rule once inspections begin, and inspect even more frequently than that when negative evidence is accumulated. Utilize evidence from previous inspections to justify either restoration or another inspection. Cancel inspections and hesitate to restore the process at the end of a production run. Consider using scheduled restoration, in which restoration is carried out regardless of the results of any inspections. Implementation, limitations, and extensions are addressed.dynamic statistical process control, Bayesian dynamic programming, inspection delay, quality control, sequential sampling, lot sizing, scheduled maintenance and restoration, inspection deferral, inspection cancellation

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W e consider a multi-stage inventory system with stochastic demand and processing capacity constraints at each stage, for both finite-horizon and infinite-horizon, discounted-cost settings. For a class of such systems characterized by having the smallest capacity at the most downstream stage and system utilization above a certain threshold, we identify the structure of the optimal policy, which represents a novel variation of the order-up-to policy. We find the explicit functional form of the optimal order-up-to levels, and show that they depend (only) on upstream echelon inventories. We establish that, above the threshold utilization, this optimal policy achieves the decomposition of the multidimensional objective cost function for the system into a sum of single-dimensional convex functions. This decomposition eliminates the curse of dimensionality and allows us to numerically solve the problem. We provide a fast algorithm to determine a (tight) upper bound on this threshold utilization for capacity-constrained inventory problems with an arbitrary number of stages. We make use of this algorithm to quantify upper bounds on the threshold utilization for three-, four-, and five-stage capacitated systems over a range of model parameters, and discuss insights that emerge.

We consider a nonstationary, stochastic, multistage supply system with a general assembly structure, in which customers can place orders in advance of their future demand requirements. This advance demand information is now recognized in both theory and practice as an important strategy for managing the mismatch between supply and demand. In conjunction, we allow expediting of components and partially completed subassemblies in the system to provide the supply chain with the means to manage the stockout risk and significantly enhance cost savings realized through advance demand information. To solve the resulting assembly system, we develop a new method based on identifying local properties of optimal decisions. This new method allows us to solve assembly systems with multiple product flows. We derive the structure of the optimal policy, which represents a double-tiered echelon basestock policy whose basestock levels depend on the state of advance demand information. This form of the optimal policy allows us to: (i) provide actionable policies for firms to manage large-scale assembly systems with expediting and advance demand information; (ii) prove that advance demand information and expediting of stock both reduce the amount of inventory optimally held in the system; and (iii) numerically solve such assembly systems, and quantify the savings realized. In contrast to the conventional wisdom, we discover that advance demand information and expediting of stock are complementary under short demand information horizons. They are substitutes only under longer information horizons.