[SOLVED] RSM 270 Introduction to Operations Management

RSM 270 Introduction to Operations Management
This is the sample questions for lecture 5 for your preparation.
Problem 1 In a Drs office, patients schedule appointments with the receptionist in advance. The mean duration of each appointment is 1-hour but can vary between 30 minutes and 2- hours. If an appointment runs long, Doctors will stay after hours to insure that all scheduled patients get served. Unfortunately, there is a lot of variability with regards to whether a patient actually shows up for their appointment. In fact, as high as 33% of all patients with a scheduled appointment do not show up! A result of this, many appointment slots are unused due to the large number of no-show patients. Dr. has asked the Operations Department to look into increases the utilization of the doctors in his practice (primary concern). while also keeping the throughput of the system at current levels. What are some recommendations you can give him?
Increase the number of patients that are being referred to the practice by marketing to a larger pool of primary care physicians and ask the receptionist to overbook patients to appointments (i.e., book multiple patients into the same appointment slot).

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Problem 2 A service organization can directly benefit from pooling it servers (workers) in one of the following two forms:
Reduce customers waiting without having to staff extra workers OR Reduce the number of workers while maintaining the same responsiveness.
Problem 3 Jane has been hired by an airline to help them with the waiting time of the customers in the check-in line. The airline has 3 counters now, each staffed by one employee. Currently passengers form one line and being served FCFCS. Jane thinks that redesigning the system may help to decrease the waiting time of passengers. Jane redesign the queues so there would be a dedicated queue and a dedicated server for each type of passengers (first class, business, economy). No customer crosses between servers. economy class arrives at the rate of 19 customer per hour, business class at the rate of 13 passengers per hour, and first class at the rate of 4 customers per hour. Each of the employees take on average 3 minutes to serve a customer. Assume arrivals follow a Poisson process and service time is exponentially distributed. Compare the time customers spend waiting in the two system designs. Also calculate the time each customer spend in the systems.
In the first case, we have M/M/3 queue. The input rate is = 19 + 13 + 4 = 36 customers
per hour. = 1/3 customer per minute = 1/3 60 = 20 customers per hour. Since we
consider M/M/3, Ca = Cs = 1. Also = = 36 = .6. Therefore using the formula for c 320
multi servers we have
2(c+1) 8 Iq = 1 =.6
1.6=.589,
Tq = Iq = .589 = .01636minutes = .98 minutes,
T =Tq +E[s]=.98+3=3.98minutes.

In the suggested system by Jane we have 3 M/M/1 queues. The first queue has 1 = 19 = .95, 20
the second queue has 2 = 13 = .65, and 3 = 4 = .2. Using PK formula for each queue we 20 20
1 21 .952
Iq = 1 = 1.95 =18.05,
Tq1 = 18.05 = .95hours = 57 minutes,
Iq = 1 = 1.65 =1.207,
Tq2 = 1.207 = 5.57 minutes,
Iq = 1 = 1.2 =0.05,
Tq3 = 0.05 = 0.0125 hour = .75 minutes,
T1 =57+3=60minutes
T2 =5.57+3=8.57minutes
T3 =.75+3=3.75minutes.
First class customers prefer the new design, however the average waiting time (as well as the real flow time in the new system is increased dramatically). Average real flow time in the new system design is
6019+8.5713+3.754minutes. 36

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