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Assignment 2 that we had to do as an assignment for submission...

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Instructor: Wenyi Xia

COMM204-921 2019S Assignment 2

Please provide details of your calculation and reasoning. You can either type in the space provided in this assignment or hand-write and scan your answers. Please submit your assignment on Canvas. Only PDF format is accepted. Due date: 11:59 pm, Friday, May 24.

Question 1 Consider the following process flow diagram:

The plant manager wants to know, on average: (a) How long does an order (A or B) stay in the order processing area?

(b) How long does it take an A order to work its way through the plant?

(c) How long does it take a B order to work its way through the plant?

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Instructor: Wenyi Xia

COMM204-921 2019S

(d) How long does it take the average order (A or B) to work its way through the plant?

Question 2 Consider a bagel store selling three types of bagels that are produced according to the process flow diagram outlined below. We assume the demand is 180 bagels a day, of which there are 30 bagels grilled cheddar & veggie, 110 veggie only, and 40 cream cheese. Assume that the workday is 10 hours long and each activity is staffed with one worker.

Moreover, we assume the following activity times:

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Instructor: Wenyi Xia

COMM204-921 2019S

Activity times are independent of which bagel type is processed at a resource (for example, cutting a bagel takes the same time for a cream cheese bagel as for a veggie bagel). (a) Where in the process is the bottleneck for each kind of bagel? Where is the bottleneck for the product mix? Is it possible to satisfy the demand for the whole day?

(b) Given the product mix, how many units can the process produce within one hour?

Question 3. (Note: Parts (a), (b) and (c) are based on the ATM machine example below, whilst part (d) is a general question.) A bank installs an ATM and observes that the customers arrive at a rate of 15 per hour and the arrivals follow a Poisson distribution (the inter-arrival times between two customers follow an exponential distribution). The ATM has a fixed non-random service time of 3 minutes per customer. (Hint: this is a M/D/1 process.) (a) What is the percentage of time that the ATM is idle?

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Instructor: Wenyi Xia

COMM204-921 2019S

(b) Calculate the average time spent by a customer in this system.

(c) Over time, the ATM machine becomes slower. If the ATM machine slows down and requires 5 minutes per customer, what happens to the utilization?

(d) In general, what is the optimal utilization of a resource? Briefly discuss.

Question 4 Alex owns a one-chair shop. He is told that his customers would exhibit a Poisson arrival distribution (equivalently inter-arrival time is exponential distributed), and that his service time follows an exponential distribution. In addition, Alex’s market survey data indicate that customers arrive at a rate of two per hour. It will take Alex an average of 20 minutes to give a haircut. Based on these figures, find the following (Hint: M/M/1 process): (a) The average utilization of Alex’s time

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Instructor: Wenyi Xia

COMM204-921 2019S

(b) The average number of customers waiting

(c) The average time a customer waits

(d) The average time a customer is in the shop

Alex is considering the addition of a second chair (a second barber). Customers would be selected for a haircut on a first come first served basis from those waiting. Alex has assumed that both barbers would take an average of 20 minutes to give a haircut, and that the business would remain unchanged with customers arriving at a rate of two per hour. Find the following information to help Alex decide if a second chair should be added (Hint: M/M/2 process):

(e) The average number of customers waiting.

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Instructor: Wenyi Xia

COMM204-921 2019S

(f) The average time a customer waits.

(g) The average time a customer is in the shop.

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