Operations exam | Good Grade Guarantee!
This exam consists of 6 numbered questions, all of which have sub-questions. A point value is given for each question and sub-question.
Please write your answers on the exam in the places provided, and show your calculations in the space provided. You may use spreadsheets to assist you in obtaining your solutions. Please provide copy of the spreadsheet when you used it.
1. Deco Pottery (20 points)
A pottery company makes two different types of products—plates and vases. The basic shapes are made out of clay at separate work stations—one for plates and one for vases. Both types are made one at a time by hand. It takes a worker an average of 12 minutes to form a plate, and it takes a worker an average of 20 minutes to form a vase. There is one worker at the plate forming station and 3 workers at the vase forming station. After being formed, the raw pottery pieces all go to a single oven where they are baked until hard. The oven can accommodate either of the pottery types, but plates and vases are always baked in separate batches. The oven can hold 460 plates at a time or 230 vases at a time. It takes 24 hours (including loading and unloading) to bake the clay to its proper hardness (regardless of pottery type).
After baking the vases move to a vase glazing station where workers use glaze to hand-paint designs on the pieces. Each worker does one piece at a time, and it takes an average of 30 minutes per piece. There are three workers at this work station. After baking, all of the plates move to a separate plate glazing station where they receive a simple coat of a single-color glaze. Each worker does one piece at a time, and it takes an average of 20 minutes per piece. There are two workers at this work station.
After glazing, all pieces (plates and vases) go to a single oven (different from the previous oven) where they are baked to set the glaze. This oven can hold 300 plates or 200 vases at a time, and plates and vases are always baked in separate batches. It takes 24 hours (including loading and unloading) to bake pieces until the glaze is set (regardless of pottery type).
The following is the process flow diagram for this system.
Vase Making (3)
Oven 1 Hardening
Plate Glazing (2)
Vase Glazing (3)
Oven 2 Glaze Setting
(6 points) Assuming that the process runs 24 hours per day, and that in the long run half of the pieces Deco Pottery makes are plates and half are vases, calculate the processing rate (in pieces per hour) for each work station. (Recall that the processing rate of a step is the maximum capacity of that individual step in the system.)
Make plates processing rate _________________ (pieces/hr)
Make vases processing rate _________________ (pieces/hr)
Oven 1 (clay hardening) processing rate _________________ (pieces/hr)
Plate glazing processing rate _________________ (pieces/hr)
Vase glazing processing rate _________________ (pieces/hr)
Oven 2 (glaze setting) processing rate _________________ (pieces/hr)
(5 points) Current market demand is for 100 plates per day and 100 vases per day. Does the company have sufficient capacity to meet demand? Briefly justify your answer. (Note that the time to make plates and vases will be more than 24 hours. However, this question is about capacity to meet demand. So, a piece sold on a particular day may have started production several days before it is sold.)
Answer: Yes No (Bold and underline one)
(4 points) Suppose that Deco Pottery learns that its second oven is near the end of its life. The company isn’t sure that it wants to invest the money to purchase a new oven, so it is considering using the first oven to bake the original pieces and also to set the glaze. Baking and glaze setting for plates and vases would all be done in separate batches (i.e., four different types of batches). Plate batches (for either baking or glaze setting) would contain 460 plates, while vase batches (for either baking or glaze setting) would contain 230 vases. If Deco Pottery decides to do this, what is the maximum number of plates and vases that they could produce per day assuming that they still want to produce equal numbers of each?
Plate processing rate _________________ (pieces/day)
Vase processing rate _________________ (pieces/day)
(5 points) (For this question, assume the original problem setting – i.e., assume that both ovens are still available.) Glaze Your Own is a chain of stores that provide customers with unglazed pottery that customers then decorate with glaze in the Glaze Your Own store. They have approached Deco Pottery with an offer to purchase 100 unglazed vases per day from the company. (Producing these vases does not require Deco Pottery to do the glazing or the final baking that sets the glaze.) Does Deco Pottery have enough capacity to accept this new contract in addition to its existing production of 100 plates per day and 100 vases per day? Justify your answer.
