1 MSIN207P – Product, Technology and Operations Management Sample Questions OM Overview / Process Analysis and Selection / Little’s Law 1. List two ways to measure the quality of a consumer product (e.g., iPad) and two reasons for increasing product variety. Explain either with a short definition or an example. 2. Fill in the table below using only the words “low” or “high”. Product Volume Machine Setup Frequency Labor Skills Job Shop Flow Shop 3. Fill in the table below using only the words “low” or “high”. Product Variety Finished Goods Inventory Delivery Speed Make-to-Order Make-to-Stock 4. Atlas Inc. is a toy bicycle manufacturing company producing a 5 inch small version of the bike that Lance Armstrong rode to win his first Tour de France. The assembly line at Atlas Inc. consists of 7 work stations, each performing a single step. Stations and processing times are summarized below. Step 1 (30 sec): The plastic tube for the frame is cut to size Step 2 (20 sec): The tube is put together Step 3 (35 sec): The frame is glued together Step 4 (25 sec): The frame is cleaned Step 5 (30 sec): Paint is sprayed onto the frame Step 6 (45 sec): Wheels are assembled Step 7 (40 sec): All other parts are assembled to the frame Under the current process layout, workers are allocated to the stations as shown below. Worker 1: Steps 1 and 2 Worker 2: Steps 3 and 4 2 Worker 3: Step 5 Worker 4: Step 6 Worker 5: Step 7 a. What is the capacity of this assembly line, in finished units/hour b. What is the utilization of Worker 4, ignoring the production of the first and last unit c. How long does it take to finish production of 100 units, starting with an empty process d. What is the average labor utilization of the workers, ignoring the production of the first and last unit e. Assume the workers are paid $15 per hour. What is the cost of direct labor per unit 5. On a typical weekday in January, 4,200 customers visit the London IKEA. It is estimated that, on average, there are 350 customers in the store. Assuming that the store is open 14 hours a day, how much time does the average customer spend in the store 6. In 2015, University College London Hospital admitted 14,965 patients. In 2016, a 20% increase in admissions is expected. Currently the hospital has 390 beds. Assume the hospital operates 365 days a year (and, please assume one patient per bed!). a) If the average patient stays in the hospital 8 days, how many beds were empty, on average, in 2015 b) On average, how many beds do you expect to be empty in 2016 7. The total number and gender mix of employees in a certain company remains constant. Due to turnover, on average the company hires 150 men and 200 women each year. It is estimated that on average a woman stays 50% longer than a man. What proportion of the employees are women 8. The Internal Revenue Service Department of Tax Regulations writes regulations in accord with laws passed by Congress. On average, the department completes 300 projects per year. The Wall Street Journal reports that, as of October 11, 1997, the number of projects currently “on the Department’s plate” is 588. Nevertheless, the department head claims that average time to complete a project is less than six months. Do you have any reason to disagree Why or why not 9. A bank finds that the average number of people waiting in line during lunch hour is 10. On average, during this period 2 people per minute leave the bank after receiving service. On average, how long do bank customers wait in line 10. At the drive-through counter of a fast-food outlet, an average of 10 cars waits in line. The manager wants to determine if the length of the line impacts potential sales. Her study reveals that, on average, 2 cars per minute try to enter the drive-through area, but 25% of 3 these cars are dismayed by the long line and simply move on without entering the line and placing orders. Assume that no car entering the line leaves without service. On average, how long does a car spend in the drive-through line 11. Checking accounts at a local bank carry an average balance of $3,000. The bank turns over its balance six times a year. On average, how many dollars flow through the bank each month Queuing Theory – Waitline Management 1. The Bijou Theater in Hermosa Beach, California, shows vintage movies. Customers’ average inter-arrival time is 12 seconds. The ticket seller averages 9 seconds per customer. The standard deviation of inter-arrival time is 12 seconds, and the standard deviation of service time is 5 seconds. On average, how long is the waiting line (exclude the one being served) 2. During my office hours, students arrive at an average rate of 12 per hour. Assume Poisson arrivals. I can help students at an average rate of 20 per hour. Assume the time each student takes is exponentially distributed. a. How many students are waiting on average b. I am concerned that students wait too long. As a remedy, I decide to spend exactly 3 minutes with each student. How many students are waiting on average now 3. On the “Super Lucky Day”, engaged couples arrive at the County Clerk’s Office in a Poisson pattern with an average rate of 8 couples per hour. The time it takes to issue a marriage license is exponentially distributed, with an average of 6 minutes. a. How many couples are in the County Clerk’s Office on average b. How long does it take for a couple to get a marriage license, on average c. What is the probability that a couple is served immediately d. What is the probability that three or more couples are in line 4. At Champions League Final week, Jo, an enterprising former football player, set up a stand to for a 1-minute photo shoot for fans for $5. Demand was overwhelming, and “customers” were arriving at an average rate of 54 per hour, (the arrivals tended to follow a Poisson process). Jo soon discovered that not every photo shoot took exactly 1 minute: instead, the “service time” was distributed exponentially, with an average of 1 minute per customer. What was the average time that a customer spent in the queue and in the system After the first day, Jo started receiving complaints from impatient customers about the long waiting time. Fortunately, Jo’s friend and old teammate, Lo, was