mgmt 361 (ch5,6,7,8)

For one and the same process, what scenario corresponds to a higher variation?

A three sigma process

A summer camp that offers one-week programs faces the challenges of long queues as parents try to check in their children each Saturday morning. If they were to add more staff to assist with the check-in process, then which of the following will occur? The average time parents wait decreases. The maximum time the parents wait decreases. The average number of parents waiting to check in their child decreases.

(i),(ii),(iii) Adding capacity reduces the average waiting time, the maximum waiting time, and the average number of parents waiting.

A milling process has an upper specification of 2.058 millimeters and a lower specification of 1.921 millimeters. A sample of parts had a mean of 1.96 millimeters with a standard deviation of 0.014 millimeters. What standard deviation will be needed to achieve a process capability index of 2.0?

0.01142 Process capability index = (USL − LSL)/(6 × Standard deviation). Therefore, Standard deviation = (USL − LSL) / (6 × Process capability index) = (2.058 − 1.921) / (6 × 2) = .01142.

CloudRack provides web hosting services on their 9 servers. When a person requests a page from one of their hosted websites, the server must find the page and send it to the person's browser. These requests arrive at the rate of 400 per second. The coefficient of variation of the interarrival times is 2. The processing time for a server is 0.02 second with a coefficient of variation of 2. On average, how much time does a request take to be filled (i.e., include time waiting for a server and the actual processing by the server)?

0.0731 Given interarrival time (a = 1/400 sec), processing time (p = 0.02 sec), number of servers (m = 9), coefficient of variation of interarrival times = 2, and coefficient of variation of processing time = 2, compute time in queue = 0.0531 sec, then add processing time of 0.02 sec. Total time to complete request = 0.0731 seconds.

Larry Ellison starts a company that manufactures high-end custom leather bags. He hires four employees. Each employee only begins working on a bag when a customer order has been received and then she makes the bag from beginning to end. The average production time of a bag is 1.9 days, with a standard deviation of 2.3 days. Larry expects to receive one customer order per day on average. The interarrival times of orders have a coefficient of variation of one. What is the expected duration, in days, between when an order is received and when production begins on the bag?

0.22 days Given interarrival time (a = 1 day), production time (p = 1.9 days), number of servers (m = four employees), coefficients of variation of interarrival time (one), and standard deviation of production time (2.3 days, coefficient of variation = 1.2105), compute time in queue = 0.22. Tq=(1.94)(0.48002(4+1)√−11−0.4800)(12+(1.2105)22)=(0.4800)(0.3809)(1.2327) = 0.22 daysTq=1.940.48002(4+1)-11-0.480012+1.210522=0.48000.38091.2327 = 0.22 days

C&A is making steel rods with an average diameter of 1 mm. The process has a standard deviation of 0.2 mm. The upper and lower specification limits are 1.2 mm and 0.8 mm respectively. What is C&A's process capability index?

0.33 Process capability index = (1.2 − 0.8)/(6 × 0.2) = 0.333.

A company making tires for bikes is concerned about the exact width of its cyclocross tires. The company has a lower specification limit of 22.7 mm and an upper specification limit of 22.9 mm. The standard deviation is 0.1 mm and the mean is 22.8 mm. What is the process capability index for the process?

0.3333 Cp =USL − LSL=22.9 − 22.7/6*0.1=0.3333

Larry Ellison starts a company that manufacturers high-end custom leather bags. He hires four employees. Each employee only begins working on a bag when a customer order has been received and then she makes the bag from beginning to end. The average production time of a bag is 2.1 days with a standard deviation of 2.8 days. Larry expects to receive one customer order per day on average. The inter-arrival times of orders have a coefficient of variation of 1.What is the expected duration, in days, between when an order is received and when production begins on the bag (i.e. include the time waiting to start production but do not include the time in production)?

0.38 Tq=(2.1/4)(0.5333^sqrt(2(4+1))-1)/1-.5333)(1^2+1.33^2/2)= (.53)(.5227)(1.3889) = 0.38 days

C&A's potato chip filling process has a lower specification limit of 9.5 oz. and an upper specification limit of 10.5 oz. The standard deviation is 0.3 oz. and the mean is 10 oz. What is the process capability index for the chip filling process?

0.56 (USL − LSL)/(6 × Standard deviation) = (10.5 − 9.5)/(6 × 0.3) = 0.555556.

Pharma Dev develops and markets new technological products to be used in health care. The development of a new product operates as follows.When a new technology meets the requisite market potential, a new patent is filed. Patents are granted for a period of 12 years starting from the date of issue. Once the patent is filed, the new technology is developed at one of its three independent development centers, and is then launched to the market. Each product is developed at only one center, and each center can only develop a single patented technology at a time. On average, Pharma Dev files a new patent every 5 months (with standard deviation of 5 months). The average development process lasts 12 months (with standard deviation of 24 months). Utilization: What is the utilization of Pharma Dev's development facilities?

0.8

A grinding process has an upper specification of 1.649 inches and a lower specification of 1.507 inches. A sample of parts had a mean of 1.57 inches with a standard deviaiton of 0.026 inches. What is the process capability index for this system?

