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Homework answers / question archive / COPYRIGHTED MATERIAL, DO NOT CIRCULATE CARLSON SCHOOL OF MANAGEMENT, UNIVERSITY OF MINNESOTA SCO 3001 Final Exam (Spring 2021) 120 minutes in total: Section 4 Date, time, and submission • • Section Final Exam Time and Date 2 Mon, May 10: 10:30am–12:30pm 4 Sat, May 8: 10:30am–12:30pm 5 Sat, May 8: 01:30pm–03:30pm You must upload your work to Canvas by the deadline
COPYRIGHTED MATERIAL, DO NOT CIRCULATE CARLSON SCHOOL OF MANAGEMENT, UNIVERSITY OF MINNESOTA SCO 3001 Final Exam (Spring 2021) 120 minutes in total: Section 4 Date, time, and submission • • Section Final Exam Time and Date 2 Mon, May 10: 10:30am–12:30pm 4 Sat, May 8: 10:30am–12:30pm 5 Sat, May 8: 01:30pm–03:30pm You must upload your work to Canvas by the deadline. Late submission will be penalized 2 point per minute. o This means that if you realize that you submitted “wrong files” or “incomplete pictures” 35 minutes after the deadline, you will get no credit for this exam. Points • There is a total of 70 points (19 + 18 +17 + 16) in the final exam, but your total points will be multiplied by 2/7 to obtain a maximum of 20 points toward your final grade. • You will get 0 points if you don’t show sufficient supporting work regardless of your answer. • Round your answers to one decimal point where applicable. Proctoring • You are required to log into the Zoom lectures and turn your video on. • You are required to keep your camera on during the entire exam period. • You may leave after 90 minutes for any reason. • You are not allowed to speak up during the entire exam. • If you log into Zoom more than 5 minutes late, you will be given 0 credit for this exam. • If you turn off your camera during the exam, you will be given 0 credit for this exam. • You may take a few short breaks (without my permission) during the exam. • You will be recorded by UMN Zoom. • You are allowed to use virtual background. • The recording will not be posted on Canvas. • The recording will only be used to check for potential academic misconduct. • Exam will be proctored via Zoom by PA’s and professor. • You can ask questions via Zoom chat but are not allowed to show your calculations in chat. 1 COPYRIGHTED MATERIAL, DO NOT CIRCULATE CARLSON SCHOOL OF MANAGEMENT, UNIVERSITY OF MINNESOTA Submission via Canvas • You can submit your work multiple times and your most recent submission will be graded. Option 1: Type in computer (can be combined with Option 2 below) • • • Type your answers in this WORD file and upload in WORD or in PDF format. Make sure you upload the correct file including your work. No other format (such as .pages) will be accepted. Option 2: Write on paper • • • • You can write your solution on paper and scan or take pictures of your work clearly. Scanned file must be in PDF format. Pictures must be in JPEG or JPG or PNG format. Then upload all the file(s) in the CORRECT SEQUENCE. No other format (such as .heic) will be accepted. Option 3: Write on tablet • • • You can write your solution on tablet and upload in WORD or PDF format. Make sure you upload the correct file including your work. No other format (such as .one) will be accepted. General policy • You must attend all the midterm and final exams in YOUR ENROLLED SECTION. • Open: book, lecture notes/recordings, practice problems solutions, homework solutions. • Collaboration of any sort on exams is strictly prohibited and will be reported to the university and result in an “F” in the course grade. By taking the exam online, you agree and adhere to the University’s policies regarding academic integrity. PLEASE DOUBLE CHECK AFTER YOUR SUBMISSION. We will not grade anything you submit via email or Canvas inbox. If you find that you submitted wrong files or incomplete pictures, you need to immediately upload the correct files or complete pictures. Late submission will be penalized 2 points per minute. You will get no credit if your work is submitted 35 minutes past the deadline. 