OIS Homework (Statistics)

OIS 3660 Homework 1, Fall 2016

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University of Utah

David Eccles School of Business

OIS 3660: Fall 2016: HW1

Due Monday September 19th, 11:59PM

Q1. Cruz runs a bakery. She has an oven that bakes 20 cookies at a time. It takes 40 minutes on average

for her to bake a cookie. What is the average number of cookies Cruz bakes an hour?

Q2. Clare works at the front desk of DESB. Between 10:30am and 11:00am, 10 students stop by to ask

questions on average. It usually takes 3 minutes to answer a question. What is the average number of

students either waiting or asking questions to Clare at the front desk? (Be careful when you find the

flow rate for this question!)

Q3. Hayden commutes to school from Park City. It usually takes her 40 minutes to get to school. She

finds that there are, on average, 60 cars that travel to school each hour from Park City. What is the

average number of cars on the way to school from Park City?

Jake’s Beer, Bait, & Tackle Co. (Q4-Q6)

Jake’s Beer, Bait, & Tackle Co. is a small chain of fishing tackle stores in northern Minnesota. In 2009,

the company’s revenue was $4,300,000 and its cost of goods sold was $3,200,000. Assume 52 weeks and

365 days per year. Assume that the annual inventory holding cost for Jake’s is 40%.

Q4. Jake keeps only 5.5 days-of-supply of inventory on average because much of his inventory is live bait

and micro-brew beer, both of which have a short shelf life. What is his annual inventory turns? (Round

your answer to two decimal places)

Q5. Given that he has 5.5 days-of-supply of inventory on average, how much inventory does Jake

have on average (in $)?

Q6. What is the inventory holding cost (in $) of an item that costs Jake $20 and is sold to his customers

at $30? (Round your answer to two decimal places)

OIS 3660 Homework 1, Fall 2016

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B&K Consulting (Q7-Q9)

B&K is a strategy consulting firm that divides its consultants into three classes: Associates, Managers,

and Partners. The firm has been stable in size for the last 30 years, and on average, there have been 200

Associates, 60 Managers, and 20 Partners.

The work environment at B&K is rather competitive. After four years of working as an Associate, a

consultant goes “either up or out”; that is, becomes a Manager or is dismissed from the company.

Similarly, after working as a Manager for six years, a Manager either becomes a Partner or is dismissed.

The company recruits MBAs as Associates; no hires are made at the Manager or Partner level.

Q7. How many new MBA graduates does B&K hire every year? (Hint: Think of the Associate stage

itself as a process and use Little’s law to find the number of MBA graduates that are hired each year.

The following picture may help.)

Q8. What percentage (in %) of new hires at B&K will become Managers (as opposed to being

dismissed after 4 years of working as an Associate)? (Hint: Think of the Manager stage itself as a

separate process and find how many managers should be appointment each year. The following picture

may help.)

Q9. Every year, 2 Managers are promoted to Partner level. How many years on average does a

Partner stay in the company as a Partner?

4 years

200 Associates ? Associates/year

6 years

60 Managers ? Managers/year

OIS 3660 Homework 1, Fall 2016

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A Simple Process (Q10 – Q13)

Consider the following process that makes customized suits. When an order is placed, measurement is

taken, which takes 30 minutes to complete. After taking the measurement, materials are prepared and

cut, and this takes one hour. Once the materials are prepared and cut, the materials are sewed. Sewing

takes 2.5 hours on average per order. The process operates for 10 hours a day. The following picture

summarizes the process.

Q10. What is the capacity of the process in [suits/day]?

Q11. Assume that the demand for the customized suit is 0.2[suits/hour]. What should the flow rate of

the process be in [suits/day]?

Q12. Assume that the demand for the customized suit is 0.5[suits/hour]. What is the implied utilization

(in %) of the Sewing stage?

Q13. Assume that the demand for the customized suit is 0.5[suits/hour]. What is the utilization (in %)

of the Measuring stage?

Howard County Hospital (Q14-Q19)

The Howard County Hospital is assessing its Emergency Department (ED) capacity so it knows how to

expand as the county population grows. The hospital has the following information about the ED:

Resource Number

Nurses 12

Physicians 5

X-ray Technicians 4

Examination rooms 10

Trauma bays 3

On average, nurses need to spend 35 minutes with each patient that comes in. Additionally, physicians

need to spend an average of 19 minutes with each patient. Each technician can X-ray up to 5 patients

per hour. All patients have to go through one nurse, one physician and the X-ray.

Preparing/cutting Materials

30 minutes 1 hour 2.5 hours

Taking Measurement

Sewing

OIS 3660 Homework 1, Fall 2016

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Q14. What is the total capacity of Nurses, as in the maximum number of patients the Nurses can see in

one hour? Round your answer to one decimal place.

Q15. What is the total capacity of the X-Ray Technicians (max number of patients that can be X-rayed

in one hour)? Round your answer to one decimal place.

Thereafter, the patients are parsed into two categories: 20% of all patients that come into the ED are

trauma victims that need to be placed in a trauma bay. The other 80% of the patients go into normal

examination rooms. Each trauma patient spends an average of 30 minutes in a trauma bay before

leaving the ED (usually then being admitted to the main part of the hospital), whereas non-trauma

patients spend an average of 45 minutes in an examination room before leaving the ED.

Q16. Suppose on average 50 patients come to the emergency department every hour. What is the

implied utilization (in %) at the trauma bays? (Recall there are 3 trauma bays.)

Q17. Suppose on average 50 patients come to the emergency department every hour. What is the

implied utilization at the examination rooms (in %)? (Recall there are 10 examination rooms.)

Q18. Which resource is the bottleneck?

a) Nurses b) Physicians c) X-Ray Technicians d) Examination Rooms e) Trauma Bays

Q19. Suppose we hired one more physician so that the total number of physicians becomes 6. What will

be the capacity of the process, as in the maximum number of patients the Emergency Department can

treat in one hour? Round your answer to one decimal place

Q20. Which of the following statements is TRUE?

a. Implied utilization of a bottleneck stage is always greater than 100%. b. Utilization of a bottleneck stage is always equal to 100%. c. A non-bottleneck stage has excess capacity compared to the bottleneck stage, and the implied

utilization of a non-bottleneck stage is always less than 100%.

d. A non-bottleneck stage has excess capacity compared to the bottleneck stage, and the utilization of a non-bottleneck stage is always less than 100%.

e. It is possible for utilization of a stage to exceed 100%.