INDU311 Midterm

INDU 311 Midterm Exam COURSE Simulation of Industrial Systems NUMBER INDU 311 SECTION EXAMINATION Midterm Exam DATE October 28, 2021 TIME & PLACE Room: 11:45-13:00 # OF PAGES PROFESSOR LAB INSTRUCTOR Dr. Ali Akgunduz MATERIALS ALLOWED o NO o YES (PLEASE SPECIFY) CALCULATORS ALLOWED o NO o YES SPECIAL INSTRUCTIONS: Please make sure that you have no communication device with you. Cell Phones should not be in your possession during the exam. Answer the following questions. You may only use the ENCS approved calculators Show your work. Without the procedure, sole answers will not be considered. Name: _______________________________ I.D.: ______________________ Surname, given names X X 1

INDU 311 Midterm Exam Answer the following modeling questions using Arena modules. Your model should focus only the parts described in the question. If data/information is not provided, please do not make assumptions . Modeling and Knowledge in IE Questions Question 1A: (15 Points) Parts arrive at a manufacturing shop in boxes. Time Between Arrivals is exponentially distribute with average 30 minutes. Once the box arrives at the warehouse, it is opened. The number of items in the box varies between 10 to 20 uniformly distributed. Once the items are removed from the box, they wait for a worker to bring them to a workstation for machining. The worker visits the warehouse once every 10 minutes and removes exactly 10 items. Machining time is TRIA(10, 12, 20) minutes. Once the machining job is completed, parts are removed from the system. Question 1B: (15 Points) Parts arrive at a manufacturing shop individually. Time Between Arrivals is exponentially distributed with average 1 minutes. Arrived parts are stored in the warehouse. Before they are stored on shelves, parts are placed on a pallet. Each pallet can accommodate 10 to 20 items (uniformly distributed). A worker periodically visits the warehouse (once every 20 minutes) to remove one of the pallets and bring them to a machine shop. Machining time is TRIA(10, 12, 20) minutes. Once the machining job is completed, every 10 parts are packed in a box and removed from the system. Question 2A: (10 Points) Parts arrive to a receiving station with an average of every 5 minutes, exponentially distributed. Twenty percent of the parts are sent to Work center 1 and remaining seventy percent sent to Work center 2 by a single forklift. Forklift can travel 20 meters per minute. Distance between stations: From To Distance (mis) Receivi ng WC1 100 Receivi ng WC2 200 WC1 WC2 200 Question 2B: (10 Points) Parts arrive to factory through its two receiving docks. Twenty percent of the parts arrive at Receiving 1 and remaining seventy percent arrive at Receiving 2. Next, parts are sent 2

INDU 311 Midterm Exam Question 3A: (10 points) Patients arrive at a clinic with an average of 30 minutes, exponentially distributed. When the nurse is available, first the nurse examines them (NORM(10, 1) minutes). Next, patient and nurse wait for the doctor to arrive. Once the doctor is available, the patient is treated for approximately UNIF(10, 30) minutes. After the doctor, the patient leaves the system. Question 3B: (10 points) Parts arrive at a repair center with an average of 20 minutes, exponentially distributed. First a worker does the preliminary cleaning. (TRIA(3, 4, 10) minutes). Next, the worker waits for the supervisor to arrive. Once the supervisor is available, they complete the repairing operation UNIF(20, 120) minutes. Question 4A: (15 points) Based on the collected 200 data, an industrial engineer performed below illustrate analysis in order to test if a selected distribution is acceptable to represent the data in a simulation model. a) Based on the below given histogram, what are the potential distributions to represent collected data in a simulation model? b) Which distribution has this industrial engineer select? (Hint: Already calculated parts in the table) c) Complete the table and make a conclusion for α = 10% if the distribution that industrial engineer has selected is good choice to represent the data? 4

INDU 311 Midterm Exam 12 14 16 18 20 22 24 26 28 30 0 5 10 15 20 25 30 35 40 45 Low High Observation s Expected Chi- Square Averag e 20 10 12 5 2.86 1.61 St. Dev. 3.5 12 14 13 8.57 2.29 Mod 24 14 16 23 Min 10 16 18 24 20.00 0.80 Max 30 18 20 29 25.71 0.42 20 22 39 31.43 1.82 22 24 28 37.14 2.25 24 26 23 26 28 12 20.00 3.20 28 30 4 6.67 1.07 Total 200 200 Question 4A: (15 points) Based on the collected 200 data, an industrial engineer performed below illustrate analysis in order to test if a selected distribution is acceptable to represent the data in a simulation model. a) Based on the below given histogram, what are the potential distributions to represent collected data in a simulation model? b) Which distribution has this industrial engineer select? (Hint: Already calculated parts in the table) c) Complete the table and make a conclusion for α = 10% if the distribution that industrial engineer has selected is good choice to represent the data? Low High Observation Expecte Chi- Averag 20 5

INDU 311 Midterm Exam Question 1 : Assume that grocery store opens its doors to customers at 7 AM and closes its doors for the incoming customers at 10 PM. Cashiers (5 of them) continue offering service until all the customers leave the grocery store. One of the cashiers has a dedicated queue. Those who select the queue must be served by this cashier. 25% of the customers selects the single queue with single server cashier. Other four cashiers have a single queue. When one of the cashiers is available, customers moved to the available cashier from this single queue. Processing times at cashiers are uniformly distributed with a = 2 and b= 5 minutes with single queue-single service cashier, and triangularly distributed with a = 1, b = 8 and c = 4 minutes with multi cashier single que system. Model the problem using Arena blocks. 7

INDU 311 Midterm Exam Question 2 : Two different types of products are being manufactured through 3 workstations. All raw materials arrive to a warehouse station. Products are transported to stations using forklifts. Each type follows a different job sequence as shown in below table. All parts leave the system through an Exit station. Product 1 Warehouse Machine 1 Machine 2 Exit Station Product 2 Warehouse Machine 2 Machine 3 Exit Station Distance between all workstations are: Warehouse Machine 1 Machine 2 Machine 3 Exit Station Warehouse 0 100 120 130 160 Machine 1 0 60 100 140 Machine 2 0 60 50 Machine 3 0 100 Exit Station 0 Machining Time NORM(5, 1) mins. UNIF(10, 30) mins TRIA(10, 12, 30) mins Number of operators 3 5 6 There are two forklifts, and both can travel 20 meters per minute. At each workstation, there is a machining operation. Machining times and the number of operators at each workstation are provided in above table. Parts arrive to this manufacturing system in average every 2 minutes, following an exponential distribution. Once the company produces 1000 items, it finishes the day. Model this system using Arena blocks. 8

INDU 311 Midterm Exam Question 3: For the following parameters, generate two random numbers and one triangularly distributed random variets for triangular distribution with parameters a = 100, b= 200 and c= 130. Z 0 = 4560 c = 576 a = 12540 m = 2505647 10

INDU 311 Midterm Exam 11