spring2022_final_Answer key (All Answers are Correct) University Of Chicago MBA 42201

University of Chicago Booth School of Business Operations Management Spring 2022 Linwei Xin Final Exam, Spring 2022 Print Name: Registered Section (circle one): 01– Thursday 8:30–11:30am 81– Thursday 6–9pm 85– Saturday 1:30–4:30pm I pledge my honor that I have not violated the Booth Honor Code during this examination. Signature: Instructions: 1. PRINT your name legibly at the top of this page. 2. Sign the Booth honor code before submitting your solutions. 3. The exam is open books and notes. You can also use a calculator (including the one on your computer). However, during the exam, you are not allowed to visit websites other than the Canvas website for the course. You are also not allowed to discuss anything related to the exam with your peers, until the grading is completed. 4. Maximum total points you can get in this exam is 40. 5. Points for each question are shown in brackets. 6. You are allowed to work on your exam at most for 3 hours. At the end of the exam you will have an additional 15m to (i) scan your answers or take their photos, (ii) combine everything in a single pdf file, and (iii) submit the pdf file on Canvas. Use the following naming convention when you submit your solutions: “Final Lastname F”. When you downloaded the exam, a timer has started on Canvas. You need submit your solutions within 3h 15m of the start of the timer. Any submissions after that will be considered late. 7. For problems 1–6, if a question requires analysis you must show your work for each question in order to receive credit. Partial credit is awarded for partial success on each attempted question. 8. Please be clear in your work. It is hard to grade a sea of numbers on each page. State carefully what you know and what formulas you are going to use. It is your responsibility to ensure that your answers (and scanned pages/photos) are legible. GOOD LUCK! 1 1. [4 points] Amber Lime, an aspiring comedian in Chicago, had to look for day jobs when the pandemic hit the entertainment industry. She was able to find a part time job as an associate at the Hyde Park oce of Parcel Express, a national parcel shipping company. Like many other shipping companies, Parcel Express su↵ered from disruptions in their shipment networks due to several reasons. One reason was the unexpected explosion in the volume of return shipments due to the boost in online shopping. To partially streamline their local operations, Hyde Park oce of Parcel Express assigned Amber and a coworker to handle all the return shipments from the customers. They have two tasks. • Step 1: Amber checks whether the customer has printed the correct return label. If a customer does not have a correct return label, Amber directs them to a nearby printing facility. The probability that Amber sees a correct return label upon a customer visit is 70%. Here, each customer visit is counted separately, so for example, if a customer with an incorrect return label visits the oce, and then comes back to the oce after going to the printing facility, two visits are counted even though the customer is the same on both visits. • Step 2: If the return label is correct, the package is placed on a conveyor belt which goes to the temporary storage area. Amber’s coworker then sorts the package and places them in bins to be loaded onto vehicles. The inter-arrival times of customer visits for return shipping are distributed exponentially with an average of 5 minutes. Amber can check return labels at a rate of 30 per hour, and her service times are exponentially distributed. Amber’s coworker can sort a package in 6 minutes on average, with a standard deviation of 1 minute. Hint: Draw a process flow diagram of the return package accepting and sorting process. 2 Label ta5min Checking Sorting Call Mr301hr 70 ts 6min CE I 5 1 301 v (a) [2] Assuming the system is in steady state, how many customers are waiting to be served in Step 1, on average? (b) [2] Assuming the system is in steady state, how long does a return package spend on average in the temporary storage area before Amber’s coworker sorts them? 3 MIM I queue fi g 605perhour 30 perhour 3 0.4 INYg CTg CT ts CT CIII ts If ByBurke's Theorem the interarrivaltimes to sorting stage are exponentially distributed Cal L E gs where Is 12 0.7 8Hperhour Is 86 0.84 Ctg I x 6 x 9TH 16 1875 minutes 2. [3 points] After working in the Parcel Express for a few months, Amber was transferred to a distribution center owned by the same shipping company. Due to the hit of Covid-19, there is an increase in demand of last-mile delivery. Since the distribution center needs more employees for delivery, they decided to hire temporary employees to help the daily operations of the center. Most of these workers looking for temporary jobs have limited time they want to spend working in the distribution center and there is a large volatility in how long the workers may want to work at the distribution center. Suppose temporary workers leave the distribution center at a rate of 10 workers per week with a standard deviation of 4 workers per week. The distribution center needs to recruit new temporary workers constantly. Each time there is a new group of new workers joining in, the distribution center needs to train them. We consider the number of new temporary employees recruited from one recruiting trip one batch. The cost for one recruiting trip and training one batch of new employees is $5000. The recruiting and training process takes about 1 week. In the distribution center, each temporary employee is paid $1000 per week as salary. The distribution center wants to ensure that the probability that no temporary workers are available to work is less than 10 percent. Using a model from class, suggest a recruiting policy for the center so that they minimize recruitment and training cost and salary, while keeping sucient number of workers to meet their performance target. Your policy should detail when to initiate a recruiting trip and a target for the number of workers to recruit on each trip. 4 a EM 2 10 901 service level Using the standard normal table 89.971 Zsa1.28 Rt LA Za TF 1 10 1.28 4 1 15.12 3. [3 points] Amber had to watch her spending more carefully due to the high inflation caused partly by the pandemic. Her cell phone company has just introduced a new billing plan, “Your Choice.” Under the plan, one chooses her allotment of cell phone minutes at the beginning of each month. The monthly bill is then a fixed charge of $10, plus 8 cents f