BUAD 311 Operation Management Case Analysis 2
West Coast University
Prof. Chen MW 10 A.M Spring 2009
Yoan Jo Michiel Josana Patricia Lingkam
Contents 1. West Coast Overview 2. Summary of The Problem 3. Capacity Analysis 4. Waiting Time Analysis 5. Recommendation
West Coast University 1. West Coast Overview West Coast University is a university that provides The Student Health Services (SHS), a care in a primary care clinic and specialty clinic, and The Primary Care Clinic (PCC), serving most medical needs. Students come to PCC to get the treatment from common diseases to emergencies. The PCC offers appointment and walk-in system that operates on a first-come-first-serve basis. PCC has 5 full time and three part time Nurse Practitioners (NP), five full time and four part time Physicians (MD), and six medical assistants (MA), and support staff personnel. Staff members are considered as part time if they work for less than 30 hours per week.
2. Summary of The Problem The West Coast Student Health Services has most of its service for the students’ most medical needs in Primary Care Clinic. Because of this matter, the clinic faces some problems related to its service and get some negative comments form its patient lately. These are the problems that the clinic encounters from servicing its patient: First, the arrival time of the patients are random that leads to a problem since the clinic cannot estimate the exact time of arrival and the approximate number of walk-in patients. Second, the patients can choose their own favorite physicians to provide care for them. This kind of system brings a trouble for the clinic since the requested clinicians might not be available and the patients will try to wait until they available or else they might came back other time later. As a result, this problem can cause the other clinicians to have more idle time and the utilization rate of non-requested clinicians will be low. Third, The clinic also prioritizes the urgent walk-in patient over others patients that can cause more delay time for patients that already wait to be serviced or the patient with appointment. Fourth, according to the survey, there are .5% of respondents had problem with long waiting time, 14% had problem in obtaining appointments in an appropriate mode, 6.7% had problem with facility problems. After finding the problems that they had with their service, the clinic tries to purpose a new system that can solve these problems. The clinic hopes that by creating a new system they can reduce the waiting time to 20 minutes or less, reduce the delay for seeing a team a team clinician that takes a day to only one day, and only less than 5% of patients cannot see their preferred team when they came to walk-in clinic.
3. Capacity Analysis The average arrival rate () = 85 + 84 + 75 + 69 + 64 = 377 patients/week
Physicians and Nurse Practitioner (MD and NP) Service rate () of MD and NP = 1/ms = 1/25 = 2.4 patients/hour The number of MD = 22 + 14 + 22 + 16 + 26 = 100 clinicians/week Capacity of MD = 100 x 2.4 = 240 patients/week The number of NP = 11 + 7 + 11 + 8 + 13 = 50 clinicians/week Capacity of NP = 50 x 2.4 = 120 patients/week Total number = 100 + 50 = 150 clinicians/hour Total capacity = 240 + 120 = 360 patients/week The average arrival rate is larger than the capacity that we have to hire more clinicians. Medical Assistant (MA) The number of MA = 11 + 8 + 11+ 8 + 12 = 50 clinicians/week Capacity of MA = 50 x 17.14 = 857 patients/week
4. Waiting Line Analysis Medical Assistant (MA) The average arrival rate () = 377/40 = 9.425 patients/hour Average inter-arrival time (ma) = 1/ = 1/9.425 = 6.37 min Service rate () = 1/ms = 17.14 patients/hour Average service time (ms) = 3.5 min Number of servers = 50/40 = 1.25 clinicians The utilization rate () = = 9.425 = 44% s 1.25x17.14 Wq = ma . 2(S+1) . ca2+cs2 = 1- 2 = 6.37 . 0.442(1.25+1) . 1+1 = 1.99 min 1-0.44 2 Physicians and Nurse Practitioner (MD and NP) The average arrival rate () = 377/40 = 9.425 patients/hour Average inter-arrival time (ma) = 1/ = 1/9.425 = 6.37 min
Standard deviation (sa) = 6.37 min Service rate () = 1/ms = 1/25 = 2.4 patients/hour Average service time (ms) = 20 min + 5 min = 25 min Standard deviation (ss) = 25 min Because the inter-arrival and service time is exponentially distributed, the coefficient of variation of arrival (ca) and service (cs) = 1 Number of servers = 150/40 = 3.75 clinicians The utilization rate () = = 9.425 = 105% s 3.75x2.4 The utilization rate is greater than 100%; therefore we decide to add more clinicians. Adding 1 more full time clinicians (40 hours/week): Number of servers = 4.75 clinicians The utilization rate () = = 9.425 = 83% s 4.75x2.4 Wq = ma . 2(S+1) . ca2+cs2 = 1- 2 = 6.37 . 0.832(4.75+1) . 1+1 = 19.92 min 1-0.83 2 The goal is to make the total waiting time to be less than 20 minutes. If we add 1 more full time clinicians, the total waiting time would be 19.92 + 1.99 = 21.91 min, which is still more than 20 minutes. Adding 2 more part time or 1 full time and 1 part time clinicians (60 hours/week): Number of servers = 5.25 clinicians The utilization rate () = = 9.425 = 75% s 5.25x2.4 Wq = ma . 2(S+1) . ca2+cs2 = 1- 2 = 6.37 . 0.752(5.25+1) . 1+1 = 9.21 min 1-0.75 2 Total waiting time would be 9.21 + 1.99 = 11.2 min and we could reach the goal.
