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Operations management Session 3: Measures: Capacity, Time, and More

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Session 3 Operations Management2 Previous Week What are the key concepts learned in the last week?

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Session 3 Operations Management3 Class Objectives Review of the last week How do we quantitatively evaluate a process? Capacity Time Other? Littles Law A general rule that links various performance measures Examples Summary

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Session 3 Operations Management4 Analyzing Business Process InputsOutputs Our purpose is to examine a transformation process from the perspective of flows. The unit being transformed is typically referred to as a job and can represent a customer, an order, material, money, information, etc. Transformation Process

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Session 3 Operations Management5 Throughput Rate In general, the inflow rate and the outflow rate fluctuate over time. Define the average in (out) flow rates as the long-run average number of jobs that flow into (out of) the system. In a stable environment, the average inflow rate is equal to the average outflow rate The average flow rate through the system is referred to as the throughput rate assessed as the number of jobs per unit time.

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Session 3 Operations Management6 Measure: Capacity Definition: The number of units, per unit of time, that can be processed. Examples: A casher can serve 20 customers per hour The capacity of a server is 30000 hits per min A worker can assemble 2.22 hamburgers per min A stove can cook 20 hamburgers per min or 0.33333 per second (Note: Units are important!) It is a rate: Units/Time

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Session 3 Operations Management7 Process Capacity Raw Material CookAssembleDeliver Patties cook in 60 seconds; the stove holds 20 patties. Assembly of a hamburger takes 27 seconds per hamburger. 10 workers are available to assemble hamburgers. What is the capacity of the cooking stage? What is the capacity of the assembling stage? What is the capacity of the process?

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Session 3 Operations Management8 Analysis Cooking First 20Second 20Third 20 1:002:00 3:00 1020 1:271:54 Assembly Suppose an order for 60 hamburgers is placed. What will happen? 3040 2:272:54 5060 3:273:54 If order continues to come, how many more hamburgers do we produce for every minute?

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Session 3 Operations Management9 Bottleneck Analysis The stove, operating 100% of the time, can push out: 20 hamburgers / 1 minute = 20 hamburgers per minute. The workers, operating 100% of the time, can push out: 10 hamburgers / 27 seconds = 22.2 hamburgers per minute. The stove is the bottleneck resource; it pushes out the slowest amount of hamburgers per time period.

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Session 3 Operations Management10 Calculating Capacity The capacity of a process is determined by the slowest (bottleneck) resource. To calculate the bottleneck resource, calculate the amount of stuff each resource can push out per unit time. The bottleneck resource is the resource that pushes out the least amount of stuff per unit time. Would hiring an additional worker increase the revenue?

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Session 3 Operations Management11 Utilization Rate

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Session 3 Operations Management12 Utilization Rate Utilization rate is a measure of efficiency. It measures the percentage of products/services that the process is producing what it is designed (suppose) to do. An example: The capacity of a cashier in Starbucks is 96 customers per shift. The cashiers throughput rate is only 72 customers per shift. What is the capacity utilization? 72/96 = 0.75

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Session 3 Operations Management13 Utilization Rate What is the meaning of the number 0.75? The cashier is busy only 75% of the time. 25% of the time the cashier is idle and not doing any productive work. What are the managerial implications?

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Session 3 Operations Management14 Utilization Rate Can utilization rate be greater than 1?

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Session 3 Operations Management15 Measure: Time How long it takes to turn patties into burgers? Cooking First 20Second 20Third 20 1:002:00 3:00 1020 1:271:54 Assembly 3040 2:272:54 5060 3:273:54

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Session 3 Operations Management16 Throughput Time Different units may spend different amount time. What is throughput time? The average time a unit stays in the system

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Session 3 Operations Management17 Throughput Time Average time a customer spends in a bank Average time a book stays at the Amazon.coms warehouse How do we measure throughput time? Customer arrivesService beginsService ends Throughput Time WaitingProcessing Book arrivesStoredOrder arrivesPickedPackagedShipped Throughput Time

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Session 3 Operations Management18 Flow Measures: Work in Process Work in Process (WIP) Inventory: the number of units at a point of time. Example 1: The WIP in Disneyland is the number of customers waiting, eating, resting, or playing in Disneyland. Example 2: The WIP in Space Mountain is the number of customers waiting for or riding in Space Mountain.

