COMM 204 Midterm Review: Key Concepts & Practice Questions

Page | 1 ` P R E P A R E D B Y 2021 Midterm Review Session COMM 204 Matt Chin

Page | 2 Topic .............................................................. Page Operations Frontier ............................................ 3 Process Analysis ................................................ 4 Utilization ............................................................ 8 Inventory Build-Up ............................................. 9 Little’s Law ........................................................ 12 Variability in Processes ................................... 15 Extra Questions ................................................ 18 TABLE OF CONTENTS

Page | 3 The Operations Frontier The operations frontier determines if the organization is operating at a time and cost- efficient balance. If they are on the curve, they are at the edge of what they can accomplish given their maximum levels of efficiency. If they are below the curve, they are operating inefficiently. If they are operating outside of the curve, they have innovated, and the curve needs to be moved outwards to reflect their innovation. Time Flexibility Cost Effectiveness Inefficient Efficient

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Page | 4 Process Analysis Key Terms: Flow Units: Items that flow through the process (i.e. a phone manufacturer’s unit flow item is a phone) Activities: Transformation steps in the process. Represented as rectangles. Resources: What is needed to perform activities (workers, raw materials, etc.) Buffers: Storage for flow units Represented as triangles. Decision Points : Fork in the road. Represented as Diamonds. Theoretical Flow Time: Amount of time that a flow unit takes to move from start to finish in the process. Unit Load: Amount of time that a resource needs to process a flow unit. Capacity Rate: Maximum possible output rate (ex. 3 phones per minute) Bottleneck: The activity that determines the capacity rate of the entire process. (There may be more than one bottleneck per process. Activity Buffers Decision Point

Page | 5 us.cmp.ca facebook.com/ubccmp

Page | 6 Practice Questions: Q1: In the example above, what is the… a. Theoretical Flow Time? 50 seconds b. Unit load of worker 3? 15 seconds c. Capacity rate of worker 3? 60/15 = 4 bbts per minute d. Capacity rate of worker 2? 60/20 = 3 bbts per minute e. Bottleneck? Worker 2 is the bottleneck because they have the highest unit load. Otherwise known as the lowest capacity rate . f. Capacity Rate of the process? 3 bbts per minute g. For this question only: The owner of the bubble tea shop decides to buy a new, faster blender that takes 10 seconds to blend drinks. Who is the new bottleneck? Worker 1 and worker 3 h. For this question only: The owner of the bubble tea shop decides to do takeout only, so worker 1’s unit load has now been reduced to 10 seconds. What is the capacity rate of the process? 3 bubble teas per minute

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Page | 7 Practice Questions Continued: Q2: A bubble tea shop offers two flavors: milk tea and strawberry tea. Both teas require worker 1 to take the order, which takes 15 seconds, and worker 3 to put on the lid and deliver, which takes 15 seconds. The strawberry tea also requires worker 2 to blend for 20 seconds, while the milk tea requires worker 2 to mix for 10 seconds. a. Draw a flow diagram that represents this process. b. If the menu got rid of the strawberry tea and offered milk tea, what would be the bottleneck and the capacity rate? Bottleneck = worker 1 and worker 3 Capacity rate = 60/15 = 4 bbts per minute Take order (15 seconds) Milk Tea Strawberry Tea Mix (10 seconds) Blend (20 seconds) Order Complete Add lid and deliver (15 seconds)

Page | 8 c. If there are 100 strawberry orders/hour and 60 milk tea orders per hour, what is the bottleneck? More Key Terms: Throughput Rate: Actual output rate (minimum of capacity rate and input rate) Input Rate: Rate at which flow units arrive at the process and can begin being processed. Flow Time: Average time for a unit to move through the system. Cycle time: Average time between completion of units.

Page | 9 Utilization Utilization = Throughput Rate / Capacity Rate Implied Utilization = Input Rate / Capacity Rate Q3: Complete this table assuming the process has a throughput rate of 2 teas per minute. Resource Capacity Rate Utilization Worker 1 4 Teas per Minute 2/4 = 50% Worker 2 3 Teas per Minute 2/3 = 67% Worker 3 4 Teas per Minute 2/4 = 50%

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Page | 10 Inventory Build-Up Discrete Model Average Inventory = (Sum of Inventory) / Total Slots Q4. Calculate the average inventory using the above chart. (400 + 500 + 200 + 100) / 4 = 300 0 100 200 300 400 500 600 Month 1 Month 2 Month 3 Month 4 Discrete Inventory Model

Page | 11 Q5. Complete the output and inventory chart. Period Input from last period Production Output Inventory 0 0 0 0 400 1 900 1000 1000 400+900- 1000 = 300 2 900 900 900 300+900- 900 = 300 3 700 600 600 300 + 700+ -600 = 400 4 0 600 400 0 Q5B. What is the average inventory? (300 + 300 + 400 + 0) / 4 = 250

