BUAD 311 Final: Module 1

Which of the following is false? a) Flow rate is always less than or equal to process capacity. b) Cross-training workers can improve process utilization rate. c) In general, make-to-stock systems can fulfill customer demand faster than make-to-order systems. d) None of the above

d) None of the above

5. The Gaughan & Tiberti Library wants to provide computers for students to check emails. There will be one common queue for all computers, and each computer is used by one student at a time. On average, there are 15 students arrivals per hour, and each student spends 10 minutes on the computer. To control the waiting time, the library wants no more than 90% utilization of the computers. What is the minimum number of computers they should have? A) 3 computers B) 6 computers C) 9 computers D) 12 computers

A) 3 computers Notes: (A). p = 10min. a = 60/15=4min. To ensure at most 90% utilization, i.e. 10/(m * 4) <= 0.9, we need m >= 10/4/0.9=2.78. That is we need at least 3 computers.

. Customers send e-mails to a help desk of an online retailer every 2 minutes, on average, and the standard deviation of the interarrival time is also 2 minutes. The online retailer has Tom 16 units/hour Dick 12 units/hour Harry 18 units/hour 3 three employees answering e-mails. It takes on average 4 minutes to write a response e-mail. The standard deviation of the processing times is 3 minutes. How many emails would there be, on average, that have been submitted to the online retailer but not yet answered? Choose the closest answer. A) 0.5 emails B) 0.7 emails C) 1.5 emails D) 2 emails

B) 0.7 emails Notes: (B). a=2 mins, SD_a=2 mins, CV_a=(SD_a)/a=2/2=1 p=4 mins, SD_p=3 mins, CV_p=(SD_p)/p=3/4=0.75 m=3 u=p/ma=4/(3(2))=0.67 T_q=p/m u^(√(2(m+1) )-1)/(1-u) (CV_a^2+CV_p^2)/2=1.489 mins I_q=T_q/a=1.489/2=0.744 emails

2. The world has a population of 7.6 billion and the average life expectancy is 71.5 years. On average, how many babies are born every day? A) 7.6 billion × 71.5 × 365 B) 7.6 billion ÷ 71.5 ÷ 365 C) 71.5 years ÷ 7.6 billion × 365 D) None of the above

B) 7.6 billion ÷ 71.5 ÷ 365 Notes: (B) by Little's Law. 7.6 billion is the WIP, 71.5 years is the flow time, and the number of babies born each day is the flow rate.

5. "Inventory Turnover = Annual Cost of Goods Sold ÷ Average Inventory" is an application of Little's Law. Which of the following statement is TRUE? A) The annual cost of goods sold corresponds to flow rate, and the average inventory corresponds to WIP. B) Inventory turnover corresponds to flow time. C) Inventory turnover corresponds to flow rate. D) Inventory turnover corresponds to WIP.

B) Inventory turnover corresponds to flow time.

4. Which of the following statements are FALSE? i. The resource that has the lowest output is the bottleneck of the system. ii. In the presence of statistical fluctuations, a system that balances system capacity with demand can lead to large WIP. iii. Pooling two lines of two servers into one line decreases waiting time, and increases the utilization rate of servers. 2 iv. Reducing the standard deviation of the service time, while keeping the average service time unchanged, will reduce the queue length. v. Reducing the time it takes to complete an activity at a resource will increase the overall system capacity. A) Answer: iii, iv, & v. B) Answer: i & v. C) Answer: i, iii, & v. D) Answer: i, ii & iv.

C) Answer: i, iii, & v. Notes: (i) False. The resource with the lowest capacity is the bottleneck.. (ii) True from The Goal. (iii) False. Pooling does not change the overall utilization, if utilization is not greater than 100%. (iv) True, according to the waiting time formula. (v) False. It is only true if the resource is the bottleneck.

All else being equal, which of the following will always reduce the waiting time? A) Combining two queues B) Decreasing the average customer inter-arrival time C) Decreasing the variability of the service time D) Decreasing customer expectations.

C) Decreasing the variability of the service time Notes: (A) does not reduce the waiting time if the customers or servers are heterogeneous, in which case the variability would increase after combining. (B) leads to increased waiting time. (D) does not affect the actual waiting time.

Which of the following statements is FALSE? A) Moving the bottleneck to the beginning of the process sets the pace of the entire process. B) Make-to-stock processes are more responsive, while make-to-order processes are more customizable. C) In Little's Law, "average WIP" refers to the average WIP across different workstations. D) Flexibility increases resource utilization and process capacity.

C) In Little's Law, "average WIP" refers to the average WIP across different workstations.

2. Which of the following statements is FALSE? A) If you double the number of servers, the waiting time in queue will reduce by less than half. B) If customers are heterogeneous and need different process times, pooling their waiting lines may increase the waiting time. C) The coefficient of variation for an exponential distribution is always 1. D) More capacity near the end of the process is better than more capacity near the beginning of the process.