Answer: Yes No (Bold and underline one)
The Raleigh-Chapel Hill Expressway (20 points)
The North Carolina state legislature is considering constructing a fast speed (70 mph), high volume expressway, linking the cities of Chapel Hill and Raleigh. Bonds will be issued to finance construction with revenue for tolls ultimately paying for the project. Toll booths will be placed on the Raleigh-to-Chapel Hill side of the expressway. Chapel Hill-to-Raleigh traffic will not be delayed. The expressway will have eight lanes (four in each direction). Cars traveling from Raleigh to Chapel Hill will enter the expressway at the outer loop of Raleigh and not get off until just before the outskirts of Chapel Hill.
It is estimated that rush hour traffic from Raleigh to Chapel Hill will be 930 cars per hour. The current plan is to construct four toll booths, positioned just before the Chapel Hill exit. The plan also assumes that the toll booths will be staffed by people who receive the toll ($2) and possibly distribute change to drivers. Studies show that it takes on average 15 seconds for a toll booth operator to handle a single car (this quantity includes the time it takes for a driver to enter and exit the booth). Assume that arrivals of cars to the booth is a Poisson process and the processing times of cars at the booths are exponentially distributed. The drivers are smart. No one will wait in line when there is an available toll booth. (In other words, this is a single queue with multiple servers.)
(3 points) During a single rush hour, how much total time (among all four tool booths) is devoted to processing cars? (Note that the answer here is not the expected waiting time.)
Busy time during the rush hour ________________________ minutes
(3 points) What is the average amount of time spent waiting before the transaction begins?
Time waiting in line _____________________________________minutes
(3 points) What is the average number of cars waiting to enter the toll booths?
Queue length ___________________________cars
The expressway has opened and the forecasts were inaccurate. The arrival rate is actually 1000 cars per hour. (This information applies to the rest of the problem.)
(3 points) Describe what typical rush hour cars will experience as they approach the toll booth.
To meet the actual demand of 1000 cars per hour, the construction engineers are considering the following plan: drivers are given the option of purchasing a radio frequency identification device (RFID) that will allow them to pass through the toll booth area quickly (one car every three seconds and there is no variability in the service time). For safety reasons, providing this option removes two of the toll booths, despite the fact that cars will only be able to enter the RFID-enabled booth one at a time. (As a result, there will be two old booths and one new RFID-enabled booth). It is estimated that 58% of the cars will use the RFID equipment, leaving 42% to drive through the manned stations.
(4 points) Calculate the total capacity or service rate (in cars per hour) of the RFID and non-RFID routes through the toll system.
RFID lane capacity _______________________ cars per hour
Non-RFID lane capacity _______ ___________ cars per hour (total for the two lanes)
(4 points) What is the probability that drivers in the RFID lane have to wait (in the system) longer than 4 seconds?
Inventory Growth (10 points)
A new manager that has just joined a company learns that average inventory at the company’s distribution center (DC) has increased by about 50% over where it was two years ago. The DC serves multiple regions facing independent demands with similar means and similar standard deviations and it uses a base stock policy to manage its inventory. When the manager investigates this increase further, she discovers that sales of products that pass through this DC have increased by about 50% during that time period.
(5 points) If the increase in average inventory is due to a 50% increase in the average demand in each region, but the variability of demand in each region has not changed, should she be pleased with the distribution center’s inventory performance, concerned, or neither? Explain your answer.
(5 points) If the increase responds to an increase, over the last two years, in the number of regions that the DC serves, and now all regions face independent demands with similar means and similar standard deviations (that is, sales at the old regions have not changed, but the DC now serves around 50% more regions than two years ago), should she be pleased with the distribution center’s inventory performance, concerned, or neither? Explain your answer.
Staffing Requirements (12 points)
A famous IT consulting firm BracKenzie and Co, henceforth called the Firm, has a consulting project implementing ERP at a large telecom firm, henceforth called the Client. The project manager, Mr. Grisham, is in the process of submitting a staffing proposal to his client for the project. The labor requirement is estimated to follow a normal distribution with mean 3000 person-hours and a standard deviation of 400 person-hours.
