How to solve

Consider a small pharmacy where one pharmacist, one administrative assistant and one cashier work.

On average, $80\%$ of the customers come to fill prescriptions and $20\%$ purchase only over the

counter $($OTC$)$ medication.

Customers who come in to fill a prescription drop off their script with the cashier and each brings

only one script. This step takes on average $5$ minutes per customer.

The pharmacist fills all prescriptions and this step takes on average $15$ minutes per customer. After

spending $15$ minutes on a script, the pharmacist realizes that $20\%$ of the scripts are problematic and

cannot be filled as is$.$ Those scripts are routed to the administrative assistant for problem resolution.

The administrative assistant, on average, spends $40$ minutes resolving an issue on a script. Assume

that all problems are eventually resolved. Those scripts are routed back to the pharmacist to be

filled and this step takes $10$ minutes.

All customers pay the cashier. Check$-$out is on average $3$ minutes for an OTC customer and $6$

minutes for a customer who came in to fill a script.

The pharmacist and the cashier work $8$ hours a day while the administrative assistant works $4$ hours a day.

a$.$ Compute the capacities of the pharmacist, administrative assistant and the cashier in customers per

day.

b$.$ What is the maximum number of customers this pharmacy can serve in a day? Which employee is

the bottleneck?

c$.$ Assume that the pharmacy redesigns the process and requires the cashier to ask a few questions at

drop in$.$ This increases prescription drop$-$off time to $6$ minutes per customer but reduces the

percentage of problematic scripts to $10\%.$ Please explain $($and demonstrate by calculating

before$/$after capacities$)$ if the process redesign increases$/$decreases or does not affect the capacity

of the pharmacy.