Enhancing operational efficiency of hospitals using discrete event simulation

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Healthcare needs have grown and healthcare organizations have become large and complex. In populous country like India, hospitals are not able to provide sufficient facilities to the patients.

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International Journal of Management (IJM) Volume 11, Issue 4, April 2020, pp. 32-43, Article ID: IJM_11_04_005 Available online at http://www.iaeme.com/ijm/issues.asp?JType=IJM&VType=11&IType=4 Journal Impact Factor (2020): 10.1471 (Calculated by GISI) www.jifactor.com ISSN Print: 0976-6502 and ISSN Online: 0976-6510 © IAEME Publication Scopus Indexed ENHANCING OPERATIONAL EFFICIENCY OF HOSPITALS USING DISCRETE EVENT SIMULATION Dr. Kimsy Gulhane Assistant Professor, Shri Ramdeobaba College of Engineering and Management, Nagpur, India Dr. Amir Khan Assistant Professor, Shri Ramdeobaba College of Engineering and Management, Nagpur, India Rijuta Joshi Assistant Professor, Shri Ramdeobaba College of Engineering and Management, Nagpur, India ABSTRACT Healthcare needs have grown and healthcare organizations have become large and complex. In populous country like India, hospitals are not able to provide sufficient facilities to the patients. As a result, patients have to wait for long times in queues. Many times there are not sufficient drugs available in stock. Purpose of research is to achieve operational excellence in hospital by applying simulation. Operational excellence of the hospitals means that  Patients have to wait for less time in queues.  There is no shortage of drugs. For this, simulation is used. Simulation is a technique where experiments are conducted using models. These models represent real-world systems. Simulation for queues of hospital:- Arrival times of patients and Service time of the server is collected from hospital. Then histogram is plotted. From the histogram, data is identified with a particular distribution and then new arrival and service times are generated using random variate generator of that distribution. Using these values, simulation is conducted. Output of simulation is analyzed. If it is found that server is overloaded, then decision to add new server is taken. http://www.iaeme.com/IJM/index.asp 32 editor@iaeme.com
Dr. Kimsy Gulhane, Dr. Amir Khan and Rijuta Joshi Simulation for inventory management of hospital:- Data for demand and lead time is collected from the hospital. Then data is identified with a particular distribution using histogram. New demand and lead time values are generated using random variate generator of a particular distribution. Using these values simulation is conducted. After simulation, if shortage is more then reorder level can be changed or order size can be changed. Major results Operational excellence can be achieved through appropriate decision making as result of simulation. Output of simulation is analyzed and modifications in queuing and inventory are done. This will lead to operational excellence of hospitals. Keywords: operational efficiency, hospitals, Simulation, queues, inventory. Cite this Article: Dr. Kimsy Gulhane, Dr. Amir Khan and Rijuta Joshi, Enhancing Operational Efficiency of Hospitals Using Discrete Event Simulation, International Journal of Management, 11 (4), 2020, pp. 32-43. http://www.iaeme.com/IJM/issues.asp?JType=IJM&VType=11&IType=4 1. INTRODUCTION Simulation is a technique where experiments are conducted using models. These models represent real-world systems. Healthcare organizations have become larger, complex and costly. The needs of healthcare have grown and so there is a need that decision should be taken appropriately. Also there is the need of having accurate policies. Simulation is valuable as it can provide evidence of how to cope with these complex health problems. 2. SIMULATION FOR QUEUES OF HOSPITAL To start simulation 50 values of Inter-arrival times are collected as follows: Table 1 50 values of Inter- arrival time 1.5 0.5 2.0 0.5 0.5 2.5 3.0 4.0 3.5 7.0 2.0 1.0 1.0 2.5 0.5 2.5 6.0 4.5 5.0 3.0 0.5 6.0 2.5 1.0 3.5 9.0 3.0 2.0 0.5 5.0 0.5 0.5 3.5 4.0 5.0 3.5 6.0 5.0 8.0 2.5 4.0 5.0 3.0 7.0 1.5 1.5 2.0 4.0 0.5 0.5 From the above data, frequency table is prepared as: Table 2 Frequency table Range frequency 0-2 20 2-4 17 4-6 9 6-8 3 8-10 1 total 50 http://www.iaeme.com/IJM/index.asp 33 editor@iaeme.com
