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Concordia University *

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INDU 6311

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Apr 3, 2024

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Contents Mazhar ........................................................................................................................................................ 1 Destiny/Susmita .......................................................................................................................................... 2 Destiny/Susmita .......................................................................................................................................... 3 Destiny/Susmita .......................................................................................................................................... 4 Team on Saturday (8PM) ............................................................................................................................. 5 Matt ............................................................................................................................................................. 5 Saad ............................................................................................................................................................. 6 Dhruvin ........................................................................................................................................................ 7 Team on Saturday (8PM) ............................................................................................................................. 8 Model 1 = 1ST Alternative Model 2 = 2ND Alternative Model 3 = 3RD Alternative NEXT MEETING SAT 8PM – 835H Output Analysis of Model 1 Mazhar 1. State and explain the run parameters by answering the following. a) State how many replications you ran: We ran all the three alternative with 122 number of replication. b) Provide an explanation of how you calculated the above number of replications: Initial Number of Replications = n 0 = 20 Confidence Interval = CI = 95%
Alpha = = 0.05 Based on Method 3 n = n 0 β 0 β For Alternative 1: Key Performance Indicator Average Current Half Width ( β o ) Current Error (%) Desired Half Width ( β ) No of Replications (n) Final No of Replication Wait time to see doctor without priority 20.4785 0.98 0.04785506 8 1.023925 19 32 Wait time to see nurse 2.5655 0.03 0.01169362 7 0.128275 2 Doctor wait time priority 1 15.7622 0.41 0.02601159 7 0.78811 6 Doctor wait time priority 2 17.2173 0.62 0.03601029 2 0.860865 11 Doctor wait time priority 3 24.1691 1.52 0.06289021 9 1.208455 32 Total time in system priority 1 35.2427 0.96 0.02723968 4 1.762135 6 Total time in system priority 2 36.5906 1.07 0.02924248 3 1.82953 7 Total time in system priority 3 43.5569 1.75 0.04017733 1 2.177845 13 Last Time When Patient Leaves System 628.34 10.65 0.01694942 2 31.417 3 Total Time in System for Patient 39.7211 1.14 0.02870011 2 1.986055 7 For Alternative 2: Key Performance Indicator Average Current Half Width ( β o ) Current Error (%) Desired Half Width ( β ) No of Replications (n) Final No of Replication Wait time to see doctor without priority 52.4926 5.11 0.097347055 2.62463 76 Wait time to see appointment doctor without priority 47.8589 3.92 0.08190744 2.392945 54 Wait time to see nurse 2.811 0.06 0.021344717 0.14055 4 Doctor wait time priority 1 19.574 0.75 0.038316134 0.9787 12 Doctor wait time priority 2 26.0451 1.21 0.046457875 1.302255 18 Doctor wait time priority 80.4677 9.39 0.116692785 4.023385 109
3 122 Doctor wait time priority 1 appointment patient 48.0727 5.93 0.123354835 2.403635 122 Doctor wait time priority 2 appointment patient 48.5123 4.16 0.085751449 2.425615 59 Doctor wait time priority 3 appointment patient 47.3924 3.8 0.080181632 2.36962 52 Total time in system priority 1 48.3294 2.5 0.051728348 2.41647 22 Total time in system priority 2 52.5132 1.52 0.028945103 2.62566 7 Total time in system priority 3 89.2476 6.53 0.073167234 4.46238 43 Last Time When Patient Leaves System 742.95 24.87 0.033474662 37.1475 9 Total Time in System for Patient 57.1716 3.56 0.062268679 2.85858 32 Total Time in System for Appointment Patient 66.9744 4.18 0.062411907 3.34872 32 For Alternative 3 : Key Performance Indicator Average Current Half Width ( β o ) Current Error (%) Desired Half Width ( β ) No of Replications (n) Final No of Replication Wait time to see doctor without priority 55.4494 5 0.090172301 2.77247 66 88 Wait time to see appointment doctor without priority 17.9753 0.3 0.016689568 0.898765 3 Wait time to see nurse 2.8036 0.03 0.010700528 0.14018 1 Doctor wait time priority 1 21.4001 0.98 0.045794179 1.070005 17 Doctor wait time priority 2 28.7041 2.04 0.071069987 1.435205 41 Doctor wait time priority 3 82.7143 8.67 0.104818635 4.135715 88 Doctor wait time priority 1 appointment patient 17.958 0.78 0.043434681 0.8979 16 Doctor wait time priority 2 appointment patient 17.8941 0.4 0.022353737 0.894705 4 Doctor wait time priority 3 appointment patient 18.0324 0.37 0.020518622 0.90162 4 Total time in system priority 1 39.3832 1.11 0.028184607 1.96916 7
