Deck 2: Process Flow Measures

Question 1

Customers walk into a bank and are served at an average rate of 20 per hour. One average there are 5 people waiting in queue to be served. How long does the average customer wait in queue?

Answer 1

Throughput R = 20 per hour,
Inventory I = 5
Waiting time in queue T = I/R = 5/20 = 0.25 hours = 15 minutes.

Question 2

At a hospital emergency room, patients come in at the rate of 20 per hour and on average, are processed at the rate as well. Patients wait in queue till they are called in for registration. After registration, patients are taken to an inner area where they are assigned a bed where they wait till an intern is ready to see them. Once an intern sees them, she either identifies them to be a routine case, prescribes medication and releases them, or she admits them to the hospital for further tests and treatment. On average, it is found that there are 30 patients waiting for registration and another 20 waiting to be seen by an intern.A study has determined that 75% of the patients simply require routine treatment. A new system separates the emergency room into two treatment areas, one for routine care and another for emergency cases. A triage nurse who assigns the patient to one of the two tracks sees a patient after registration. Patients for routine care are seen by an intern who either prescribes medication and releases them or determines that the triage nurse has made a mistake and the patient really needs emergency care. In this case the patient is moved to the emergency track. Patients for emergency care are seen by an intern who either admits them for further treatment or determines that they really are routine cases, prescribes medication and releases them. It is determined that there are, on average, 20 people waiting to be registered, 5 waiting to be seen by the triage nurse, 10 waiting to be seen by an intern in the emergency area, and 10 waiting to be seen by an intern in the routine care area. One average, 75% of the patients are classified by the triage nurse as needing routine care.
(a) On average, how long did patients spend in the emergency room before the triage system (either before being released or admitted)?
(b) On average, how long do patients that are finally admitted to the hospital spend in the emergency room after the introduction of the triage system? Assume that the triage nurse makes no mistake in identifying a patient as needing routine or emergency care.
(c) On average, how long do patients spend in the emergency room after the triage system is introduced (either before being released or admitted)? Assume that the triage nurse makes no mistake in identifying a patient as needing routine or emergency care.

Answer 2

a.
Throughput = 20 per hour
Average Inventory = 20 + 30 = 50
Average flow time = Average inventory / Throughput = 50 / 20 = 2.5 hours.
b. Registration:
Average Inventory = 20
Throughput = 20 per hour
Average flow time = 20 / 20 = 1 hour
Triage:
Average Inventory = 5
Throughput = 20 per hour
Average flow time = 5 / 20 = 0.25 hour
Admit:
Average Inventory = 10
Throughput = 5 per hour
Average flow time = 10 /5 = 2 hours
Average time spent by people admitted = 1 + 0.25 + 2 = 3.25 hours
c. In this case we have
Average Inventory = 20 + 5 + 10 + 10 = 45
Throughput = 20 per hour
Average flow time = 45 / 20 = 2.25 hours.

Question 3

A car repair shop has two hoists where cars can be lifted for repair work. Currently customers come in at the rate of 4 per hour and are processed at a similar rate. On average 8 cars are waiting to be processed, 4 needing routine repairs and 4 needing major repairs. People are served on a first come first serve basis.
(a) How long do customers wait on average before being processed?
(b) The repair shop owner feels that he is losing many customers needing routine repair because of the long wait. He dedicates one hoist for routine repair and one for major repairs. A study indicates that routine repairs are processed at the rate of 3 per hour and major repairs at the rate of 1 per hour. There are now 5 people waiting on average for routine repairs and 3 waiting on average for major repairs. How long does each type of customer now wait before being served?
(c) With the new system, what is the average waiting time over all customers?

Answer 3

(a) For the current process we have
Inventory, I = 8 cars,
Throughput, R = 4 cars per hour.
Thus,
Flow time, T = I/R = 8/4 = 2 hours.
Cars wait an average of 2 hours before being served.
(b) At the routine repair hoist, we have
Inventory, I = 5 cars,
Throughput, R = 3 cars per hour.
Thus,
Flow time, T = I/R = 5/3 = 1.67 hours.
Cars wait an average of 1.67 hours before being served at routine repairs.
At the major repairs hoist we have
Inventory, I = 3 cars,
Throughput, R = 1 car per hour.
Thus,
Flow time, T = I/R = 3/1 = 3 hours.
Cars wait an average of 3 hours before being served at major repairs.
(c) With the new system, we have
Inventory, I = 5 + 3 = 8 cars,
Throughput, R = 3 + 1 = 4 cars per hour.
Thus,
Flow time, T = I/R = 8/4 = 2 hours.
Cars wait an average of 2 hours before being served even in the new system.

Question 4

A product sold at a supermarket has a shelf life of 21 days. If daily demand averages 100 units, what is the maximum inventory that the supermarket should carry.

Question 5

Accounts Receivable (AR) receives an average of 1,000 payments per week. There is an average of 500 checks waiting to be deposited.
(a) What is the average time spent by each check waiting to be deposited?
(b) Assume that the checks coming in are either small or large. Small checks are for an average of $500 and large checks are for an average of $5,000. 20% of the checks coming in are large with the rest being small. Currently no distinction is made between the large and small checks. As a result 20% of the checks waiting to be processed are large. Is it worth reallocating resources so that large checks wait an average of 0.3 weeks while small checks wait an average of 0.8 week before being processed?

Question 6

A firm has seen its demand quadruple over a 2 year period. During the same period, the number of turns has doubled. What has happened to inventories over the same period?