5. Recommendation 1. Rescheduling/ Changing daily shift If we pay attention to the average daily patients arrival time, we could see that most patients come to the PCC before noon. On the other hand, more clinicians available after the lunch break. PCC should try to change the clinicians schedule in order to meet the demand. 2. Appointment capacity and arrival Total MD and NP available = 300 clinicians/week Total capacity for appointment patients = 300 x 2.4 = 720 patients/week The percentage of patients comes for walk-in is 60% (377 patients/week) and 40% are appointment. The average arrival rate () = 40/60 x 377 = 251.33 patients/week = 6.28 patients/hour Number of servers = 300/40 = 7.5 clinicians The utilization rate () = = 6.28 = 35% s 7.5x2.4 Based on the low utilization rate, we recommend PCC to transfer some clinicians from the appointment service to walk-in, because 65% of the times, appointment clinicians are idle. 3. From the assumption that patients are willing to meet any physicians or nurse available, we recommend that the additional clinicians of PCC should be two part-time nurses. This recommendation is based on the economic issue. 4. Based on the below analysis, we recommend that PCC has to change its current system to the option 1 of new system, which has 2 teams of 6.375 clinicians, because the patients’ waiting time will only be 0.50 minutes. Total number of servers (walk-in and appointment) = 5.25 + 7.5 = 12.75 clinicians The total average arrival rate () = 9.425 + 6.28 = 15.705 patients/hour Average inter-arrival time (ma) = 1/ = 1/15.705 = 3.82 min Standard deviation (sa) = 3.82 min Service rate () = 1/ms = 1/25 = 2.4 patients/hour
Average service time (ms) = 20 min + 5 min = 25 min Standard deviation (ss) = 25 min Because the inter-arrival and service time is exponentially distributed, the coefficient of variation of arrival (ca) and service (cs) = 1 Current system– patients request any preferable clinicians (12.75 M/M/1) The total average arrival rate () = 15.705/12.75 = 1.23 patients/hour The utilization rate () = = 1.23 = 51% s 1x2.4 Wq = ma . 2(S+1) . ca2+cs2 = 1- 2 = 3.28 . 0.512(1+1) . 1+1 = 1.74 min 1-0.51 2 New system with risk-pooling system– patients choose between several teams of clinicians Option 1 (2 M/M/6.375) 2 teams of 6.375 clinicians The total average arrival rate () = 15.705/2 = 7.8525patients/hour The utilization rate () = = 7.8525 = 51% s 6.375x2.4 Wq = 3.28 . 2(S+1) . ca2+cs2 = 1- 2 = 3.28 . 0.512(6.375+1) . 1+1 = 0.50 min 1-0.51 2 Option 2 (3 M/M/4.25) 3 teams of 4.25 clinicians The total average arrival rate () = 15.705/3 = 5.235 patients/hour The utilization rate () = = 5.235 = 51% s 4.25x2.4 Wq = 3.28 . 2(S+1) . ca2+cs2 = 1- 2 = 3.28 . 0.512(4.25+1) . 1+1 = 0.75 min