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Total time in system priority 2 45.0381 1.66 0.036857683 2.251905 11 Total time in system priority 3 81.2205 5.91 0.072764881 4.061025 43 Last Time When Patient Leaves System 695.34 18.3 0.02631806 34.767 6 Total Time in System for Patient 59.3934 3.5 0.058929107 2.96967 28 Total Time in System for Appointment Patient 37.3242 0.67 0.01795082 1.86621 3 So we maximum form all the three alternatives which is 122. c) Insert a screenshot of your run parameters (should match your model!):
2. Present a table of 95% confidence intervals for all major performance metrics in table format, corresponding to the setting above. (Note I am not listing all performance metrics, you can add all the ones you used in your analysis.) Destiny/Susmita Alternative 1: Performance Metric Average 95% Confidence Interval Wait time to see Nurse 3.06 [3.0279, 3.0921] Wait time to see Doctor Priority 1 Patient 18.3 [18.113, 18.487] Priority 2 Patient 22.2 [21.895, 22.505] Priority 3 Patient 66.2 [63.36, 69.04] Total time in the system Priority 1 Patient 38 [37.653, 38.347] Priority 2 Patient 41.8 [41.411, 42.189] Priority 3 Patient 85.7 [ 82.78, 88.62] Average Nurse Queue Time (Waiting Time) 0.617 [0.588, 0.646] Last Time when patient leaves the system 707 Average Doctor Queue Time (Waiting Time) 30.1 [28.58, 31.62] Average Doctor Queue Time without Priority (Waiting Time) 43.9 [42.38, 45.52]
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Destiny/Susmita Alternative 2: Performance Metric Average 95% Confidence Interval Wait time to see Nurse 2.8 [ 2.7791, 2.8209] Wait time to see Doctor Priority 1 Patient 20.3 [19.981, 20.619] Priority 2 Patient 26.6 [26.045, 27.155] Priority 3 Patient 82.6 [78.76, 86.44] Wait time to see Appointment Doctor Priority 1 Patient 48.8 [46.23, 51.37] Priority 2 Patient 48.7 [46.43, 50.97] Priority 3 Patient 48.8 [46.46, 51.14] Total time in the system Priority 1 Patient 48.9 [47.86, 49.94]
Priority 2 Patient 53.1 [52.286, 53.914] Priority 3 Patient 91.5 [88.78, 94.22] Latest time a patient leaves the clinic Day 1 342 [ 337.11, 346.89] Day 2 338 [333, 343] Day 3 336 [331.14, 340.86] Day 4 339 [334.5, 343.5] Day 5 339 [334.28, 343.72] Day 6 337 [332.41, 341.59] Day 7 338 [333.47, 342.53] Average Nurse Queue Time (Waiting Time) 0.384 [0.3645, 0.4035] Average Doctor Queue Time (Waiting Time) 40.5 [38.44, 42.56] Average Doctor Queue Time without Priority (Waiting Time) 54 [51.93, 56.07] Average Appointment Doctor Queue time without priority 48.8 [46.56, 51.04]
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Destiny/Susmita Alternative 3: Performance Metric Average 95% Confidence Interval Wait time to see Nurse 2.81 [2.7887, 2.8313] Wait time to see Doctor Priority 1 Patient 21.3 [20.946, 21.654] Priority 2 Patient 28.1 [27.37, 28.83] Priority 3 Patient 75.1 [71.65, 78.55] Wait time to see Appointment Doctor Priority 1 Patient 17.5 [17.229, 17.771] Priority 2 Patient 17.7 [17.525, 17.875] Priority 3 Patient 17.8 [17.64, 17.96] Total time in the system Priority 1 Patient 39.5 [39.084, 39.916] Priority 2 Patient 44.3 [43.704, 44.896] Priority 3 76.6 [74.09, 79.11]
Patient Latest time a patient leaves the clinic Day 1 331 [ 326.94, 335.06] Day 2 327 [322.13, 331.87] Day 3 323 [319.19, 326.81] Day 4 326 [321.68, 330.32] Day 5 328 [323.73, 332.27] Day 6 323 [318.64, 327.36] Day 7 324 [318.98, 329.02] Average Nurse Queue Time (Waiting Time) 0.409 [0.3894, 0.4286] Average Doctor Queue Time (Waiting Time) 27.1 [25.7, 28.5] Average Doctor Queue Time without Priority (Waiting Time) 51.2 [49.22, 53.18] Average Appointment Doctor Queue time without priority 17.8 [17.664, 17.936]
