Midterm Exam Guide: Operational Excellence FE 208

Midterm Exam Operational Excellence (FE 208) Fall 2023 Instructions: 1. Your midterm exam is a timed Canvas Quiz, which has separate upload areas for: a. the main exam document (this document), and b. any additional materials you wish to submit (e.g., “rough work”) 2. Please submit the main exam document as a PDF file. You may either: a. Use Microsoft Word to type your answers onto the main exam document directly, then choose “Save As” to save your completed work as a PDF, or b. Print out the main exam document, write on it using pen/pencil, take photos of your handwritten answers, and then combine the photos into a PDF (with specific instructions here ). 3. (Important) Please make sure to write your name and your student ID in the designated boxes at the top of this page. If you are planning to print the exam, we suggest you type your name and ID before printing. 4. (Required) Please write your answers in the boxes provided below each question. For questions requiring a numerical answer, please make sure your final answer is prominently displayed (e.g., you could write it a bit bigger, or circle it). There is sufficient space in each box for you to include your rough calculations there as well. However, if you need more space, or have done your rough work elsewhere (e.g., in Excel or on another sheet of paper), please indicate where we can find your rough work (e.g., in addition to writing the final numerical answer in the box, also write something like “See Excel – Q3a tab” or “See scrap paper page 2”). Note that if you use Excel, then please document your work by appropriately labelling the cells of your intermediate steps and adding comments so that we can easily follow what you have done. Good luck!!!

Part 1: Ambulance Diversion (10 points) Irvine Regional Hospital (IRH) has 8 beds in its Intensive Care Unit (ICU). Whenever all beds are full, the hospital goes on "diversion status", which means any ambulances picking up new patients will instead take their patients to another nearby hospital. In this manner, patients never wait for beds to get service. Average demand for the ICU is 2.5 patients/day (coming from 9-1-1 calls), while the ICU as a whole can serve patients at a rate of 3.333/day. All patients in ICU beds are served in parallel (i.e., there are enough doctors and nurses that beds are the limiting resource). For modeling purposes, we assume that arrivals are Poisson and the time a patient spends in an ICU bed is exponentially distributed. Question 1.a: How many servers are there in this queueing system? 8 servers Question 1.b: What is the expected amount of time between successive ambulance arrivals bringing patients to the ICU (also known as the inter-arrival time)? Please express your answer in hours. 9.6 hours Question 1.c: Assuming a bed is available when a trauma patient needs assistance, the patient is admitted to the ICU. What is the expected amount of time between a patient's admission to the ICU and his/her discharge? Please express your answer in hours. 28.9 hours Question 1.d: Assuming all beds are used equally often, then what is the probability that any given bed has a patient in it? Hint: This is the same as computing the utilization of the beds.

75% Question 1.e: What is the probability that all beds in the ICU are full (this is when IRH goes on diversion status)? 9%

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Part 2: Future Shop vs. Electro City (10 points) You are an investor comparing the financial records of two similar electronics retailers, Future Shop and Electro City. These retailers are fierce competitors; they have the same product mix and target markets. Both companies have their fiscal year-ends on December 31 st . Review the following financial statement excerpts and answer the questions below. Assume all inventories are saleable, i.e., none of the inventories will need to be marked down or written off like we saw in the David Berman case. Balance Sheet Excerpts As of Dec 31, 2021 As of Dec 31, 2022 Future Shop – Inventory $40M $60M Electro City – Inventory $50M $46M Income Statement Excerpts For the Year Ended Dec 31, 2021 For the Year Ended Dec 31, 2022 Future Shop – Sales $250M $300M Future Shop – Cost of Goods Sold $210M $240M Electro City – Sales $370M $360M Electro City – Cost of Goods Sold $310M $288M Question 2.a: Use Little’s Law to determine how many months on average Future Shop held its inventory before selling it. Compute this statistic for the year 2022. 3 months

Question 2.b: (Compute the same thing for Electro City) Use Little’s Law to determine how many months on average Electro City held its inventory before selling it. Compute this statistic for the year 2022. 1.91 months Question 2.c: How many times did Future Shop and Electro City turn over their inventories in 2022? Shop – 4 Electro – 6.26

Question 2.d: Based solely on inventory turns, which company is managing their inventory more efficiently? Is higher or lower inventory turns generally better, and why? Electro City is managing their inventory more efficiently. Higher inventory turns are generally better. Reduced inventory costs, Improved cash flow, less likely to be left with obsolete inventory, which can be a costly problem.

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Part 3: Three-Step Process (12 points) Consider the following process, which has three steps (i.e., three activities) which must be completed in sequence. Below each activity are four numbers: 1. The time it takes to process 1 unit at this activity. Each unit is always processed on a single machine. 2. The number of machines. Notice that some activities have multiple machines. The machines are identical and work in parallel, each working on one unit at a time. Remember, each unit is only processed on a single machine. 3. Availability, i.e., the proportion of time that the machine(s) are processing work. 4. Yield, i.e., the percentage of units that pass a quality check and continue to be processed by the downstream activity (the units that fail the quality check are immediately scrapped and exit the process). Please answer the following questions. Question 3.a: What is the capacity of Activity 1? Please express your answer in units per hour. 10 units per hour 3 2 10 minutes/unit 2 Machines 100% Availability 80% Yield 1 15 minutes/unit 3 Machines 100% Availability 90% Yield 6 minutes/unit 1 Machine 100% Availability 100% Yield

Question 3.b: What is the capacity of Activity 2? Please express your answer in units per hour. 9.6 units per hour Question 3.c: What is the capacity of Activity 3? Please express your answer in units per hour. 10.8 units per hour Question 3.d: What is the capacity of the overall 3-activity process? Please express your answer in units per hour.

Question 3.e: What is the utilization of Activity 1? Question 3.f: What is the utilization of Activity 2? Question 3.g: What is the utilization of Activity 3?

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Question 3.h: Which activities are regular bottlenecks, and which activities are yield bottlenecks? Explain your reasoning.

Part 4: Bank Teller (12 points) Customers wait in a single queue to be served by the first bank teller that is available to serve them. There are four bank tellers, and each takes on average 60 seconds to serve a customer, with a standard deviation of service time of 40 seconds. Customers arrive on average every 20 seconds, with the standard deviation of the time between arrivals of 18 seconds. From the above, we can see that the arrival rate is 180 customers/hour and the utilization is 75%. Question 4.a: What is the coefficient of variation of inter-arrival times? 90% Question 4.b: What is the coefficient of variation of service times? 66.7%

Question 4.c: On average, how long does a customer wait in line before they can talk to a teller? Please express your answer in seconds. 30 seconds Question 4.d: How many customers are waiting in the queue, on average, at any given point in time? .5

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Question 4.e: Explain in words how Little’s Law works, and why we can employ Little’s Law to compute the average number of people waiting in a queue if we know the average time that people wait. This can be useful for queuing systems that are difficult to observe or that have a large number of customers. In a queue, the items are the customers, the average time spent in the system is the average waiting time, and the average arrival rate is the number of customers arriving per unit time. Little's Law can be used to improve the efficiency of queues by reducing the average time a customer spends in the system or by reducing the arrival rate.

Midterm Exam - Fall 2023

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