Background: As was observed in the corona crisis, in situations, such as war or natural disasters or epidemic diseases, the intensity of the applicants for medical services causes congestion problems. In this situation, due to the limited capacity of the system, queuing phenomenon for service applicants and in some cases, rejection of clients occur. Reducing the length of hospital stays by improving performance productivity can compensate for the shortage of hospital beds. In order to increase the productivity of personnel and equipment, it is necessary to eliminate unemployment and improve service scheduling. One of the ways to achieve these goals is to optimize the distribution of beds between wards. In the present study, in the form of Markov chain approach, according to the referral rate and service rate, the existing beds were allocated to different wards of the hospital to maximize service and minimize rejection of patients.
Methods: The present study is an applied study conducted in 2019 for the optimal distribution of beds between the 3 wards of Shahid Faghihi Hospital in Shiraz. The research problem was modeled in the form of Markov chain approach and assuming the referral of clients according to the continuous-time Markov chain, the model parameters value was identified. The obtained mathematical model was solved by GAMS 24.1.3 software.
Results: The proposed model led to an improvement in ward performance in terms of reducing patient waiting time and increasing the number of admitted patients. The proposed model reduced patient rejection by 8.6 %. According to the patients' referral rate to the wards and the service rate of each ward, based on sensitivity analysis, the number of beds allocated to each of the 3 wards was determined.
Conclusion: Queuing theory can be applied as a tool to analyze the phenomena of the treatment system and determine the features of the waiting time, queue length, and capacity of the system. Appropriate allocation of hospital beds results in improving the efficiency and decreasing the patient rejection. Therefore, it could be useful in crisis, congestion in patients, and when increasing facilities is required.
With the expansion of competitive markets, supply chain management has become one of the critical issues facing businesses. One of the advantages of sustainable competition for companies is to make supply chain activities more efficient and effective. This paper aims at an integrated closed-loop supply chain (CLSC) problem which is multi-objective, multi-product, multi-period, and multi-level with limited capacities and uncertain conditions of demand and return products. The proposed supply chain network consists of five levels in the forward flow. There are five centers in the backward flow as well. The purpose of this network is to determine the optimal number and location of facilities required in each period and the optimal amount of the transfer flow of products or raw materials through different transportation modes between facilities. In this proposed model, three objective functions are taken into consideration. The first one minimizes all the costs. The second objective function maximizes the quality of products. The third objective function seeks to minimize the sum of deviations from the ideal score of the principal component of each supplier. The data of this research are taken from Pishro Diesel Company. To solve the proposed problem, several methods and algorithms have been used, including unscaled goal programming, boundary objectives, three single-objective meta-heuristic algorithms (PSO, RDA, and TGA), and multi-objective meta-heuristic algorithm (MOGA-II). As the results show, considering products and returned parts in products, a simultaneous practice of forward and reverse supply chains leads to better product quality, less damage to the environment, and lower costs for customers.
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