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Team on Saturday (8PM) 3. Describe any missing information about your alternatives below. Add as many alternative labels as needed. For each alternative, specify the changes you have made in the model. Please add a reference to the file name corresponding to each alternative (.doe file). Alternative 1: Current state (as in part 1) “1ST Alternative.Doe” seeks to model exactly what is stated in the question. In order to achieve 7 distinct days of 9 working hours, the “Logic Section” of “1ST Alternative.Doe” utilizes two create modules to control the “entities per arrival” variable which is “PatientsPerArrival”. Here are how the two logical entities control the working day time frames: The “Patients Arrive at Clinic” create module creates patients according to an EXPO (7) distribution. However, the entities per arrival alternates between 1 and 0 to control when the office is open and closed, respectively. The “PatientsPerArrival” variable is initially set to 1 by default in the variable table. At 540 Minutes, a logical entity is created via the “Create Stop Arrival Logic Entity” create module. This entity allows for the “PatientsPerArrival” variable to be set to 0, halting patient arrivals. Any entities still in the system will be processed. At 1440 minutes, the “Create start Arrival Logic Entity” module will create a logical entity to set the “PatientsPerArrival” variable back to 1 to allow patients to start coming to the hospital again. Every 1440 minutes, the “Create Stop
Arrival Logic Entity” and “Create start Arrival Logic Entity” will flip the “PatientsPerArrival” variable between 0 and 1 respectively to control the operating hours. The model runs for 7 total days of 24 hours however, so this will trigger the end of the work week and replication. Pending Explanation: Record KPIs, how the output is calculated. Alternative 2: Appointment-based system for one doctor with a walk-in system for the other two doctors 1. A logic is created to decrement slots every 15 minutes as a function of time. In total, there are 245 slots (7*(540/15) -7 = 245) slots from 8 AM to 4:45 PM. 2. Another logic is created for patients who calls for an appointment. Which are first checked to see if any slots are available in 7 consecutive days using decision module. So, if slots are available then the appointment patients are delayed 30 minutes which is time to reach hospital otherwise rejected. 3. After that there is increment in variable "number of appointment patients”. At same time, the status of “Appointment patient reserved” changes to 1 which indicates there are patients who got appointment. This logical entity is then disposed. 4. The “Appointment Patients Arrivals” module creates arrival of actual appointment patients one by one after a period of 15 minutes. The arrival of appointment patients is controlled by “Appointment Patients Reserved * PatientsPerArrival” in create module entities per arrival. So, if appointment patient called at 08:03 then its first delayed 30 minutes after that entities per arrival turns 1 from zero at 08:33. As “Appointment Patients Arrivals” creates entities after every 15 minutes so the earliest it can entity for appointment patient is at 08:45 AM after 08:03 AM which is first patient arrival time. 5. After that there is decrement in variable "number of appointment patients” and decision to check if any appointment patients are left. If there are no appointment patients left then entities per arrival changes to 0. 6. Appointment patients can only come if clinic is open and there are patients who got appointment. If clinic is close and “number of appointment patients” > 0 then rest of patients will start coming from next day 8 AM. The last time when appointment patient can come is 04:45 PM as arrivals stops at 04:59 PM. 7. The process is separated based on patient type using decision module. Alternative 3: Description: Explain your alternative 3. Implementation: Please provide an explanation of your implementation. Please include the file name of the file that contains your implementation
Explanation : In our alternate model 3, we have continued the modelling process by taking inspiration from the alternate 2. But, we have made some significant changes in the model that results in reduced average time for patients in the system. The changes made include: 1. Assigning priority to a patient type i.e. “Walk-in” and “Appointment patients” using “Priority” attribute upon arrival. 2. As per alternate 2, this model also gives the priority to a patient based on the pain with “lowest attribute value”. 3. Compared to the alternative 2, alternate 3 creates a combined priority by taking a product of the priority given based on patient type and the pain level of the patients by an attribute called Mixed Priority. (Mixed Priority = Patient Type Priority * Pain Type Priority). 4. In alternative 3, all the doctors are combined as a single resource with capacity 3 and catering the patients based on their attribute value of “Mixed priority”. 