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Session 3 Operations Management19 Flow Measures: Throughput rate What is the relationship between throughput rate throughput time and WIP? Time WIP Throughput rate is two unit per unit of time

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Session 3 Operations Management20 Throughput Time = (Average) WIP / Throughput Rate Example: Bank Teller Average WIP: 6 customers Throughput rate: 12 customers per hour Throughput time: 6/12 = 0.5 A customer spends (on average) 0.5 hours in the bank Littles Law

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Session 3 Operations Management21 Littles Law In the bank example on the previous overhead … Does this mean each customer spends 0.5 hours in the bank? How many customers arrive on average in an hour? How many customers leave on average in an hour?

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Session 3 Operations Management22 Implications of Littles Law Given average WIP and throughput rate, we can calculate throughput time Relatively easy to measure WIP and throughput rate Keeping WIP fixed, reducing throughput time results in a higher throughput rate. Throughput Rate = Average WIP / Throughput Time

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Session 3 Operations Management23 Implications of Littles Law Average number of customers in a restaurant: 50 Average number of customers arriving (and leaving) per hour: 30 The throughput time is 50/30 = 1.66 A customer spends (on average) 1hr and 40 mins. The restaurant is losing money. How can an OM person help?

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Session 3 Operations Management24 Admission Flow Marshall provides higher education to executives and receives about 1000 applications per month. The evaluation starts with a preliminary classification with basic information: Group A: Applicants with desired recommendations, working experience, etc. (50% of the applicants) Group B: Other applicants. (50% of the applicants) Applicants in group A will be further considered through an advanced review. Applicants in group B will be rejected.

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Session 3 Operations Management25 Admission Flow On average there were: 200 applications in the preliminary review stage 100 applications in the advanced review stage How long does group A spend in the application process? How long does group B spend in the application process? How long is the average process time?

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Session 3 Operations Management26 Admission Flow The admission process 1000 50% 200 100 Reject Process Accept Process

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Session 3 Operations Management27 Admission Flow Let us do a detailed analysis How long do the applicants spend in the preliminary review stage? TT = WIP/TR=200/1000 = 0.2 * 30 days = 6 days Applicants spend 6 days in the first stage Applicants from group B receive an answer in 6 days on average

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Session 3 Operations Management28 Admission Flow How long do the applicants from group A spend in the advanced review stage? TT = WIP/TR=100/(1000*50%) = 0.2 Applicants from group A spend 6 days on average in the advanced review stage. Applicants from group A receive answer in 12 days (6 + 6) on average.

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Session 3 Operations Management29 Admission Flow What is the average processing time? 6*0.5+12*0.5 = 9 days Is there an alternative way to calculate the average waiting time?

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Session 3 Operations Management30 Alternative Solution What is the average processing time?

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Session 3 Operations Management31 Admission Flow Littles Law holds for complicated systems.

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Session 3 Operations Management32 Emergency Room: Example Let us calculate the average waiting time in an emergency room. Imagine a system in which a patient can be treated in exactly 15 minutes. Two patients arrive at minute 15, and one patient arrives at minute 45. What is the average waiting time? Is there enough capacity?

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Session 3 Operations Management33 Emergency Room: Example Imagine the following sequence of event 1,2 15 3045 60 13 75 3 2 Waiting Service 2

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Session 3 Operations Management34 Emergency Room: Example Do we have enough capacity? What is the utilization rate? Why patients wait?

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Session 3 Operations Management35 Emergency Room: Example In the waiting room, Average WIP = (0 + 1 + 0 + 0) / 4 = 0.25 Average waiting time = Calculate average waiting time directly = (15 + 0 + 0)/3 = 5 minutes

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Session 3 Operations Management36 Emergency Room: Example For the total time spent (waiting + service), Average WIP = (0 + 2 + 1 + 1) / 4 = 1 Average waiting time = Calculate average time spent directly = (15 + 30 + 15)/3 = 20 minutes

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Session 3 Operations Management37 Emergency Room Randomness/Variability forces resource idleness and longer waiting time. Littles Law still holds.

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Session 3 Operations Management38 What Have We Learned Process Measures Throughput Rate Capacity Throughput Time WIP Littles Law

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Session 3 Operations Management39 Next Time Kristens Cookie Company Everybody: read the case and be prepared for class discussion Presenting teams: prepare a write-up and presentation for 10 minutes (exactly) Note that Kristens cookies case slides (and all case slides) will not be posted to Blackboard.

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