This paper considers the two different flow shop scheduling problems that arise when, in a two machine problem, one machine is characterized by sequence dependent setup times. The objective is to determine a schedule that minimizes makespan. After establishing the optimality of permutation schedules for both of these problems, an efficient dynamic programming formulation is developed for each of them. Each of these formulations is shown to be comparable, from a computational standpoint, to the corresponding formulation of the traveling salesman problem. Then, the relative merits of the dynamic programming and branch and bound approaches to these two scheduling problems are discussed.
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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