4. Results of comparison of alternatives (Add all the relevant metrics you have considered.) Matt a) Alternative 1 vs Alternative 2 N=122 set expo to 5 for all files compared Metric Confidence Interval for Difference of Means Significant Difference? Explain. Conclusion (e.g., is one better than the other or there is no statistical difference?) Waiting time until nurse [0.2273, 0.3047] We have the same conclusion for all metrics. There is a significant difference for each metric since "0" is not contained in their respective Confidence Intervals. This implies that we can reject the hypothesis of zero At a 95% confidence level, we can conclude that Alternative 1 has longer wait times for seeing the nurse. For this metric, Alternative 2 is better. Waiting time until doctor Priority 1 [-2.382, -1.638] At a 95% confidence level, we can conclude that Alternative 2 has longer wait times for seeing a doctor as a priority 1 patient. For
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difference for each metric at the 5% significance level. In other words, Alternative 1 and 2 are different for these metrics. this metric, Alternative 1 is better. Priority 2 [-5.004, -3.756] At a 95% confidence level, we can conclude that Alternative 2 has longer wait times for seeing a doctor as a priority 2 patient. For this metric, Alternative 1 is better. Priority 3 [-20.93, -12.07] At a 95% confidence level, we can conclude that Alternative 2 has longer wait times for seeing a doctor as a priority 3 patient. For this metric, Alternative 1 is better. Total system time [-10.59, -6.35] At a 95% confidence level, we can conclude that Alternative 2 takes longer to process patients. For this metric, Alternative 1 is better. Total system time with priority Priority 1 [-11.95, -9.85] At a 95% confidence level, we can conclude that Alternative 2 takes longer to process patients with priority 1. For this metric, Alternative 1 is better. Priority 2 [-12.176, -10.424] At a 95% confidence level, we can conclude that Alternative 2 takes longer to process patients with priority 2. For this metric, Alternative 1 is better. Priority 3 [-9.57, -1.99] At a 95% confidence level, we can conclude that Alternative 2 takes longer to process patients with priority 3. For this metric, Alternative 1 is better.
Latest time a patient leaves the clinic [-55.6, -31.8] At a 95% confidence level, we can conclude that Alternative 2 has a greater maximum time that a patient will be in the system (on average). For this metric, Alternative 1 is better.
Metric Estimated Mean Difference Half Width Waiting time until nurse 0.266 0.0387 Waiting time until doctor Priority 1 -2.01 0.372 Priority 2 -4.38 0.624 Priority 3 -16.5 4.43 Total system time -8.47 2.12 Total system time with priority Priority 1 -10.9 1.05 Priority 2 -11.3 0.876
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Priority 3 -5.78 3.79 Latest time a patient leaves the clinic -43.7 11.9 Saad b) Alternative 1 vs Alternative 3 Metric Confidence Interval for Difference of Means Significant Difference? Explain. Conclusion (e.g., is one better than the other or there is no statistical difference?) Waiting time until nurse [0.209, 0.287] We have the same conclusion for all metrics. For some metrics there is a small differernce such as the "waiting time to see a nurse" while for others we have a significant differences since "0" is not contained in their respective Confidence Intervals. This implies that we can reject the At a 95% confidence level, we can conclude that Alternative 1 has longer wait times for seeing the nurse. For this metric, Alternative 3 is better. Waiting time until doctor Priority 1 [-3.42, -2.63] At a 95% confidence level, we can conclude that Alternative 3 has longer wait times for seeing a doctor as a priority 1 patient. For this metric, Alternative 1 is better. Priority 2 [-6.7, -5.11] At a 95% confidence level, we can conclude
hypothesis of zero difference for each metric at the 5% significance level. In other words, Alternative 1 and 3 are different for these metrics. that Alternative 3 has longer wait times for seeing a doctor as a priority 2 patient. For this metric, Alternative 1 is better. Priority 3 [-13.6, -4.31] At a 95% confidence level, we can conclude that Alternative 3 has longer wait times for seeing a doctor as a priority 3 patient. For this metric, Alternative 1 is better. Total system time [1.1, 5.6] At a 95% confidence level, we can conclude that Alternative 1 takes longer to process patients. For this metric, Alternative 3 is better. Total system time with priority Priority 1 [-2.05, -0.974] At a 95% confidence level, we can conclude that Alternative 3 takes longer to process patients with priority 1. For this metric, Alternative 1 is better Priority 2 [-3.25, -1.8] At a 95% confidence level, we can conclude that Alternative 3 takes longer to process patients with priority 2. For this metric, Alternative 1 is better. Priority 3 [5.12, 13.2] At a 95% confidence level, we can conclude that Alternative 1 takes longer to process patients with priority 3. For this metric, Alternative 3 is better. Latest time a patient leaves the clinic [7, 26.8] At a 95% confidence level, we can conclude that Alternative 1 has a greater maximum time that a patient will be in
