This work provides a comprehensive analysis of a general periodic review production/inventory model with random (variable) yield. Existence of an order point whose value does not depend on yield being random is proved in the single period case without specifying the yield model and using a very general cost structure. When yield is a random multiple of lot size, the nonorder-up-to optimal policy is characterized for a finite-horizon model. The finite-horizon value functions are shown to converge to the solution of an infinite-horizon functional equation, and the infinite-horizon order point is shown to be no smaller than when yield is certain.

This work concerns the advance scheduling of elective surgery when the operating rooms' capacity utilization by emergency surgery, as well as by elective procedures, is uncertain. New requests for bookings of elective surgery arrive each day. Such procedures preferably would be performed as soon as possible, but admitting too many patients may result in exceeding a day's capacity, possibly necessitating turning away some emergency cases. So the problem facing the hospital at the start of each day is how many of the additional requests for elective surgery to assign for that day. We provide a stochastic dynamic programming model for this aggregate advance scheduling problem. The model has some novel mathematical features. We analyze it and characterize the nature of the optimal policy, which is not necessarily of a control-limit type. Plausible numerical examples which confirm our theoretical results and provide additional insights are reported.health care, hospitals, dynamic programming, applications, probability, stochastic model applications

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To reduce lead-time and its variability, modern supply and transportation contracts often specify the frequency of, and volume available for, future deliveries in advance even when final demand is somewhat uncertain (Yano and Gerchak [Yano, C. A., Y. Gerchak. 1989. Transportation contracts and safety stocks for just-in-time deliveries. Manufacturing and Oper. Management 2 314--330.]). We explore the joint optimization of contract parameters and inventory control policy in such environments. We first model and derive the optimal periodic review inventory policy corresponding to a given supply contract, which generates piecewise-linear convex ordering costs. The optimal policy has two critical levels, and there is a range of stock levels for which the quantity ordered equals the contract volume. To numerically compute the critical levels, we model consecutive inventory levels as a Markov Chain, whose steady-state distribution is used to compute the holding, shortage and transportation costs. We then use the resulting total costs to derive the optimal contract volume. Various examples are provided. The optimal contracted delivery frequency can also be computed.inventory-production, stochastic, transportation, models, dynamic programming, applications, probability, Markov processes