V. Big-Box Pharmacy (45 points) Big-Box Pharmacy operates out of the back of Big-Box retailer and caters to its customers. Typical pharmacy scripts are handled in a "streamlined" three step process: 1. The first step is manual and involves a single pharmacy assistant taking the prescription from customers; assisting them; then inputting the data into the BigBox information system. The time to assist customers is exponentially distributed with an average of 200 seconds per customer. 2. The second step is an automated and proprietary digital BigBoxAssure.M procedure that scans the script and checks for "No-refills", and performs the Drug Utilization review (safety check). BigBoxAssure step always takes 150 seconds to process a script. On average 90% of the scripts are approved at the end of this step and move on to the Pharmacist for fulfillment, while 10% are rejected and the customer notified by text message while they are still in the store. Rejected prescriptions are not able to be re-processed. 3. The third step at the lone Pharmacist, takes exponentially distributed processing time for an approved prescription, with an average of 300 seconds. This includes calling the customer once the prescription is ready to be picked up and handing over the prescription. Customers typically remain in the area for the entire duration from drop-off to pick-up. Weekday demand is 10 arriving prescriptions per hour, while weekends see 14 prescriptions coming in per hour. Assume that the inter-arrival times follow an exponential distribution for all steps (ie. the standard deviation of inter-arrival times is the same as the mean). a) (12 points) Determine the bottleneck and the hourly capacity for BigBox Pharmacy's operation, calculated in average scripts (dropped-off by customers) per hour. Step Capacity (Average Submitted Scripts/Hour) Assistant Bottleneck: BigBoxAssure Pharmacists System