2 COPYRIGHTED MATERIAL, DO NOT CIRCULATE CARLSON SCHOOL OF MANAGEMENT, UNIVERSITY OF MINNESOTA Problem 1: Process Management (19 points) A field office of Minnesota Department of Vehicle Services provides two types of services: issuing new licenses and renewing existing licenses. On average, 110 customers per hour arrive at this office. This office follows this process: every customer is required to see a receptionist for screening for COVID. Unfortunately, 10 customers per hour are turned away because they have some COVID symptoms. The rest of the customers are directed to one of three stations: • 65% go directly to Issue License. • 15% are required to take an eye test first. Only 80% of people pass the eye test and the remaining 20% exit. The customers who pass the eye test proceed to Check Document. • 20% proceed to Check Document. 10% of the people who go through Check Document do not meet the document requirements and exit, while 90% proceed to Issue License. Data on each station are provided in the following table: Reception Eye Test Check Document Issue License Workers 2 2 4 6 Activity time per worker (min) 0.5 5 6 3 Show how you calculate demand, capacity, and implied utilization = demand / capacity. a) (2 points) What is the implied utilization of Reception? (leave one decimal point, e.g., 80.0%) 3 COPYRIGHTED MATERIAL, DO NOT CIRCULATE CARLSON SCHOOL OF MANAGEMENT, UNIVERSITY OF MINNESOTA b) (3 points) What is the implied utilization of Eye Test? (leave one decimal point) c) (3 points) What is the implied utilization of Check Document? (leave one decimal point) d) (3 points) What is the implied utilization of Issue License? (leave one decimal point) 4 COPYRIGHTED MATERIAL, DO NOT CIRCULATE CARLSON SCHOOL OF MANAGEMENT, UNIVERSITY OF MINNESOTA e) (3 points) Which station is the bottleneck? Does the local DMV have enough capacity to handle all the demand in the current set up? Explain your answer. f) (5 points) Suppose the local DVS decides to cross-train workers in the Eye Test station and the Check Document station. What is the implied utilization of the new station? (leave one decimal point) 5 COPYRIGHTED MATERIAL, DO NOT CIRCULATE CARLSON SCHOOL OF MANAGEMENT, UNIVERSITY OF MINNESOTA Problem 2: Linear Optimization (18 points) Hospital administrators must schedule nurses so that the hospital’s patients are provided with adequate care. At the same time, in the face of tighter competition in the health care industry, they must pay careful attention to keeping costs down. From historical records, administrators estimated the minimum number of nurses to have on hand for the various times of the day and days of the week, as shown in the following table. Shift Time Minimum number of nurses needed 1 Midnight-4am 5 2 3 4am-8am 8am-noon 12 14 4 noon-4pm 8 5 6 4pm-8pm 8pm-Midnight 14 10 Nurses work 8 hours a day in two consecutive shifts. As a result, in each shift, there are two types of nurses: those that started in the previous shift (and are now working their second shift), and those that just started in this shift (and will be working in the next shift as well). Formulate an optimization problem that determines the minimum total number of nurses required to fulfill the schedule above. We allow the number of nurses to be fractions in this problem, that is, we do not require them to be integers. [Hint: We solved parts a, b, c, in class.] a) (3 points) What are your decision variables? Briefly explain. b) (2 points) What is your objective? Please specific maximize or minimize. 6 COPYRIGHTED MATERIAL, DO NOT CIRCULATE CARLSON SCHOOL OF MANAGEMENT, UNIVERSITY OF MINNESOTA c) (7 points) What are your constraints? You solved this problem in Excel Solver and obtained the following. Constraints Cell $C$41 $C$42 $C$43 $C$44 $C$45 $C$46 Name Midnight-4am demand 4am-8am demand 8am-noon demand noon-4pm demand 4pm-8pm demand 8pm-Midnight demand Shadow Allowable Allowable Price Increase Decrease 1 5 3 0 2 12 1 1E+30 2 0 3 1E+30 1 1E+30 3 0 3 5 d) (2 points) If the Midnight-4am demand increases to 10, what is change in the total number of nurses? Do we have to resolve this problem in Excel Solver again? e) (2 points) If the 8pm-Midnight demand reduces to 6, what is the change in the total number of nurses? Do we have to resolve this problem in Excel Solver again? f) (2 points) Can you ever have infinitely many solutions when solving a linear program? If no, please explain the reasons. If yes, please give an example with infinitely many solutions. 