Due to changing patient loads and demand patterns over time, assigning bed complements for various medical services in a hospital is a recurring problem facing the administrators. For a large public health care delivery system, we present an approach for periodically reallocating beds to services to minimize the expected overflows. Using a queueing model to approximate the patient population dynamics for each service---with admission rates provided by forecasts---the expected overflows under each configuration are computed via a Normal loss integral. Bed allocation is done in two stages. First, we establish a base line requirement for each service so that it can handle a prescribed amount of patient load based on a yearly projection of demand. We then use marginal analysis to distribute the remaining beds to minimize the expected total average overflows while taking month-to-month demand fluctuations into account. The proposed model requires only a modest amount of computation, because of several simplifying assumptions, which were tested for reasonableness. For the two largest services, we used empirical data to evaluate the nonhomogeneous Poisson representation of admissions, and we performed simulation experiments to assess the extent of discrepancy in performance characteristics caused by the ignorance of day-of-week effect on admission rates. In view of the intrinsic complexity of the underlying system, the results obtained from the validation studies suggest that the model is relatively "robust" with respect to the case under consideration. It is hoped that the simplicity of the model and the usefulness of the results will induce practitioners to use this type of formal analysis for bed allocation in an institutional setting on a routine basis.health care: hospital inpatient services, queues: applications, marginal analyses

This paper examines issues in building decision support models for budgeting nursing workforce requirements in a hospital. We determine regular-time, overtime, and agency workforce levels for various skill classes in a budget cycle. We introduce a family of eight models ranging from a single-period, aggregate and deterministic model to a multiperiod, disaggregate and probabilistic model. In a single-period model, we ignore the time-varying nature of demand for nursing hours. Aggregation is done over the nurse skill class mix. For probabilistic models, we consider demand uncertainty. Using empirical data, we evaluate the effects of level of sophistication in model building and in information requirements on their relative performances. The results suggest that ignoring the time-varying nature of demand does not induce gross errors in budget estimates. However, ignoring demand uncertainty produces underestimates (about five to six percent) of budget needs---a consequence of a Madansky (Madansky, A. 1960. Inequalities for stochastic linear programming problem. Management Sci. 6 197--204.) inequality. It also induces added costs to the system due to implementing nonoptimal regular-time workforce levels. Finally, we find that a simple formula using a single-period demand estimate gives excellent approximations to the budget estimates obtainable from the more precise models.health care: hospitals, programming: linear, applications, programming: stochastic

This paper considers a multi-product dynamic lot-size problem. In addition to a separate set-up cost for each product ordered, a joint set-up cost is incurred when one or more products are ordered. We present a dynamic programming formulation for finding the optimal ordering policy that calls for a smaller state space than that proposed by Zangwill. As a convenient substitute, we also introduce a very simple heuristic procedure and two of its variants. For the two-product problem we report computational experience for evaluating the performance of these procedures.

This paper investigates the use of a discrete-time semi-Markov process to model a system that deteriorates in usage. Replacement rules that are (1) state-dependent, (2) state-age-dependent, and (3) age-dependent are proposed. The system operating costs and replacement costs are functions of the underlying states. The optimization criterion is the expected average cost per unit time. Under the first two replacement rules, the paper generates semi-Markov decision processes so that optimal policies can be obtained by the policy-iteration method. Sufficient conditions for the existence of an optimal control-limit state-dependent replacement rule are derived. For the age-dependent policy, the objective function is obtained so that the minimization can be carried out over the integers. An illustrative example is given at the end.