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University of Washington *
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301A
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Industrial Engineering
Date
Feb 20, 2024
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The following problems will help you prepare for the final exam. However, this set of practice questions should be used only as a guideline. The exam may cover question types beyond those presented here. If you are very comfortable with the questions here, the readings for each class, the examples we discussed in class, and the homework questions, then you are very well prepared for the exam.
Economic Order Quantity (EOQ) 1.
A large law firm uses an average of 40 packages of copier paper a day. The firm operates 260 days a year. Storage and handling costs for the paper are $3 a year per package, and it costs approximately $6 to order and receive a shipment of paper. a)
What order size would minimize total annual ordering and carrying costs? b)
Compute the total annual cost using your order size from part a) c)
c)
The office manager is currently using an order size of 200 packages. The partners of the firm expect the office to be managed “in a cost-efficient manner.” Would you recommend that the office manager use the optimal order size instead of 200 packages? (Justify your answer by calculating the annual saving if switching from 200 packages to the optimal order size.) 2.
Cathy Cooper is a purchasing manager for a computer cable manufacturing company. The company uses 10,000 copper connectors at a steady rate over the year, and it currently manufactures connectors itself at a cost of $40 a unit. Each setup for a production run costs the company about $5,000, and the company bases its annual inventory holding costs on a 15% cost of capital. Cathy is considering buying connectors from an outside supplier. Supplier A charges $42 per unit, plus a fixed cost of $200 per shipment. Supplier B charges $42.50 per unit with a $100 extra per-shipment fee. Both suppliers require payment upon receipt of the goods. What should Cathy do? Buy from A? From B? Or continue to have the company produce the parts itself? EOQ with Quantity Discount 3.
Estimated demand for gold-filled lockets at Sam's Bargain Jewelry and Housewares is 2,420 lockets a year. Manager Veronica Winters has indicated that ordering cost is $45, and that the following price schedule applies: 1 to 599 lockets, $.90 each; 600 to 1,249 lockets, $.80 each; and 1,250 or more, $.75 each. What order size will minimize total cost if carrying cost is 20 percent of price on an annual basis? 4.
Grocer.com uses 88,000 boxes a year. Annual carrying cost is 20% of the purchase price, and ordering costs are $32. The following price scheme applies (all-unit discount). Determine: a)
The optimal order quantity. b)
The number of orders per year.
Number of Boxes Price per Box 1,000 to 1,999 $1.25 2,000 to 4,999 1.20 5,000 to 9,999 1.15 10,000 or more 1.10 Re-Order Point (ROP) 5.
A shoe store sells one item that is supplied by a vender who handles only that item. Demand for that item recently changed, and the store manager must determine when to replenish it. The manager wants a probability of at least 95 percent of not having a stockout during lead time. The manager expects demand to be a dozen units a day and have a standard deviation of 2 units a day. Lead-time is a constant four days. Assume normality and that seasonality is not a factor. a)
When should the manager reorder to achieve the desired probability? b)
What’s the expected number of units short per order cycle? c)
Assume 365 days a year. Also assume that the store orders 100 of that item each time an order is placed. What’s the expected number of units short per year? Moreover, suppose each unit short costs the store $30, what is the store’s annual shortage cost 6.
A manager is ordering lubricant with EOQ = 900 pounds and ROP = 423 pounds. Average daily usage is 45 pounds, which is normally distributed and has standard deviation of three pounds per day. Average lead time is nine days, with a standard deviation of 2 days. a)
What is the risk of a stockout? b)
Assume 260 business days a year for the company. What is the expected number of units short per year? c)
Suppose each unit short costs the company $10, what is the company’s annual shortage cost? The Single-Period Newsvendor Model 7.
Textbook Chapter 12 (14
th
edition) or Chapter 13 (13
th
edition) problem 37. 8.
Textbook Chapter 12 (14
th
edition) or Chapter 13 (13
th
edition) problem 39. Hint: in the problem statement "Labor, overhead, meat, buns, and condiments cost 50 cents per burger", "meat" refers to the beef. Since each pound of beef costs $1 and can make four burgers, 25 cents of the 50 cents are for beef, and the other 25 cents are for "labor, overhead, buns, and condiments." The cost of shortage, Cs, refers to the potential profit that's lost due to insufficient beef. Therefore, when you calculate this potential profit, you need include all the costs. On the other hand, when you calculate the cost of excess, Ce, you should consider beef only, because "labor, overhead, buns, and condiments" do not get salvaged.
Queueing Systems 9.
Problem 1b, Chapter 18 in textbook. 10.