Page | 12 Continuous Model Average Inventory=Area under the curve/total time Ri(t): input rate at time (t) Ro(t): output rate at time (t) ∆ R(t): instantaneous inventory accumulated at time (t) (slope) ∆ R(t)= Ri(t)- Ro(t) I(t): Number of units of inventory in process at time (t) For a straight line: I(t2)=I(t1)+ ∆R* (t2-t1) Q6. Calculate average inventory Q6B. What is the instantaneous rate of inventory accumulated at 2:00? 0 2 4 6 8 10 12 14 12:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00

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Page | 13 Little’s Law Average Inventory (I): The average number of units or customers in the system. Average Throughput Rate (R): The average actual output rate (the lower of capacity rate and input rate) Average Flow Time (T): The average time for a unit to move through the system. Little’s Law is a relationship that describes these three variables Inventory = Throughput Rate * Flow Time Q7. Imagine you are standing outside of a Walmart for 5 hours. You notice that 50 people exit the store while you were standing there. You also notice that people spend, on average, 30 minutes inside Walmart. How many people would you expect to be inside Walmart at any given moment?

Page | 14 Day in Inventory: Average number of days that a unit of inventory is held. Days in Inventory = Cost of Inventory * 365 / COGS Inventory Turnover: How many times the inventory has been replaced a year. Inventory Turnover = COGS / Average Inventory = Cost of Output / Cost of Input Q8. Given COGS = $20,000, Inventory Turnover = 8 times, solve for average inventory Q9. Given COGS = $20,000, average inventory = $5000, what is days of inventory?

Page | 15 Variability In Process

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Page | 16 Types of Queues

Page | 17 Q10: At Starbucks, Mary is the only server and can serve 45 customers per hour. On average, a new customer enters the store every 2 minutes. There are, on average, three customers in the store. a) What is the utilization? How long do customers have to wait in line? c=1 1/λ=2 mins μ =45/hr=0.75/min I=3 p=? Tq=? p= λ/cμ Tq=T-Ts =0.5/1(0.75) =(I/λ) - (1/μ) =67% =(3/2)-(1/0.75) =0.17 minutes b) A second employee, Tim, joins Mary in the afternoon. Tim can serve customers just as quickly as Mary, and the store stays just as busy while they are together (inter-arrival time does not change). Service times and interarrival times are both exponentially distributed. Using PK formula, determine the average number of people waiting in line. c=2 1/λ=2 mins μ =45/hr=0.75/min I=3 Iq=? M/M/2

Page | 18 Extra Practice Questions 1. A manager at Starbucks wants to decrease queue time. Give 3 examples of ways to do this. Hire another worker, decrease variability in service/interarrival time, innovate, etc. 2. In an M/M/2 queue that has a utilization of 0.8, what is the Iq?

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Page | 19 3. On Sundays, Julia is the only nail tech at Nailz Express Salon. From experience, she knows that customers entering the salon arrive in a poisson distribution, and her service time follows an exponential distribution. Customers typically come in at a rate of 3 per hour, and it takes Julia 12 minutes to do someone’s nails . a) What is the average utilization of Julia’s time? b) On average, how long must a customer wait to be served? c) How long are customers spending in the salon on average? T = ? T = Ts + Tq = 0.2 + 0.225 = 0.425 hours

Page | 20 4. The flow diagram below represents the production line for a meal at a restaurant. Each step has 1 worker, and order for both types meals come in at the same rate. a) What is the capacity rate of the process? Since the bottleneck is the server, the capacity rate is 60/30 = 2 meals per minute b) If the head chef can hire one more worker, what step would this worker be assigned to, and what would the new bottleneck and capacity rate of the process be? The new worker should be assigned to the bottleneck step, so they would be a server. The new bottlenecks would now be the griller (60/(30*0.5) = 4/min), the plater (60/15=4/min), and the servers (60/30/2=4/min), making the new capacity rate of the process 4 meals per minute.

Page | 21 5. A call center receives 100 calls per hour from noon until 5pm. The center can process 90 calls per hour from noon until 3pm, and 60 calls per hour from then onwards. Draw an inventory chart with inventory on the y-axis and the inventory at each hour on the x-axis. How many calls will be on hold at each hour: 1pm: 10 calls 2pm: 20 calls 3pm: 30 calls 4pm: 70 calls 5pm: 110 calls 6pm: 50 calls 7pm: 0 calls 8pm: 0 calls 0 20 40 60 80 100 120 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00

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CMP COMM 204 Review Session Solutions

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