Enhancing Operational Efficiency of Hospitals Using Discrete Event Simulation Using this table, histogram is plotted as follows: Figure 1 Histogram Average= 162/50 = 3.24 From above histogram, data is exponentially distributed. 50 values of service time are collected as follows: Table 3 50 values of Service times 1.5 1.0 3.0 1.0 3.0 3.0 2.0 3.0 3.5 3.0 4.0 3.5 2.5 3.5 5.0 3.5 4.0 3.0 3.5 4.5 3.5 1.0 3.5 4.0 3.0 3.0 2.5 2.5 1.5 2.0 3.0 2.0 2.5 1.0 2.0 2.5 1.5 4.5 4.0 5.0 5.0 3.0 3.5 3.0 1.5 4.0 3.5 3.5 2.0 3.0 From the above data, frequency table is prepared as: Table 4 Frequency table 1 Range frequency 0-1 4 1-2 9 2-3 22 3-4 10 4-5 5 Total 50 http://www.iaeme.com/IJM/index.asp 34 editor@iaeme.com
Dr. Kimsy Gulhane, Dr. Amir Khan and Rijuta Joshi Using this table, histogram is plotted as follows: Figure 2 Histogram Service times are normally distributed. Mean= 143.5/50= 2.87 Std. deviation= 1.04 Following programs generate 20 new values from exponential and normal distribution. Figure 3 Program of random variate generator for exponential distribution http://www.iaeme.com/IJM/index.asp 35 editor@iaeme.com
Enhancing Operational Efficiency of Hospitals Using Discrete Event Simulation Figure 4 Program of random variate generator for normal distribution Output for the above two programs is taken and that is used as input for simulation. This will be referred as first replication. 2.1. First Set of output Figure 5 Output values (exponentially distributed) http://www.iaeme.com/IJM/index.asp 36 editor@iaeme.com
Dr. Kimsy Gulhane, Dr. Amir Khan and Rijuta Joshi Figure 6 Output values (normally distributed) These output values are used as input for simulation. This will be referred as first replication. Table 5 Replication 1 Customer Inter- Arrival Service time Time service Time Waiting time Idle time number arrival time begins service ends in of server time queue 1 --- 0 1 0 1 0 0 2 5 5 3 5 8 0 4 3 2 7 2 8 10 1 0 4 2 9 1 10 11 1 0 5 1 10 2 11 13 1 0 6 2 12 3 13 16 1 0 7 2 14 1 16 17 2 0 8 2 16 2 17 19 1 0 9 8 24 3 24 27 0 5 10 3 27 2 27 29 0 0 11 0 27 4 29 33 2 0 12 6 33 3 33 36 0 0 13 0 33 1 36 37 3 0 14 3 36 4 37 41 1 0 15 2 38 3 41 44 3 0 16 3 41 2 44 46 3 0 17 0 41 2 46 48 5 0 18 1 42 4 48 52 6 0 19 0 42 3 52 55 10 0 20 3 45 3 55 58 10 0 Simulation time= 0 to58min. Server utilization = total time server is busy /total simulation time =49/58= 84.48% Average waiting time= 2.5 min. http://www.iaeme.com/IJM/index.asp 37 editor@iaeme.com
Enhancing Operational Efficiency of Hospitals Using Discrete Event Simulation Average utilization of all the replications is calculated as: Table 6 Server Utilization Replications Server utilizati on 1 84.48% 2 100% 3 81.81% 4 98.3% 5 79.71% 6 81.82% 7 73.24% 8 98.11% 9 70.13% 10 91.67% Average 85.93% utilization Since the average utilization is more than 80%, server is over utilized. The solution is to have another server. 3. SIMULATION FOR INVENTORY MANAGEMENT OF HOSPITAL 3.1. About the Real System There are many medicines that are required on large scale in the hospital. For the purpose of simulation, antibiotics are considered here. To start simulation, daily demand and lead time is required. This data is also called input values. These values are collected from the hospital. 3.2. Daily Demand 20 values of daily demand for antibiotics are collected as: 57,55, 57 ,70, 75 ,18 ,20 ,34, 40, 36 ,60, 58 ,53 ,38 ,63 ,64, 85 ,90,35,62 A histogram is plotted for the above values as: Figure 7 Histogram 3 http://www.iaeme.com/IJM/index.asp 38 editor@iaeme.com
Dr. Kimsy Gulhane, Dr. Amir Khan and Rijuta Joshi We get the curve of normal distribution from the histogram hence we get an inference that data belongs to normal distribution. Mean and std. Deviation of normal distribution are then calculated as: Mean (µ) =53.5 Standard Deviation (σ) = 10.7 A random variate generator for normal distribution is used to generate new values of demand X=µ+σZ For this, X= 59.6+10.7Z Where, Z1= (-2lnR1)1/2cos2πR2 Z2= (-2lnR1)1/2sin2πR2 Figure 8 Random variate generator for normal distribution http://www.iaeme.com/IJM/index.asp 39 editor@iaeme.com
Enhancing Operational Efficiency of Hospitals Using Discrete Event Simulation Figure 9 Output values Now 14 new values for daily demand are generated using 14 random numbers as: Table 7 Daily demand values Daily demand 50 36 48 34 32 42 26 47 33 45 31 38 40 49 Lead time: The data for lead time is collected for 50 days. Table 8 Lead time Lead time days probability 1 10 0.2 2 10 0.2 3 10 0.2 4 10 0.2 5 10 0.2 50 http://www.iaeme.com/IJM/index.asp 40 editor@iaeme.com