7 COPYRIGHTED MATERIAL, DO NOT CIRCULATE CARLSON SCHOOL OF MANAGEMENT, UNIVERSITY OF MINNESOTA Problem 3: Inventory Management (17 points) Formulas you may need for this problem: 2?? ? ?? = √ ; ?(? ∗ ) = √2???; set-up cost ?? ? ; holding cost ?? ; 2 safety stock = ??√L; ROP = ? ? + ?? A local appliance store in Los Angeles has an annual demand of 1,200 high-end refrigerators (on average 3.288 per day). Regardless of the number of units it orders each time, it pays the supplier $1,000 for flat-rate shipping and an additional $2,000 for each refrigerator. For example, if it orders 2 units then it pays $1,000 + $2,000*2 = $5,000. The holding cost of refrigerators come from two sources: (i) annual interest rate of 5% for the purchase cost, and (ii) annual storage cost of $1,200 for each refrigerator. Currently, this store orders once a month. a) (2 point) What is the current annual setup cost? b) (2 point) What is the current annual holding cost? c) (2 points) If the current annual setup cost from a) and annual holding cost b) were the same, can we claim for 100% that the total inventory related cost in e) has already achieved a minimum? Please explain your answer whether your answer is yes or no. [Hint: annual set ?? ?? up cost formula is ? and the annual holding cost formula is 2 .] 8 COPYRIGHTED MATERIAL, DO NOT CIRCULATE CARLSON SCHOOL OF MANAGEMENT, UNIVERSITY OF MINNESOTA Now let’s think about an optimal way of ordering which minimizes the inventory related cost. d) (2 points) What is the Economic Order Quantity? (Round to the nearest integer) e) (2 points) What’s the annual optimal inventory related cost? (Round to the nearest integer) f) (1 point) Under what scenario, can EOQ and C(Q*) have the same value? Assume D, S > 0. Next, suppose the daily demand of refrigerators follows a normal distribution with mean 3.288 and std dev is 0.5. The lead time is 1 week, and the management wants to ensure a 95% service level (the corresponding z-value is 1.64). g) (2 points) What is safety stock (SS)? (Round to the nearest integer) h) (2 points) What is the ROP? (Round to the nearest integer) i) (2 points) What is the average inventory level? (Round to the nearest integer) 9 COPYRIGHTED MATERIAL, DO NOT CIRCULATE CARLSON SCHOOL OF MANAGEMENT, UNIVERSITY OF MINNESOTA Problem 4: Inventory Management (16 points) Lebanon Hills Mountain has a trail near Minneapolis. Many hikers attempt the trail, but quit before they reach the top. Park services have kept track of how many hikers historically made it to the top. This probability distribution is shown below: Number of Hikers 47 48 49 50 51 52 53 54 55 or more Fraction of Days 0.05 0.05 0.05 0.05 0.1 0.1 0.2 0.2 0.2 For clarity, the second row is the fraction of days in the last year where that many hikers made it to the top. For example, 52 people made it to the top during 10% of days. John wants to start a small business selling ice-cold, fruit juice to the hikers. He realizes that he can sell drinks at the very start of the hike to hikers for $1. If, however, he carries the drinks to end of the hike, himself, he can sell them at the end of the hike to very tired and sweaty hikers for $2. (Hikers at the end of the hike definitely want a fruit juice and are willing to pay a premium.) John can fit 100 drinks (with ice) on his motorcycle to bring to the trail. His backpack can only fit 52 drinks in it (with ice), and he is strong enough to carry it to the top while completely full if he wants. However, by the end of the day all the ice melts, and the fruit juice gets warm and spoils, so anything he doesn’t sell he has to throw away. He is trying to decide how many drinks to sell at the bottom of the hike, and how many to try and sell at the top of the hike. a) (4 points) From a revenue maximizing perspective, how many drinks should John carry to the top of the hike? [Hint: largest feasible s such that P(D < s)
