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Problem 1 (a)

Problem 1 (a). 1. Time Travelers Insurance Company (TTIS) processes 12,000 claims per year. The average processing time is 3 weeks. Assume 50 weeks per year. a) What is the average number of claims that are in process? R per week = 12,000/50 = 240 claims/week RT = I

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Problem 1 (a)

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  1. Problem 1 (a) 1. Time Travelers Insurance Company (TTIS) processes 12,000 claims per year. The average processing time is 3 weeks. Assume 50 weeks per year. • a) What is the average number of claims that are in process? R per week = 12,000/50 = 240 claims/week RT = I I = 240(3) = 720 claims waiting

  2. Problem 1(b) 50% of all the claims that TTIS receives are car insurance claims, 10% motorcycle, 10% boat, and the remaining are house insurance claims. On average, there are, 300 car, 114 motorcycle, and 90 boat claims in process. b) How long, on average, does it take to process a car insurance claim? I = 300 car R = 0.5(240) =120 claims/wk TR = I T(120) = 300 300/120= 2.5 weeks car 0.5 0.1 720 motorcycle 0.1 boat 0.3 house

  3. Problem 1(c) c) How long, on average, does it take to process a house insurance claim? Average # of claims in process = 720 720–300 car–114 motorcycle–90 boat = 216 Average # of claims for house: I = 216 House claims are 1- 0.5-0.1-0.1 = 0.3 of all claims R = 0.3(240) = 72 TR = I T = I/R T = 216/72= 3 weeks

  4. Problem 2 • 2. Consider a roadside stand that sells fresh oranges, and fresh orange juice. Every hour, 40 customers arrive to the stand, and 60% purchase orange juice, while the remaining purchase oranges. Customers first purchase their items. Customers that purchased oranges leave immediately after purchasing their oranges. Any customer that ordered orange juice must wait while the juice is squeezed. There are 3 customers on average waiting to purchase either oranges or orange juice, and 1 customer on average waiting for orange juice to be squeezed. 40 0.6(40) = 24 3 1

  5. Problem 2 • How long on average must customers that purchase fresh orange juice wait? • In the ordering process • RT =I  40T = 3  • T = 3/40 hours  T = 60(3/40) = 4.5 minutes • In the juice squeezing process • RT =I  24T = 1  • T = 1/24 hours  T = 60(1/24) = 2.5 minutes • Average waiting time = T = 4.5 + 2.5 = 7 minutes 40 24 3 1

  6. Problem 3(a) • 3. A recent CSUN graduate has opened up a cold beverage stand “Stop n Slurp” in Venice Beach. She takes life easy and does a lot of surfing. It sounds crazy, but she only opens her store for 4 hours a day. She observes that on average there are 120 customers visiting the stand every day. She also observes that on average a customer stays about 6 minutes at the stand. • a) How many customers on average are waiting at “Stop n Slurp”? • R = 120 in 4 hours  R = 120/4 = 30 per hour • R = 30/60 = 0.5 per minute • T = 6 minutes • RT = I  I = 0.5(6) = 3 customers are waiting

  7. Problem 3(b) • She is thinking about running a marketing campaign to boost the number of customers per day. She expects that the number of customers will increase to 240 per day after the campaign. She wants to keep the line short at the stand and hopes to have only 2 people waiting on the average. Thus, she decides to hire an assistant. • b) What is the average time a customer will wait in the system after all these changes? • R = 240/(4hrs*60min) = 1 person/minute • I = 2 • Average time a customer will wait: • T = I/R = 2/1 = 2 minutes

  8. Problem 3(c) • The business got a lot better after the marketing campaign and she ended up having about 360 customers visiting the stand every day. So, she decided to change the processes. She is now taking the orders and her assistant is filling the orders. They observe that there are about 2 people at the ordering station of the stand and 1 person at the filling station. • c) How long does a customer stay at the stand? • R = 360/4 hours = 1.5 people/minute • I = 2 (ordering station) and 1 (filling station) = 3 • RT = I  1.5T = 3  T = 2 minutes 360/4hrs 2 1

  9. Problem 3 • A recent UCLA graduate has opened up a competing cold beverage stand “Slurps-on-the-go”. The UCLA grad is not as efficient as the CSUN grad, so customers must stay an average of 15 minutes at “Slurps-on-the-go”, as opposed to 6 minutes at the “Stop n Slurp”. Suppose there is an average of 3 customers at “Slurps-on-the-go”. The number of customers requiring slurps each day remains at 120, as it was before the marketing campaign. But now the 120 is divided between the “Stop n Slurp” and “Slurps-on-the-go”.

  10. Problem 3(d) • d) By how much has business at the “Stop n Slurp” decreased? • First find how many customers “Stop n Slurp” is losing to “Slurps-on-the-go” • At “Slurps-on-the-go” we have I = 3 people and T = 15 minutes • TR = I  15R = 3  R= 1/5 per minute • R = 60(1/5) = 12 customers per hour or = 48 customers/day • Business at “Stop n Slurp” has decreased by 48 customers/day • The new (lower) arrival rate to the “Stop n Slurp”? • 120-48 = 72 customers/day

  11. Process Flow Example • e) What is now the average number of customers waiting at the “Stop n Slurp”? • R = 72/day = 72/(60min*4hrs) = 0.3/minute • T = 6 minutes • RT = I  I = 0.3(6) = 1.8 customers

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