Dr. Kimsy Gulhane, Dr. Amir Khan and Rijuta Joshi Figure 10 Random variate generator for uniform distribution Lead time is uniformly distributed. The range for uniform distribution is between 1 to 5 days. By using random variate generator for uniform distribution, new values of lead time can be generated as: X= KR Here, K=5. X=5R Figure 11 Output values (lead time) http://www.iaeme.com/IJM/index.asp 41 editor@iaeme.com
Enhancing Operational Efficiency of Hospitals Using Discrete Event Simulation Table 9 Lead time values R X=KR X(lead time)(rounded up) 0.11 0.5 1 0.36 1.8 2 0.25 1.2 2 0.37 1.8 2 0.26 1.3 2 0.75 3.7 4 0.10 0.5 1 0.20 1 1 0.19 0.95 1 0.91 4.55 5 Last column shows the new values of lead time generated using random numbers. These values along with daily demand values act as the input data for the simulation. Table 10 Simulation table for inventory system day Stock level(I) Order quantity Lead time Daily demand shortage (I+50) 1 70 - - 50 - 2 20 70 1 36 14 3 0 - - 48 48 4 50 - - 34 - 5 16 66 2 32 16 6 0 - - 42 42 7 0 - - 26 26 8 66 - - 47 -- 9 19 69 2 33 14 10 0 - - 45 45 11 0 - - 31 31 12 69 - - 38 31 13 38 - - 40 2 14 0 70 - 49 49 From the above table, we calculate average shortage as: 14+48+16+42+26+14+45+31+31+2+49 = 22.71 14 From above simulation, average shortage is 22.71.Average demand for 14 days is 39.35.In 14 days, there is more shortage and so it has to be minimized. This can be done by changing the reorder point or by changing the order quantity. 4. CONCLUSION Using simulation, it is suggested that another server is required as one server is overloaded. From above simulation, average shortage is 22.71.Average demand for 14 days is 39.35.In 14 days, there is more shortage and so it has to be minimized. This can be done by changing the reorder point or by changing the order quantity. This can be repeated by taking other values for reorder level and size and simulation can be performed again The simulation procedure can be summarized as: http://www.iaeme.com/IJM/index.asp 42 editor@iaeme.com
Dr. Kimsy Gulhane, Dr. Amir Khan and Rijuta Joshi  Data collection  Identifying distribution from histogram.  Using random variate generator for generating new values  Simulate  Analyze the output To increase accurateness we can simulate for more values. The values can be generated using random variate generator for that particular distribution. To improve the efficiency and accurateness the procedure can be programmed so that many values can be generated and simulation of data can be done for that. REFERENCES [1] Banks, J. (2010). Discrete-event system simulation. Upper Saddle River, NJ: Prentice Hall. [2] Devore, J. L. [1999], Probability and Statistics for Engineers and the Sciences, 5th ed., Brooks/Cole, Pacific Groove, CA. [3] Feller, W. [1968], An Introduction to Probability Theory and Its Applications, Vol. I, 3rd ed., Wiley, New York. . [4] Gordon, G. [1975], The Application of GPSS V to Discrete System Simulation, Prentice- Hall, Englewood Cliffs, NJ. [5] Hadley, G., and T. M. Wh1tin [1963], Analysis of Inventory Systems, Prentice-Hall, Englewood Cliffs, NJ. [6] Innes, W. W., and D. C. Montgomery [1990], Probability and Statistics in Engineering and Management Science, 3rd ed., Wiley, New York. [7] Law, A. M., and W. D. Kelton [2000], Simulation Modeling &Analysis, 3d ed., McGraw- Hill, New York. [8] Papoulis, A. [1990], Probability and Statistics, Prentice Hall, Englewood Cliffs, NJ. [9] Bratley, P., B. L. Fox, And L. E. Schrage [1996], A Guide to Simulation, 2d ed., Springer- Verlag, New York. [10] Cox, D. R, and P. A. W. Lewis [1966], The Statistical Analysis of Series of Events, Methuen, London. [11] Durbin, J., "Tests of Serial Independence Based on the Cumulated Period gram," Bulletin of the International Institute of Statistics. [12] S. C. Gupta and V. K. Kapoor “Fundamental Of Mathematical Statistics” [13] Adel K. Mahmoud, Khalaf Nasralla and Suha K. Shihab, [2018], 3d Fe-Simulation of Thermally Assisted Turning of Inconel-718 for Cutting Forces Prediction International Journal of Design and Manufacturing Technology, 9(2), pp.1-12 [14] M.S.V. Vara Prasad, Ch. Nagabhushanam and K. Krishna Murthy, [2016], A Numerical Simulation of Symbols for CPFSK Modulation. International Journal of Electronics and Communication Engineering and Technology, 7(6), pp. 107–112. [15] Miss. Snehal S. Mule, Prof. Dr. Shrinivas A. Patil, Prof. Dr. S.K. Chinta, [2013], A Simulation of Colour Strength Measurement System For Printed Fabric Using Fuzzy Logic, International Journal of Electronics and Communication Engineering & Technology, 4(6), pp. 29–39. http://www.iaeme.com/IJM/index.asp 43 editor@iaeme.com