Problem Set 1 (Due Monday, November 6, 2023) Note: The full mark of this problem set is 60 . You must show your work to fully justify your answers. 1. True or False (2 points) a. (1 point) Efficiency measures how well a process performs to meet customer requirements or to create value. (Justify your answer) b. (1 point) Capacity Rate =1/ Flow Time. (Justify your answer.) 2. Process Flow Analysis (12 points) A certain product X consists of two major parts A and 8 . For the final assembly part A goes through the following two stations: painting color ( 3 mins), drying the new paint (10 mins), In parallel to part A, part B goes through the two stations: painting color (5 mins), drying the new paint ( 8 mins). Then the finished two parts will be connected ( 5 mins). Before the final packing station ( 3 mins), the product X is re-examined (Smins). Assume this is a fully automated process. a. (2 points) Draw a simple linear flow chart. b. ( 2 points) What is the theoretical flow time to finish one piece of X (ignoring time spent waiting in buffers between machines)? c. (2 points) Which station is the bottleneck? Justify your answer. d. (2 points) Assuming the production has been started up in the morning and is running smoothly now. What is the time between two finished pieces of X? Show your calculations. e. (4 points) Draw a Gantt chart for the production of the first three pieces of X in the morning. Use different colors/patterns or numbers (1,2,3) to distinguish the bars for the three different pieces of X. 3. Product-Process Matrix (3 points) Firms often fail to match their product with the appropriate process; in other words, they are not on the diagonal of the product-process matrix. What are the drawbacks of being above or below the diagonal? You may limit your answer to one short paragraph. 1 a. (1 point) If the arrival rate for loading trucks is 9 trucis per hour, what is the mean time between artivals (in minutes)? b. (7 points) Benry the Barber owns a one-chair shop. As Barber College, they told Benny that his customers would exhibit an exponential acrival distritution and that he would provide an exponential vervice distritution. His market survey data indicate that customers arrive at a rate of 2 per hour. It will take Benny an average of 20 minutes to give a haircut. Based on these figures, find the following (Show vour calculation steps): i. Identify arrival rate, service rate, Ca and Cs. ii. The werage number of customers waiting: ii. The average time a customer waits; h. The average namber of customers in the shop; v. The werage time a customer spends in the shop; vi. The average utilization of Benny's time (in $(6); vi. Which notation do we use to describe this queuing model? c. (4 points) Benny the Barber is considering the addition of a second chair. Customers would be selected for a haircut on of first-come-first-serve basis from those waiting. Benny has assumed that both barbers would take an average of 20 minutes to give a haircut, and that business would remain unchanged with customers arriving at a rate of 2 per hour. Find the following information to help Benny decide if a second chair should be added (Show vour calculation steps); i. The average number of customers waiting: i. The average time a customer waits; ii. The average time a customer spends in the shop; iv. Which notation do we use to describe this queuing model? 3 7. Project Management (13 points) A company must perform a maintenance project consisting of seven activities. The activities, their predecessors, and their respective time estimates are shown belowr: a. 3 points) What is the totat time required to complete the project? Now we are adding cost information into the above table (time in darys): 1. The averate nimber of custement waitine: ii. The averape time a cicitemed mala. ai. The averase brme a cuntsmer spends in the ahoe. iv. Which notation do we une to deacribe thin qurures model? 3 7. Froject Managerent [13 points] A company muat perform a maintenance proiect consisting of ueven activeties. The Wow we are adsine coot information inbo the above table Dime in days! b. It poinct what is the totak normal cout? minimum cost, what in the total cost of the pronct? 5 how rour calculubien and reasonine seps) minimum coit, what is the total coct of the profect? What is the onder in 4. Product Mix (6 points) Consider a batel store selling three types of bagel that are produced according to the process flow diagram outlined below. We assume the demand is 150 bagels a dow, of which there are 30 griled vecse, 80 vegsie only, and 40 cream cheese. Assume that the workday is 8 hours long and each activity is staffed with one worker. Moreover, we assume the following activity times: - Cut 3min/ bagel - Grilled Stuff 10 min/pagel - Veggies 5 min/oagel - Cream Cheese 4 min./bagel - Wrap 2 min.bagel Activity times are independent of which bagel type is processed at a resource (for example, cutting a bagel takes the same time for a cream cheese bapel as for a vegele bagell. a. (4 points) Where in the process is the bottleneck to satiofy the daily demand? Explain your andwer. (Hint: vou may want to consider the daily demand as a batch and check the flow time of each activity) b. (2 points) Will the batel store be able to satisfy the daily demand? Please explain why or why not. 5. Imventory Build-up and Little's Law (12 points) a. (9 peints) Consider a firm that operates a cannery. Ale fach brought in by a fleet of fishirg boats are processed at the cannery. The firm alse has a freezer of unlimited size that stores unprocessed fish. There are three seasons. The fleet veids 2,400 tons/month during the first third of the vear, 3,600 tons/month during the middle third and only 600 tons/month durine the final third. The cannerr's processing capacity equals 2,000 tons/month. i. (3 points) Draw an imventory build-up dlagram for one vear. ii. (2 points) What is the average monthly imventory? iii. (2 points) What is the average system throughput rate? iv. (2 points) Determine the average waiting time for fish in the freeser before beirs processed. 2 b. (3 points) Wal-Mart imports 3,000 pairs of shees from an overseas factery every month. Each order from Wal-Mart poes through several stages before it gets to the stores: How many pairs of shoes are tied up as inventory at the warehouse and the emire wupply chain, respectively? Show your calculation steps. Problem Set 1 (Due Monday, November 6, 2023) Note: The full mark of this problem set is 60 . You must show your work to fully justify your answers. 