Because the Client is large and influential, the Client pays the Firm for exactly as many hours as are required to complete the project. It is unlikely however, that unutilized time of the consultants will be used up on other projects on short notice, and therefore the Firm will continue to pay $175 per hour to its project staff, per hour without any revenue.
On the other hand, since the project is high-profile, if the work requirements exceed the budgeted person-hours, the Client will hold the Firm accountable for project completion. The Firm will then have to pay $250 per person-hour to hire contract consultants on short notice to make-up for the remaining work requirements.
(5 points) Mr. Grisham has asked you for advice on how many person-hours the Firm should allocate to this project with the Client?
The Firm Should Allocate Person-Hours
(3 points) What would the hourly rate for the contract consultants have to be (as opposed to the current rate of $250), in order for you to advise Mr. Grisham to allocate exactly 3000 person-hours to the project?
$ per Person-Hour
(4 points) Given your answer in part (a), what is the expected number of contract consultant hours to be utilized (at the hourly rate of $250)?
Expected number of contract consultant hours is
5. Miscellanea (26 points)
Bullwhip Effect (3 points)
Suppose that all stages in the supply chain had tracked their inventory positions (instead of net inventory) while playing the Beer Game. In addition, suppose that all stages had made their ordering decisions based on their inventory positions. What would have been the impact on the Bullwhip Effect? Explain your answer.
Printed Circuit Boards (5 points)
You are a supplier of printed circuit boards (PCBs). Production of the circuit boards consists of several steps – Surface Mounting, Baking, and Final Assembly. Surface Mounting puts integrated circuits (ICs) and other components on a PCB. These PCBs are then Baked as a batch and kept in an oven for some time so that the ICs are soldered onto the PCBs. Finally, these PCBs are taken and manually assembled into a case, and wired with connectors. The processing rate at the Surface Mounting station is of 10 PCBs/minute, the processing rate for Baking is of 2 PCBs/minute, and the processing rate for Final Assembly is 4 PCBs/minute. If there are on average 20 units of WIP and the system is working at capacity, what is the throughput time for PCBs?
Psychology of Waiting (3 points). Read the following description of an airline flight.
“I arrived at the airport two hours early since it was Monday morning and I knew that there would be a lot of traffic. I debated whether to check in my baggage, but decided that it was light enough, and the effort and inconvenience of carrying it with me was less than the inconvenience of waiting for my checked in baggage to arrive when I reached New York. Check-in was quick, since Delta had installed a lot of self-check-in kiosks. However, at the security checkpoint there was a long queue, and I resigned myself to a long wait. After 15 minutes I began to regret my decision not to check in my large handbag, since it was beginning to hurt my shoulder. When I reached the end of line, TSA personnel directed groups of passengers to the different security gates. I took off my shoes and took my laptop out of the case, but had to wait for additional trays in order to put my cell phone, PDA and keys. Some other travelers who did not have to wait for trays skipped ahead of me. Fortunately my security gate was very quick. I noticed that one person had to turn back and re-enter a number of times at another gate- the folks behind him were getting impatient. I boarded the plane, and settled down for the flight. However, after taxiing to the runway, the pilot announced that due to the number of planes already waiting for departure, we would be delayed by about 15 minutes. I could see the other planes taking off on the runway, since I always take window seat. The couple seated next to me had a 9 month old baby, and I chatted with them about the baby’s first steps.”
Find incidents in this description that illustrate the principles stated in the article on the psychology of waiting lines. UNDERLINE the phrases in the description, number them 1, 2, 3 and state the corresponding principles in the space below. The same incident may illustrate more than one principle.
Global Financial Corporation (2 points)
Consider the Global Financial Corporation case that we discussed in Week 2 of distance (post residency). As noted in the case, the total average processing time for a standard loan was under 2 days, while the total average processing time for a new loan was under 3 days. However, standard loans were taking about 11 days to get processed and new loans were taking about 12 days to get processed.