available to work at the stand, and could serve customers at the same rate as Jo. The only question was whether 4 to have two separate queues (one each for Jo and Lo), or a single queue of customers. With two separate queues, the average arrival rate to each queue was half of the total (i.e., 27/hour) and followed Poisson process. No jockeying between lines was permitted. Which system was better in terms of waiting time Inventory Management 1. A large automobile repair shop installs about 1,250 mufflers per year, 18 percent of which are for imported cars. All of the imported car mufflers are purchased from a single local supplier at a cost of $18.50 each. The shop uses a holding cost based on a 25% annual interest rate. The setup cost for placing an order is estimated to be $28. a. Determine the optimal number of imported car mufflers the shop should purchase each time an order is placed, and the time between placements of orders. b. If the replenishment lead time is six weeks, what is the reorder point based on the level of on-hand inventory c. The current reorder policy is to buy imported car mufflers only once a year. What is the additional holding and setup cost incurred by this policy 2. A local machine shop buys hex nuts and molly screws from the same supplier. The hex nuts cost 15 cents each and the molly screws cost 38 cents each. A setup cost of $100 is assumed for all orders. This includes the cost of tracking and receiving the orders. Holding costs are based on a 25% annual interest rate. The shop uses an average of 20,000 hex nuts and 14,000 molly screws annually. a. Determine the optimal size of the orders of hex nuts and molly screws, and the optimal time between placements of orders of these two items. b. If both items are ordered and received simultaneously, the setup cost of $100 applies to the combined order. Compare the average annual cost of holding and setup if these items are ordered separately; if they are both ordered when the hex nuts would normally be ordered and if they are both ordered when the molly screws would normally be ordered. (i) Average annual cost when ordered separately (ii) If both are ordered when the hex nuts are normally ordered (every 0.5164 years), then the hex nut cost is the same. Molly screw cost is only the holding cost: (iii) If both are ordered when the molly screws are normally ordered (every 0.3878 years), then the lot size for the hex nuts is: 3. List four reasons for holding inventory and three reasons for not holding inventory. Explain shortly. 5 4. Daily demand for the ice creams at I-Scream parlor is normally distributed with a mean of 100 quarts and a standard deviation of 40 quarts. The owner has the ice cream supplied by a wholesaler who charges $2 per quart. The wholesaler charges a $90 delivery charge independent of order size. The opportunity cost of capital to I-Scream is estimated to be 25% per year. Assume 360 days in the year. Assume zero lead time. (i) (7 pts) The owner thinks that the fixed charge is an important component in their costs so he decides to optimize the order quantity by focusing on the trade-off between inventory holding and setup costs. Thus, he decides to ignore the stochastic nature and use the mean of the demand as the demand rate. What is the optimal quantity (ii) The owner’s daughter raises concerns about possible loss sales due to planning for only the mean. Thus, they decide to change their policy as follows: Instead of using the mean as the demand rate, they want to apply a demand buffer to achieve a 90% service level. What is the optimal order quantity (hint: First calculate the demand rate that corresponds to 90% service and then use it to calculate the optimal order quantity) 7. Using the fixed-time period inventory model, and given an average daily demand of 15 units, 3 days between inventory reviews, 1 day for lead time, 30 units of inventory on hand, a service probability of 98 percent, and a standard deviation of daily demand is 3 units, compute the order quantity. Newsboy Problems 1. Briefly explain the trade-off faced by a newsboy. 2. Give two application areas of Newsboy inventory model. 3. The local supermarket buys lettuce each day to ensure really fresh produce. Each morning any lettuce that is left from the previous day is sold to a dealer that resells it to farmers who use it to feed their animals. This week the supermarket can buy fresh lettuce for $4.00 a box. The dealer that sells old lettuce is willing to pay $1.50 a box. Past history says that tomorrow’s demand for lettuce is normally distributed with mean 250 and standard deviation 34. At what price ($ per box of fresh lettuce) would it be optimal for the supermarket to purchase 267 boxes 4. The Gates, a popular luxury hotel in San Francisco, had a policy of overbooking the room rentals to make up for the customers who would make reservations but failed to show up. The average lost contribution for a vacant room was $20 per night if a customer reserved a room but was a “no-show”. About 10% of the guests who showed up (with reservation) but could not be honored because the hotel was full, could be placated without any extra cost to Gates. Another 30% were satisfied with being transferred to another hotel at a cost to the Gates of $3 per reservation. The remaining 60% of the guests were so upset that Gates could expect a loss 6 of future business with a net present value of approximately $50. The manager reviewed his records and found the following distribution of no-shows: Number of no-shows Probability Cumulative 1 .2 .2 2 .2 .4 3 .3 .7 4 .2 .9 5 .1 1 a. What is the expected loss in revenue by not accommodating a customer with a reservation b. What is the optimal level of overbooking that you would recommend to Gates Also review Problem Set 2 questions. Supply Chain Management, Outsourcing 1. Fill in the table below using only the words “low” or “high”. Product Variety Batch Size Efficient Supply Chain Responsive Supply Chain 2. Write two reasons for Bullwhip effect and one way to reduce Bullwhip effect other than Quick response and Vendor Managed inventory. Explain shortly. 3. List 2 benefits and 2 risks of outsourcing. Explain briefly Also review Problem Set 2 question 4.
