Providing a Model for the Optimal Allocation of Hospital Beds Based on Markov Chain Approach (Case Study: Shiraz-Shahid-Faghihi Hospital)

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.

Valuation of R&D compound option using Markov chain approach

Incorporation of technical risk in compound real options has been considered in Cassimon et al. (2011) concerning the valuation of multi-stage pharmaceutical R&D. There, the technical success probabilities at each development stage were assumed to be generated independently of each other. This assumption can be unrealistic in many applied problems, pharmaceutical R&D included. We present a valuation procedure dealing with dependent success probabilities and random development stage times. This greater flexibility allows a better description of the sequence of decision stages and results, which in turn, impact the value of the considered project. The theoretical results are illustrated through a numerical example that shows the implementation of the model to a pharmaceutical R&D problem.

PENERAPAN METODE PENGENDALIAN KUALITAS MEWMA BERDASARKAN ARL DENGAN PENDEKATAN RANTAI MARKOV (Studi Kasus: Batik Semarang 16, Meteseh)

An industrial company requires quality control to maintain quality consistency from the production results so that it is able to compete with other companies in the world market. In the industrial sector, most processes are influenced by more than one quality characteristic. One tool that can be used to control more than one quality characteristic is the Multivariate Exponentially Weighted Moving Average (MEWMA) control chart. The graph is used to determine whether the process has been controlled or not, if the process is not yet controlled, the next analysis that can be used is to use the Average Run Length (ARL) with the Markov Chain approach. The markov chain is the chance of today's event is only influenced by yesterday's incident, in this case the chance of the incident in question is the incident in getting a sampel of data on the production process of batik cloth to get a product that is in accordance with the company standards. ARL is the average number of sample points drawn before a point indicates an uncontrollable state. In this study, 60 sample data were used which consisted of three quality characteristics, namely the length of the cloth, the width of the cloth, and the time of the fabric for the production of written batik in Batik Semarang 16 Meteseh. Based on the results and discussion that has been done, the MEWMA controller chart uses the λ weighting which is determined using trial and error. MEWMA control chart can not be said to be stable and controlled with λ = 0.6, after calculating, the value is obtained Upper Control Limit (BKA) of 11.3864 and Lower Control Limit (BKB) of 0. It is known that from 60 data samples there is a Tj2 value that comes out from the upper control limit (BKA) where the amount of 15.70871, which indicates the production process is not controlled statistically. Improvements to the MEWMA controller chart can be done based on the ARL with the Markov Chain approach. In this final project, the ARL value used is 200, the magnitude of the process shift is 1.7 and the r value is 0.28, where the value of r is a constant obtained on the r parameter graph. The optimal MEWMA control chart based on ARL with the Markov Chain approach can be said to be stable and controlled if there is no Tj2 value that is outside the upper control limit (BKA). The results of the MEWMA control chart based on the ARL with the Markov Chain approach show that the process is not statistically capable because the MCpm value is 0.516797 and the MCpmk value is 0.437807, the value indicates a process capability index value of less than 1. Keywords: Handmade batik, Multivariate Exponentially Weighted Moving Average (MEWMA), Average Run Length (ARL), Capability process.

Financial Risk Information Spreading on Metapopulation Networks

The financial risk information diffuses through various kinds of social networks, such as Twitter and Facebook. Individuals transmit the financial risk information which can migrate among different platforms or forums. In this paper, we propose a financial risk information spreading model on metapopulation networks. The subpopulation represents a platform or forum, and individuals migrate among them to transmit the information. We use a discrete-time Markov chain approach to describe the spreading dynamics’ evolution and deduce the outbreak threshold point. We perform numerical simulation on artificial networks and discover that the financial risk information can be promoted once increasing the information transmission probability and active subpopulation fraction. The weight variance and migration probability cannot significantly affect the financial risk spreading size. The discrete-time Markov chain approach can reasonably predict the above phenomena.

Comparison of bus driving cycles elaborated for vehicle dynamic simulation

Due to the technological progress, new approaches such as model-based design are spreading in the development process in the automotive industry to meet the increased requirements related to lower fuel consumption and reduced emission. This work is part of a research project which focuses on dynamic modeling of vehicles aimed at analyzing and optimizing the emission and fuel consumption. To model the driver behavior, the simulation control algorithm requires a predetermined speed-time curve as an input. The completeness of this driving cycle is a crucial factor in the simulation, and as far as the legislative driving cycles are not accurate enough, it is indispensable to develop our own one representing our narrower area and driving conditions. This article considers two common drive cycle design methods, comparing the micro-trip-based approach and the Markov-chain approach. The new driving cycle has been developed applying the Markov-chain approach and compared to a driving cycle introduced in our recent paper using the micro-trip method. The comparison basis is the Speed-Acceleration Probability Distribution, which sufficiently reflects the dynamic behavior of the vehicle, and the root mean square error, including parameters such as the average speed, average cruising speed, average acceleration, average deceleration, root mean square acceleration, and idle time percentage. The representative Bus Driving Cycle for Debrecen is prepared to be applied in the vehicle dynamics simulation for evaluating and improving the fuel economy of vehicles, selecting the proper power source for various applications and the optimization of the powertrain and the energy consumption in researches to be continued.

Development of stochastic model of particulate coal fluidized bed expansion and axial structure

Particulate solids are in the state of fluidization at many stages of preparation and treatment of solid fuels. An effective drag force coefficient Cd is used to describe a mechanical contact between gas stream and an individual particle. The evaluation of the effective drag force coefficient is not limited by the force of hydraulic resistance but also includes a set of different forces. This set of forces is rather indeterminate, and a lot of empirical equations for effective drag force coefficient calculations can be found in the scientific papers. Choosing the applicable formula for calculation is often difficult. In addition, it requires taking into account the flow patterns around an individual particle. Thus, a comparative study to examine the most well-known drag force models with a uniform approach to account the flow patterns around an individual particle is important. The Markov chain approach is used as a mathematical basis for modeling of the flow patterns in a fluidized bed. The identification of the model parameters is completed and the complementation of transition matrices with the current physical properties of substances involved into the flow makes the model non-linear. The comparative study of the results obtained with using of the two correlations for drag force coefficient is performed. The stochastic model of fluidized bed expansion and axial structure has been proposed. The comparative analysis of two different scenarios of fluidized bed expansion using different drag force models has been performed. The authors developed and tested the model to describe fluidized bed expansion and axial structure on the basis of the Markov chain approach. The low certainty of physical drag coefficients models under conditions of flow patterns around an individual particle has been shown. The conducted research proves that consistent description of structure inhomogeneity of fluidized bed is possible using the nonlinear mathematical models based on mesoscale level of the object decomposition. Predictive efficiency of similar models is limited by low reliability of formula for calculation of drag force coefficient. Thus, it is possible to state the importance of further comparative research to check different formulas for calculation of gas-particle drag force coefficient in order to provide a reliable forecast of the fluidized bed height.