A Stochastic Model for an Optimal Priority Bed Distribution Problem in a Hospital Ward

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Abstract
Ward beds are a primary resource under the control of hospital management. We develop a method for determining an optimum distribution of beds in a ward by assuming that ward patients can be classified into two categories, that admissions follow Poisson distribution, and that length of stay in the ward follows the negative exponential distribution. After defining a cut-off level as “the number of beds beyond which type 2 (non-serious) patients are not admitted,” we develop a system of differential and difference (birth and death process) equations for the process. An objective function made up of shortage and holding costs is then developed and optimized for various values of cut-off priority level. An application of this model to a university teaching hospital in Cleveland is illustrated. The model is then extended to a situation where overflows are temporarily housed in a buffer accommodation or inappropriate ward.

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