Briefly explain what was driving the delays. (1 point)
Also, what recommendation could help the Global Financial Corporation meet the requirement that system throughput time be of under 10 days? (1 point)
The Case of Australian Paper Manufacturers (3 points)
Consider the case of Australian Paper Manufacturers (APM) in the “Operations-Based Strategy” article we discussed in the first distance week prior to residency. For many of the examples provided in the article, we discussed the attributes of the company’s products that customers care about, what operations principles enable the company to offer products with those attributes, and the reason why those operations principles were difficult to replicate by competitors. Provide a similar analysis for APM.
Attributes of the company’s products that customers care about:
Operations principles that enable these attributes:
Reasons why these principles were difficult to replicate:
Statistical Process Control (5 points)
NoKeya Inc. produces cellular phones. They employ a sampling procedure where they sample 200 cellular phones every day. The following table is the sample data:
Number of Defective Phones
p (Proportion of Defects)
The manager wants to use the first 7 days’ data to create the benchmark of the production process. She decides to use a p-chart to monitor the process. What is the process mean and standard deviation during the benchmark phase?
What are the resulting upper and lower control limits? Use three-sigma control limits.
Upper Control Limit: ________________________
Lower Control Limit: ________________________
Are there any day(s) when the process might be out of control? Why? (You may select one day or a range of days as the basis for your answer.)
Logistics at Burger King (5 points)
The following was taken from a Wall Street Journal article:
Burger King intends to bring smiles to the faces of millions of parents and children this holiday season with its ‘Toy Story’ promotion. But it has some of them up in arms because local restaurants are running out of the popular toys. Lynn Cullen says her four-year-old son Sam, egged on by a barrage of television ads that began late last month, had been begging for a trip to Burger King so he could get a plastic Buzz Lightyear or Woody the sheriff doll, both characters from the Walt Disney Co. movie.
But after Sam got his Burger King Kids Meal, he let out a howl of protest. Instead of a ‘Toy Story’ character, he found Esmeralda – a leftover doll from a promotion tied to ‘The Hunchback of Notre Dame,’ a far less popular Disney film.
‘There were no apologies, no voucher, they just said, “We don’t have ’em,” Ms. Cullen complains. Furthermore, when she went to a second Burger King, only to learn that it had also run out of the popular freebies, Ms. Cullen was offered a bigger, more elaborate ‘Toy Story’ doll for $2.69. ‘It’s bait and switch,’ Ms. Cullen contends. ‘It’s toying with little kids in the most cynical way.’
The ‘Toy Story’ restaurant campaign is part of one of the biggest video promotions to date from two marketers with vast experience staging such events. Every Kids Meal sold every day of the year comes with a giveaway, a program that has been in place for about six years and has helped Grand Metropolitan PLC’s Burger King increase its market share. Nearly all of Burger King’s 7,000 U.S. stores are participating in the ‘Toy Story’ promotion.
For its part, Disney has long used restaurant tie-ins to push its animated movies. The entertainment concern and a host of marketing partners, in addition to Burger King, are together spending about $150 million to promote ‘Toy Story’ on video.
Nevertheless, meeting consumer demand still remains a conundrum for the giants. That is partly because individual Burger King restaurant owners make their tricky forecasts six months before such promotions begin. ‘It’s asking to pull out a crystal ball and predict exactly what consumer demand is going to be,’ says Richard Taylor, Burger King’s director of youth and family marketing. ‘This is simply a case of consumer demand outstripping supply.’ The long lead times are necessary because the toys are produced overseas to take advantage of lower costs.
‘We don’t want to advertise things to consumers and have them come in and be disappointed,’ Mr. Taylor says. He adds that the promotion still has a month to go.
Although Burger King managers in Houston and Atlanta say the freebies are running out there, too, Mr. Taylor says he isn’t worried about making matters worse by boosting the ads for the giveaways. ‘There might be a restaurant here or there that has run out of the prizes,’ he says. But Burger King, which ordered nearly 50 million of the small plastic dolls, is ‘nowhere near running out of toys on a national level.’
Provide ONLY ONE recommendation that would have helped improve the situation with the ‘Toy Story’ promotion and discussany implementation challenges. (Limit: 200 words.)
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