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Operations Management Problems: Analyzing Capacity, Managing Bookings, and Optimizing Resources

## Analyzing the Capacity and Bottlenecks of an Orthopedist's Office

Question 1:

Process Analysis Consider an orthopedist's office in Costa Rica. All arriving patients first check-in at a reception area where they fill out the necessary paperwork. On average, it takes 10 minutes to complete check-in and there are four receptionists working at the office.

Then the patients are seen by a doctor. An average exam takes 30 minutes to complete and there are ten doctors working at the office. 40% of the patients do not need further evaluation after the exam and proceed to the reception area for check out. The remaining 60% require X-rays. X-rays are taken by the X-ray technician.

It takes on average 20 minutes to process a patient at the X-ray machine and there are three X-ray technicians and three X-ray machines. Once the X-rays are complete, the patient is seen by a doctor again who finalizes the diagnosis by looking at the X-ray. It takes on average 22 minutes for the doctor to evaluate the X-ray and finalize the diagnosis after which the patient goes to the reception area for check out. It takes 5 minutes for a receptionist to check a patient out.

(a) What is the capacity of each resource at the orthopedist's office in patients/hour

(b) Which resource is the bottleneck? What is the overall capacity of the orthopedist's office in patients/hour?

(c) Now assume that after evaluating the X-rays, the orthopedist rejects some of them because their contrast index is outside the specified tolerance limits where the lower and upper tolerance limits are set at 1.45 and 1.60 respectively.

The average contrast index for X-ray machines at the office is 1.50 and the standard deviation is 0.05. Compute the percentage of X-rays that will be rejected by the doctors.

(d) If a patient's X-ray is rejected (at the end of the 22-minute evaluation by the doctor), she has a second X-ray taken (assume that the second X-ray will always be accepted) and this new X-ray must be evaluated by the doctor before the patient receives a diagnosis and proceeds to check-out.

It takes the doctor 22 minutes to evaluate the new X-ray and provide a final diagnosis. Assuming 25% of X-rays are rejected, what is the capacity of the orthopedist's office in patients/hour? You should ignore your calculation from part (c) to answer this question.

(e) Assume that the net profit the doctor's office makes on a patient is \$50. Recalibrating the three X-ray machines at a cost of \$25,000 will ensure that the contrast index of all X-rays will fall within the tolerance limits. How long will the payback period be for this investment? Assume that the orthopedist's office is open eight hours a day, five days a week, and 50 weeks a year. This question is a continuation of part (d) above.

## Revenue Management for an Airline: Booking Levels for a Special Event

Question 2:

You have been assigned to manage booking levels for Southwest Airlines (SA). Flight SAA 703 from Chicago to Indianapolis has been the focus of attention for revenue management due to low utilization of the available seats. This flight is served by a Boeing 737 with a capacity of 150 seats in the Economy class.

The economy full fare on this flight is \$800. For Flight SA 703 scheduled on April 6th (which will arrive just in time for passengers to watch the NCAA championship basketball game), you have already accepted 100 reservations so far.

No discount fares are being offered due to the special event. Based on the past history of bookings on this flight and after making adjustments for the special event, you expect the additional demand for this flight for full-fare economy seats to be Uniformly distributed between 1 and 100 reservations.Assume that all passengers who make reservations on this flight will show up (due to the basketball game), and hence you should not overbook this flight.

You have received a message from Priceline indicating that a group of MA students from Notre Dam is willing to offer \$360 per seat for a group of at least 20 seats, and the group is willing to buy up to 50 seats at this price. Should you accept this offer? If so, how many seats are you willing to give to this group? If not, how much will the students need to offer to obtain a reservation for at least 20 seats?

Question 3:

Imagine that your factory has the following resources: 3 board stuffing machines, 2 testing machines, and 1 tuning machine.

The setup and processing times at each step are as follows:

Step Setup Time (per lot) Processing Time (per unit) Step 1 1.4 hours-Setup Time (per lot) 0.06 hours-Processing Time (per unit) Step 2 0.2 hours-Setup Time (per lot) 0.01 hours-Processing Time (per unit) Step 3 0.3 hours-Setup Time (per lot) 0.02 hours-Processing Time (per unit) Step 4 0.5 hours-Setup Time (per lot) 0.02 hours-Processing Time (per unit)

(a) If your facility was completely empty when you received an order (remember that orders arrive in batches of 60 units), how long would it take for you to process this order assuming that you process the order in a single lot of 60 units? (Remember that a lot is always processed at a single machine.)

(b) If you process each order in a single lot of 60 units, and customer orders arrive at the rate of 14 orders/day, what would be the capacity utilization at each station?

(c) How long would it take for you to process an order assuming that you instead split the order into 2 lots of 30 units each (again assuming that the facility is empty at the time the order arrives)?

(d) If you process each order in two lots of 30 units each, and customer orders arrive at the rate of 14 orders/day, what would be the capacity utilization at each station?

(e) If you bought a 3rd machine for Station 2, what would be the minimum batch size you could use and still have sufficient capacity at Station 2 to process 14 orders/day? (For this problem, do not pay any attention to Stations 1 or 3.)

(f)How long does it take to complete each step for each customer order assuming that you process the order in a single lot of 60units(remember that a lot is always processed at a single machine)