the system (on average). For this metric, Alternative 3 is better. Metric Estimated Mean Difference Half Width Waiting time until nurse 0.248 0.0393 Waiting time until doctor Priority 1 -3.02 0.395 Priority 2 -5.9 0.794 Priority 3 -8.96 4.65 Total system time 3.33 2.23 Total system time with priority Priority 1 -1.51 0.538 Priority 2 -2.52 0.722 Priority 3 9.14 4.03 Latest time a patient leaves the clinic 16.9 9.9
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Dhruvin c) Alternative 2 vs Alternative 3 Metric Confidence Interval for Difference of Means Significant Difference? Explain. Conclusion (e.g., is one better than the other or there is no statistical difference?) Waiting time until nurse [-0.0504, 0.0136] FAIL TO REJECT H0 => MEANS ARE EQUAL AT 0.05 LEVEL At a 95% confidence level, we can conclude that Alternative 2 has similar wait times for seeing the nurse with an error of [- 0.0504,0.0136]. For this metric, Alternative 2 and 3 are similar. Waiting time until doctor Priority 1 [-1.483, -0.537] We have the same conclusion for the selected metrics except waiting time until patients sees the nurse. There is a significant difference for each metric since "0" is not contained in their respective Confidence At a 95% confidence level, we can conclude that Alternative 3 has longer wait times for seeing a doctor as a priority 1 patient. For this metric, Alternative 2 is
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Intervals. This implies that we can reject the hypothesis of zero difference for the rest of the metrics at the 5% significance level. In other words, Alternative 2 and 3 are different for each metric except the first one. better. Priority 2 [-2.467, -0.573] At a 95% confidence level, we can conclude that Alternative 3 has longer wait times for seeing a doctor as a priority 2 patient. For this metric, Alternative 2 is better. Priority 3 [2.2, 12.84] At a 95% confidence level, we can conclude that Alternative 2 has longer wait times for seeing a doctor as a priority 3 patient. For this metric, Alternative 3 is better. Total system time [9.69, 13.9] At a 95% confidence level, we can conclude that Alternative 2 takes longer to process patients. For this metric, Alternative 3 is better. Total system time with priority Priority 1 [8.35, 10.51] At a 95% confidence level, we can conclude that Alternative 2 takes longer to process patients with priority 1. For this metric, Alternative 3 is better. Priority 2 [7.817, 9.743] At a 95% confidence level, we can conclude that Alternative 2 takes longer to process patients with priority 2. For this metric, Alternative 3 is
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better. Priority 3 [11.24, 18.56] At a 95% confidence level, we can conclude that Alternative 2 takes longer to process patients with priority 3. For this metric, Alternative 3 is better. Latest time a patient leaves the clinic [49.2, 72.1] At a 95% confidence level, we can conclude that Alternative 2 has a greater maximum time that a patient will be in the system (on average). For this metric, Alternative 3 is better. Metric Estimated Mean Difference Half Width Waiting time until nurse -0.0184 0.032 Waiting time until doctor Priority 1 -1.01 0.473 Priority 2 -1.52 0.947 Priority 3 7.52 5.32 Total system time 11.8 2.11 Total system time with priority Priority 1 9.43 1.08 Priority 2 8.78 0.963 Priority 3 14.9 3.66 Latest time a patient leaves the clinic 60.6 11.4
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\\filer-users\S_S17690\My Documents\ARENA LAB\Project+Assignment\ PROJECT\Final Folder\Final Folder\A1 VS A3\Total time in system by priority 1 type Patient.dat
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(Include as many tables as needed. Alternative formats accepted as long as you make it clear where there is a significant difference between alternatives and where there is not, and clearly state the conclusion that is being made.) Team on Saturday (8PM) 5. What recommendations would you like to make to MTL Clinic? Please justify your suggestions based on the above analysis.
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