Problem 1) (12 points) To support National Heart Week, the Heart Association plans to install a free blood pressure testing booth in El Con Mall for the week. Previous experience indicates that, on average, 10 persons per hour request a test. Assume arrivals are Poisson distributed from an infinite population. Blood pressure measurements can be made at a constant time of five minutes each. Assume the queue length can be infinite with FCFS discipline. a) What is the average number of people in line? (2.5 points) b) What is the average number of people in the system? (2.5 points) c) What is the average amount of time that a person can expect to spend in line? (2.5 points) d) On average, how much time will a person spend in the system? (2.5 points) e) On weekends, the arrival rate can be expected to increase to over 12 per hour. What effect will this have on the average number of people waiting in line? (2 points) 70 280 Problem 3) (12 points) U.S. Airfilter has hired you as a supply chain consultant. The company makes air filters for residential heating and air-conditioning systems. These filters are made in a single plant located in Louisville, Kentucky, in the United States. They are distributed to retailers through wholesale centers in 100 locations in the United States, Canada, and Europe. You have collected the following data relating to the value of inventory in the U.S. Airfilter supply chain: QUARTER 1 QUARTER 2 QUARTER 3 QUARTER 4 (JANUARY (APRIL (JULY THROUGH (OCTOBER THROUGH THROUGH MARCH) THROUGH JUNE) SEPTEMBER) DECER) Sales (total quarter): United States 300 350 405 375 Canada 75 60 75 Europe 30 33 20 15 Cost of goods 295 340 350 sold (total quarten Raw materials at 50 55 60 the Louisville plant (end-of-quarter) Work-in-process 100 105 120 150 and finished goods at the Louisville plant (end-of-quarter) Distribution center inventory (end-of-quarter): United States 25 27 23 30 Canada 10 11 16 5 5 Europe All amounts in millions of U.S. dollars. 40 15 5 4 a) What is the average inventory turnover (quarterly and yearly) for the firm? (10 points) b) If you were given the assignment to increase inventory turnover, what would you focus on? Why? (2 points) Problem 1) (12 points) To support National Heart Week, the Heart Association plans to install a free blood pressure testing booth in El Con Mall for the week. Previous experience indicates that, on average, 10 persons per hour request a test. Assume arrivals are Poisson distributed from an infinite population. Blood pressure measurements can be made at a constant time of five minutes each. Assume the queue length can be infinite with FCFS discipline. a) What is the average number of people in line? (2.5 points) b) What is the average number of people in the system? (2.5 points) c) What is the average amount of time that a person can expect to spend in line? (2.5 points) d) On average, how much time will a person spend in the system? (2.5 points) e) On weekends, the arrival rate can be expected to increase to over 12 per hour. What effect will this have on the average number of people waiting in line? (2 points) 70 280 Problem 3) (12 points) U.S. Airfilter has hired you as a supply chain consultant. The company makes air filters for residential heating and air-conditioning systems. These filters are made in a single plant located in Louisville, Kentucky, in the United States. They are distributed to retailers through wholesale centers in 100 locations in the United States, Canada, and Europe. You have collected the following data relating to the value of inventory in the U.S. Airfilter supply chain: QUARTER 1 QUARTER 2 QUARTER 3 QUARTER 4 (JANUARY (APRIL (JULY THROUGH (OCTOBER THROUGH THROUGH MARCH) THROUGH JUNE) SEPTEMBER) DECER) Sales (total quarter): United States 300 350 405 375 Canada 75 60 75 Europe 30 33 20 15 Cost of goods 295 340 350 sold (total quarten Raw materials at 50 55 60 the Louisville plant (end-of-quarter) Work-in-process 100 105 120 150 and finished goods at the Louisville plant (end-of-quarter) Distribution center inventory (end-of-quarter): United States 25 27 23 30 Canada 10 11 16 5 5 Europe All amounts in millions of U.S. dollars. 40 15 5 4 a) What is the average inventory turnover (quarterly and yearly) for the firm? (10 points) b) If you were given the assignment to increase inventory turnover, what would you focus on? Why? (2 points)