1. True or False (2 points) a. (1 point) Efficiency measures how well a process performs to meet customer requirements or to create value. (Justify your answer) b. (1 point) Capacity Rate =1/ Flow Time. (Justify your answer.) 2. Process Flow Analysis (12 points) A certain product X consists of two major parts A and 8 . For the final assembly part A goes through the following two stations: painting color ( 3 mins), drying the new paint (10 mins), In parallel to part A, part B goes through the two stations: painting color (5 mins), drying the new paint ( 8 mins). Then the finished two parts will be connected ( 5 mins). Before the final packing station ( 3 mins), the product X is re-examined (Smins). Assume this is a fully automated process. a. (2 points) Draw a simple linear flow chart. b. ( 2 points) What is the theoretical flow time to finish one piece of X (ignoring time spent waiting in buffers between machines)? c. (2 points) Which station is the bottleneck? Justify your answer. d. (2 points) Assuming the production has been started up in the morning and is running smoothly now. What is the time between two finished pieces of X? Show your calculations. e. (4 points) Draw a Gantt chart for the production of the first three pieces of X in the morning. Use different colors/patterns or numbers (1,2,3) to distinguish the bars for the three different pieces of X. 3. Product-Process Matrix (3 points) Firms often fail to match their product with the appropriate process; in other words, they are not on the diagonal of the product-process matrix. What are the drawbacks of being above or below the diagonal? You may limit your answer to one short paragraph. 1 a. (1 point) If the arrival rate for loading trucks is 9 trucis per hour, what is the mean time between artivals (in minutes)? b. (7 points) Benry the Barber owns a one-chair shop. As Barber College, they told Benny that his customers would exhibit an exponential acrival distritution and that he would provide an exponential vervice distritution. His market survey data indicate that customers arrive at a rate of 2 per hour. It will take Benny an average of 20 minutes to give a haircut. Based on these figures, find the following (Show vour calculation steps): i. Identify arrival rate, service rate, Ca and Cs. ii. The werage number of customers waiting: ii. The average time a customer waits; h. The average namber of customers in the shop; v. The werage time a customer spends in the shop; vi. The average utilization of Benny's time (in $(6); vi. Which notation do we use to describe this queuing model? c. (4 points) Benny the Barber is considering the addition of a second chair. Customers would be selected for a haircut on of first-come-first-serve basis from those waiting. Benny has assumed that both barbers would take an average of 20 minutes to give a haircut, and that business would remain unchanged with customers arriving at a rate of 2 per hour. Find the following information to help Benny decide if a second chair should be added (Show vour calculation steps); i. The average number of customers waiting: i. The average time a customer waits; ii. The average time a customer spends in the shop; iv. Which notation do we use to describe this queuing model? 3 7. Project Management (13 points) A company must perform a maintenance project consisting of seven activities. The activities, their predecessors, and their respective time estimates are shown belowr: a. 3 points) What is the totat time required to complete the project? Now we are adding cost information into the above table (time in darys): 1. The averate nimber of custement waitine: ii. The averape time a cicitemed mala. ai. The averase brme a cuntsmer spends in the ahoe. iv. Which notation do we une to deacribe thin qurures model? 3 7. Froject Managerent [13 points] A company muat perform a maintenance proiect consisting of ueven activeties. The Wow we are adsine coot information inbo the above table Dime in days! b. It poinct what is the totak normal cout? minimum cost, what in the total cost of the pronct? 5 how rour calculubien and reasonine seps) minimum coit, what is the total coct of the profect? What is the onder in 4. Product Mix (6 points) Consider a batel store selling three types of bagel that are produced according to the process flow diagram outlined below. We assume the demand is 150 bagels a dow, of which there are 30 griled vecse, 80 vegsie only, and 40 cream cheese. Assume that the workday is 8 hours long and each activity is staffed with one worker. Moreover, we assume the following activity times: - Cut 3min/ bagel - Grilled Stuff 10 min/pagel - Veggies 5 min/oagel - Cream Cheese 4 min./bagel - Wrap 2 min.bagel Activity times are independent of which bagel type is processed at a resource (for example, cutting a bagel takes the same time for a cream cheese bapel as for a vegele bagell. a. (4 points) Where in the process is the bottleneck to satiofy the daily demand? Explain your andwer. (Hint: vou may want to consider the daily demand as a batch and check the flow time of each activity) b. (2 points) Will the batel store be able to satisfy the daily demand? Please explain why or why not. 5. Imventory Build-up and Little's Law (12 points) a. (9 peints) Consider a firm that operates a cannery. Ale fach brought in by a fleet of fishirg boats are processed at the cannery. The firm alse has a freezer of unlimited size that stores unprocessed fish. There are three seasons. The fleet veids 2,400 tons/month during the first third of the vear, 3,600 tons/month during the middle third and only 600 tons/month durine the final third. The cannerr's processing capacity equals 2,000 tons/month. i. (3 points) Draw an imventory build-up dlagram for one vear. ii. (2 points) What is the average monthly imventory? iii. (2 points) What is the average system throughput rate? iv. (2 points) Determine the average waiting time for fish in the freeser before beirs processed. 2 b. (3 points) Wal-Mart imports 3,000 pairs of shees from an overseas factery every month. Each order from Wal-Mart poes through several stages before it gets to the stores: How many pairs of shoes are tied up as inventory at the warehouse and the emire wupply chain, respectively? Show your calculation steps