Scheduling of surgeries in the operating rooms under limited competing resources such as surgical and nursing staff, anesthesiologist, medical equipment, and recovery beds in surgical wards is a complicated process. A well-designed schedule should be concerned with the welfare of the entire system by allocating the available resources in an efficient and effective manner. In this paper, we develop an integer linear programming model in a manner useful for multiple goals for optimally scheduling elective surgeries based on the availability of surgeons and operating rooms over a time horizon. In particular, the model is concerned with the minimization of the following important goals: (1) the anticipated number of patients waiting for service; (2) the underutilization of operating room time; (3) the maximum expected number of patients in the recovery unit; and (4) the expected range (the difference between maximum and minimum expected number) of patients in the recovery unit. We develop two goal programming (GP) models: lexicographic GP model and weighted GP model. The lexicographic GP model schedules operating rooms when various preemptive priority levels are given to these four goals. A numerical study is conducted to illustrate the optimal master-surgery schedule obtained from the models. The numerical results demonstrate that when the available number of surgeons and operating rooms is known without error over the planning horizon, the proposed models can produce good schedules and priority levels and preference weights of four goals affect the resulting schedules. The results quantify the tradeoffs that must take place as the preemptive-weights of the four goals are changed.
This paper presents a model that incorporates variations in the demand rate at random time points into the inventory planning decision. These changes in demand may occur due to economic recessions, labor strife starting or ending, or other events that result in a period of time during which the rate of demand is shifted up or down from its current level. The paper uses system-point level-crossing theory to derive expressions for the distribution and expected value of on-hand inventory, ordering rate, and the expected total cost rate for a given ordering policy. A sensitivity analysis is conducted, and a number of qualitative properties are provided to illustrate the use of the results to obtain optimal order quantities.inventory, EOQ, demand disruptions, level-crossing theory
Using the latest information technology, powerful retailers like Wal‐Mart have taken the lead in forging shorter replenishment‐cycles, automated supply systems with suppliers. With the objective to reduce cost, these retailers are directing suppliers to take full responsibility for managing stocks and deliveries. Suppliers' performance is measured according to how often inventory is shipped to the retailer, and how often customers are unable to purchase the product because it is out of stock. This emerging trend also implies that suppliers are absorbing a large part of the inventory and delivery costs and, therefore, must plan delivery programs including delivery frequency to ensure that the inherent costs are minimized.
With the idea to incorporate this shift in focus, this paper looks at the problem facing the supplier who wants quicker replenishment at lower cost. In particular, we present a model that seeks the best trade‐off among inventory investment, delivery rates, and permitting shortages to occur, given some random demand pattern for the product. The process generating demand consists of two components: one is deterministic and the other is random. The random part is assumed to follow a compound Poisson process. Furthermore, we assume that the supplier may fail to meet uniform shipping schedules, and, therefore, uncertainty is present in delivery times. The solution to this transportationinventory problem requires determining jointly delivery rates and stock levels that will minimize transportation, inventory, and shortage costs. Several numerical results are presented to give a feel of the optimal policy's general behavior.
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