By looking at the two charts, we can infer that if there are 13 patients coming into the PCC on Monday and there are only 3 clinicians available to see them then they will only be able to process 7. 2 patients (2. 4 patients*3 clinicians) within the first hour which will make the line and wait time longer for every consecutive hour. The following chart shows where there is overutilization of clinicians and where more coverage is needed: This explains why there is so much dissatisfaction among patients about long service times.
So in order to adhere to Joan Carwin’s objective of a total waiting time of 20 minutes or less it is necessary to calculate how many clinicians are needed at the walk-in clinic at each given hour to try to eliminate the long waiting times. Since the arrival rate was given to us for each hour, we could calculate the average interarrival rate using the following logic: If 1/a=13 patients per hour then, a=(1/1/a)(60min)=(1/13)(60)=4. 615 minutes per customer.
After calculating the arrival rate and the average interarrival, we can also use the processing time of 25 minutes to solve for the expected waiting time for a queue by using trial and error to find the correct amount of servers so the queue time would be less than 20 minutes. The following chart includes the formulas that we used and the number of clinicians that are needed for each hour to have an expected waiting time for a queue to be less than 20 minutes: Calculations If the PCC uses this chart to assign the proposed number of clinicians for
each time period, then the wait times will be reduced to less than 20 minutes creating a much more efficient system. After carefully analyzing the information about current system at the PCC, we have developed several recommendations in order to address Carwin’s objectives. Our first recommendation is to increase the number of physicians working during times when many patients are arriving. The number of physicians working should be dependent on the number of patients that arrive during each specific hour.
The chart above (“New System: Walk-in Clinic”) conveys the amount of clinicians we plan to have working during each specific hour. This will increase the total number of hours per week necessary for clinicians to work from 150 to 202 for the Walk-In clinic, while reducing the hours spent on appointments to meet demand. By having seven clinicians working during hours of high customer traffic (maximum average 13 patients per hour) and less during hours of lower traffic, we will be able to reduce the average wait time from xxx minutes to yyy minutes.
This solution addresses Carwin’s first objective: decreasing the waiting time to 20 minutes or less. Our second recommendation is to implement a “team system” in which each physician will be assigned to a specific team of physicians. The patients would therefore be assigned to a specific team rather than a specific physician. The advantage of using this new system is that it will significantly increase customer satisfaction. In the current system, because patients request specific physicians, the probability of the requested physician being available at a particular time is relatively low.
However, in the new system, because the patients will request specific teams rather than physicians, the probability of having a specific team available at a particular time will be higher than in the current system (requesting a specific physician). Therefore, this addresses Carwin’s second objective: having less than five percent of patients unable to see their specific team when they come to the walk-in clinic. Because we plan to have at least one physician working from each team at all times, we are extremely confident that this goal will be reached.
Overall, each one of these recommendations (adjusting the number of physicians working at specific times and implementing a “team system”) addresses Carwin’s final objective: the maximum delay for seeing a team clinician should be one day. The delay will significantly be reduced because of the number of physicians working each hour and it will be easier for patients to see their requested clinicians because of the “team system. ”