All trucks traveling on Interstate 40 between Albuquerque and Amarillo are required to stop at a weigh station. Trucks arrive at the weigh station at a rate of 200 per day (according to a Poisson process), and the station can weigh 250 trucks per day (exponential service time). i)
Determine the average number of trucks waiting in line, the average time spent at the weigh station by each truck and the average waiting time before being weighed for each truck. ii)
If the truck drivers must wait long at the weigh station, some of them will start taking a different route in the future, thus depriving the state of taxes. The state of New Mexico estimates it loses 20 cents in taxes for each minute that trucks must remain at the weigh station. A new set of scales would increase the service capacity to 400 per day (still exponential service time), and it would cost $150,000 more every year to operate than the old scale. Should the state install the new scale? 11.
Wallington Copy Center is the central (i.e., monopoly) document-copying service for the famous Wallington Business School. A significant and growing part of their business is providing self-service machines so that students can make last-minute copies of class presentations (either that, or printing 90 copies in the computer lab!). For this self-service operation, arrival patterns have been analyzed, and they seem to follow a Poisson distribution, with a mean rate of 15 arrivals per hour. Service times follow an exponential distribution. With the current copying equipment, the average service time is three minutes. A new generation of machines is available that will reduce this to an average of two minutes. The average value of time for the students requiring copying is $15 per hour (hey, they're trying to rush to class!). In answering these questions, please justify all numbers used and show all work. (a)
Wallington currently leases one old-technology machine for student self-service. If a new-technology machine can be leased to replace the old machine, how much extra per hour should Wallington be willing to pay to lease the new machine? (b)
The Dean has decided that there should be a minimum service level at the self-
service. He decided to lease only new-technology machines (the current old-tech machine will be returned) to ensure that the probability that a student must wait for a machine is 5% or less. How many machines should be leased? What if this probability is lowered to 1% or less? (c)
Rather than lease the new machine, Wallington could lease an additional
, old-
technology machine. The cost of leasing an old-technology machine is $8 per hour, and leasing a new machine costs $5 more per hour. Which is better, to lease another old-technology machine, or to lease a new-technology machine to replace the current old-technology machine?
12.
I just don’t like to make toys
Someday I’d like to be a dentist
Why am I such a misfit
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I am not just a nit wit - Herbie (from Rudolph the Red-Nosed Reindeer)
Herbie has finally left Santa’s workshop and pursued his dream of becoming a dentist. He would like to know how large of a waiting room he will need for his dental office. Herbie expects 3 customers to show up per hour on average (with a Poisson distribution), and he can serve one customer in 10 minutes on average (exponential distribution). He would like to have enough chairs in the waiting room so that at least 90% of the time everyone will have a seat. How many chairs will Herbie need in the waiting room. 13.
The manager of a bank must determine how many tellers should work on Fridays. For every minute a customer stands in the bank, the manager believes that a delay cost of 50 cents is incurred. On average 2 customers per minute arrive at the bank. On the average, it takes a teller 2 minutes to complete a customer's transaction. It costs the bank $9 per hour to hire a teller. Inter-arrival times and service times are exponential. To minimize the sum of service costs and delay costs, how many tellers should the bank have working on Fridays? Conceptual Questions 14.
Recall that in picking the optimal number of servers in a queueing system, we balance the waiting cost and server cost. The approach is to increase number of servers, M
, one by one until you find the total cost starts to go up. However, is there an easier way of doing this? Some people have suggested using Linear Programming to solve this problem. That is, one can let M
be the decision variable and minimize total cost (waiting cost + server cost) in the objective function. What do you think about this? Is this feasible? (Hint: check the assumptions for linear program to see if they are all satisfied in this approach. For example, is the server cost linear in M? What about the waiting cost?) 15.
How can the “psychology of waiting” be used to better manage queueing systems (can you name three principles and give examples)? 16.
Can you name some priority schemes that can be used to manage queues? 17.
Inventory serves various purposes. For example, when there is a significant ordering/setup/shipping cost, it may make sense to order in batches of more than one, to take advantage of the economy of scale. The resulting inventory is called cycle inventory (or, cycle stock). This classification is important, because if you carry mostly cycle inventory, then to reduce the inventory, you must reduce the setup/ordering cost. Can you tell the various types of inventory and the purposes they serve? 18.
Explain how vendor managed inventory (VMI) works. For a retailer, what are the benefits and risks of VMI? What are the benefits and risks for the manufacturer? 19.
Explain how risk pooling can help to reduce inventory or improve service level. What are the tradeoffs involved in deciding whether to do location pooling? 20.
How can delayed product differentiation (a.k.a. postponement) be used to more efficiently manage a supply chain? What tradeoff may be involved? Give an example if you can. 21.
Can you explain how a revenue sharing contract or a buyback contract works? How do these contracts help to reduce stock-out at the retailing level? You can use the examples that we discussed in class.