C) The coefficient of variation for an exponential distribution is always 1. Notes: It does mention market expansion

3. A florist sells 1000 stems of roses per month, except the months of February, July, August and December, during which the monthly sales is doubled. The florist grows roses year-round in a greenhouse. Cut roses only lasts a few days, and it takes about a month to grow them back. To meet demand, what should the capacity of the greenhouse be? A) 1000 roses per month B) 1333 roses per month C) 1500 roses per month D) 2000 roses per month

D) 2000 roses per month Notes: (D) because the florist business is not make-to-stock. Roses are perishable and cannot be held as inventory.

8. In a plant, jobs will first go through station A and then station B. Currently station A is the bottleneck, and its capacity is 10 jobs/hour. Each job earns $1,000 net profit for the plant. Renting one more machine can increase the capacity of station A by 5 jobs/hour for station A. The cost of renting is $2,000 per hour, and variable operating/labor cost and maintenance cost are negligible. Should the plant pursue this option? A) No, it is not worth the rent. B) Yes, it strictly increases the profit. C) Breakeven. It does not change the profitability. D) Cannot decide unless there is more information.

D) Cannot decide unless there is more information. It depends on how the rental changes the system capacity. The capacity of station A will become 15 after renting. However, it is possible that B becomes the new bottleneck. Given the numbers, the rental option is only cost-effective if it improves the capacity by more than 2 jobs per hour, i.e., if the capacity of B is already more than 12 jobs per hour.

1. Which of the following statements is TRUE? A) Compared to MTS processes, MTO processes results in more salvage inventory (leftover from demand). B) In a process flow diagram, squares represent resources. C) Flexibility means that one job can be processed by multiple resources. D) Flexibility means that one resource can process multiple activities or types of jobs.

D) Flexibility means that one resource can process multiple activities or types of jobs. Notes: A) False. The opposite is true. B) False. In a process flow diagram, squares represent activities, which is different from resources. C) False. This is not what flexibility means. Without flexibility, a job can still be processed by multiple processes

6. In Trojan Clinic, patients used to be assigned to one physician and always were treated by that same physician. For example, Dr. Tommy's patients always visited him and never interacted with the other physicians. However, they have decided to change this. Now patients will be seen by whoever is available (i.e., not treating patients). Based on queuing theory, which of the outcomes below are likely to occur because of this change? A) The coefficient of variation of patient inter-arrival times will decrease. B) The utilization of every physician will increase. C) The average number of patients actually being seen by a physician (that is, "work in process") will increase. D) None of the above.

D) None of the above. Notes: (A) the inter-arrival time is not affected by the change in the process. (B) The utilization might increase for some physicians and decrease for others. (C) The work in process will not change because the flow rate (i.e. arrival rate) does not change and the flow time (activity time) does not change.

6. In Littlefield game round 1, on day 50 (before any machine purchases), which station was the bottleneck? a) Station 1 b) Station 2 c) Station 3 d) There was no bottleneck.

Depends on Section **Review Littlefields

5. Which of the following conclusions cannot be derived from the book The Goal? a) Making the capacity of all resources equal (balanced system) is always a good decision. b) Activating a non-bottleneck resource to its maximum is not good. c) Less variability at the beginning of the process is better than less variability at the end of the process. d) None of the above.

a) Making the capacity of all resources equal (balanced system) is always a good decision

MarshLev Food Truck serves just 3 items—burgers, burritos, and stir-fry noodles; their demands per hour are 2, 5, and 3 respectively It takes 4 minutes to prepare and serve a burger, 3 minutes to prepare and serve a burrito, and 5 minutes to prepare and serve stir-fry noodles. What is the capacity of MarshLev Food Truck in items per hour (rounded to the nearest integer)? a) 12 b) 16 c) 20 d) 30

b) 16 Average processing time=(2/10)*4+(5/10)*3+(3/10)*5=3.8 mins/unit capacity=(1 average unit/3.8mins)x60min/1hour = 15.79 units/hr

4. Consider a queueing system with a single server and some variability in inter-arrival and service times. Which of the following statements are correct given that coefficients of variations of the inter-arrival and service times are fixed? I. If average service time is fixed and average inter-arrival time is increased, then average waiting time will increase. II. If average inter-arrival time is fixed and average service time is increased, then average waiting time will increase. III. If service rate is fixed and arrival rate is increased, then average waiting time will increase. IV. If arrival rate is fixed and service rate is increased, then average waiting time will increase. a) I and III b) II and III c) I and IV 2 d) II and IV

b) II and III

2. Consider a process with multiple flows. Which of the following is false? a) Bottleneck depends on the demand mix. b) The implied utilization rate of a resource cannot be greater than 100%. c) Process capacity is determined by proportion of flow that hits the bottleneck. d) None of the above.

b) The implied utilization rate of a resource cannot be greater than 100%.

7. A store has an arrival rate of 6 customers per hour and an average service time of 4 minutes. There is one server. What is the percentage of time the system is empty (that is, there is no customer in the system)? a) 0% b) 40% c) 60% d) 66.7%

c) 60% m = 1, p=4min, a=10min, u = p/ma = 4min/(1x10min) = 40%, 1-u =60%.

3. Which of the following is false in general? a) Variability in service process leads to longer wait times. b) Queue lengths increase exponentially as utilization approaches 100%. c) Pooling customers in a common line leads to longer wait times. d) None of the above.

c) Pooling customers in a common line leads to longer wait times.