0.9103 Process capability index = (USL − LSL)/(6 × Standard deviation) = (1.649 − 1.507)/(6 × 0.026) = 0.9103.

A quality-control technician has been monitoring the output of a milling machine. Each day, the technician selects a random sample of 20 parts to measure and plot on the control chart. Over 10 days, the average diameter was 1.308 millimeters with a standard deviation of 0.05 millimeters. What is the UCL?

1.3415 The estimated standard deviation (ESD) is calculated as ESD = Standard deviation of all parts / Square root of sample size = 0.05 / Square root of (20) = 0.01118. The upper control limit is the mean plus 3 × ESD = 1.308 plus 0.03354 = 1.3415.

Huduko Inc. offers a number of computer services. One server handles its own web page. It receives requests for web pages at the rate of 76 per second. The standard deviation of these interarrival times is 0.02 second. What is the coefficient of variation of the interarrival times for this server?

1.52 Coefficient of variation = Standard deviation / Mean of interarrival time; Mean of interarrival time = 1/76. So 0.02/(1/[76) = 76 × 0.02 = 1.52.

Fiesta Gift, a whole seller for gifts, usually orders Christmas items during the annual trade show in July. An item chosen this year is a dated sterling silver tree ornament. The vendor charges $55 per unit at the time of ordering. Fiesta Gift plans to sell at a price of $80. And based on the sales pattern in previous Christmas seasons, Fiesta Gift has come up to the following estimation of the demand distribution Possible demand D=x Probability Pr(x) 1000. 5% 1500. 15% 1800. 19% 2000. 36% 2300. 25% Unsold ornament post-Christmas season is marked down to half price, at which Fiesta Gift usually is able to sell all the leftovers. 1. (No rounding if not necessary) The unit overage cost is ___ ___15___(30 %) , the unit underage cost is ____ ___25___(30 %) and the critical ratio is _____% 2. Suppose the Fiesta Gift orders q= 1800 in July. The expected profit is 3. Suppose the Fiesta Gift orders q= 2000 in July. The expected profit is

15 25 62.5% 41600 43480

If a process has a six-sigma capability, what is the process capability index?

2

CPU-on-Demand (CPUD) offers real-time high-performance computing services. CPUD owns 1 supercomputer that can be accessed through the Internet. Their customers send jobs that arrive, on average, every 4 hours. The standard deviation of the interarrival times is 5 hours. Executing each job takes, on average, 3 hours on the supercomputer and the standard deviation of the processing time is 4.5 hours. On average, how long will it take to complete a job (from the time it is submitted by the customer until the time it is completed)?

20.2 Interarrival time = 4 hours. Processing time = 3 hours. Coefficient of variation of the interarrival time = 5/4 = 1.25. Coefficient of variation of the processing time = 4.5/3 = 1.50. T = 3 + 3 × (0.75/0.25) × (1.56 + 2.25)/2 = 20.2 hours.

After a product is launched to the market, it generates a profit of US$40 million per year of patent life. After the patent expires, the product generates no profit. When the cost of leasing an office is less than ____ million dollar per year, it makes sense to lease a new office. (Round to the nearest integer)

216

Geoff Gullo owns a small firm that manufactures "Gullo Sunglasses." He has the opportunity to sell a particular seasonal model to Land's End. Geoff offers Land's End two purchasing options: Option1. Geoff offers to set his price at $65 and agrees to credit Land's End $53 for each unit Land's End returns to Geoff at the end of the season (because those units did not sell). Since styles change each year, there is essentially no value in the returned merchandise. Option 2. Geoff offers a price of $55 for each unit, but returns are no longer accepted. In this case, Land's End throws out unsold units at the end of the season. This season's demand for this model will be normally distributed with mean of 200 and standard deviation of 125. Land's End will sell those sunglasses for $100 each. Geoff's production cost is $25. 1. If Land's End chooses option 1, it would purchase Q=______ 2. If Land's End chooses option 2, it would purchase Q=__ 4. (Keep 2 decimal places for all blanks) Suppose Land's End chooses option 2 and order 275 units. Land's End's expected lost sales is ____________ ___21.09___(30 %) , expected leftover inventory is___________ ___96.09___(30 %) , and expected sales is_________

282 184 21.09 96.09 178.91

How many standard deviations is the upper control limit, UCL, above the long-run center line, X-bar-bar?

3

The organizers of a conference in the Philadelphia Convention Center are evaluating the possibility of setting up a computer area where attendees can check their e-mail on computers provided by the organization. There will be one common queue for all computers and only one person uses a computer at a time. On average there are 15 attendee arrivals per hour, the standard deviation of the time between arrivals is 4, and the average time a person spends on the computer is 10 minutes (with standard deviation 3). To ensure that waiting times are not too long, the organizers what to ensure that the utilization of the computers doesn't exceed 90%. At least how many computers do they need to have?

3

A few years ago you started your own business making organic soap bars.• In order to make bars, you need 800 kg of sustainably sourced palm oil per month.• The supplier charges $80/kg.• Ordering costs are $75 per order, and the annual carrying costs are 20 percent of the purchase price. Optimal Order Quantity = ____________ [kg/order] If the order quantity is 300 [kg/order], the company's average inventory of palm oil = ___________ [kg] If the order quantity is 300 [kg/order], how often will an order be placed (length of order cycle)? (Assume one year is 288 days) __________ [𝑑𝑎𝑦𝑠/𝑜𝑟𝑑𝑒𝑟] If the order quantity is 300 [kg/order], including the purchasing cost, the annual total inventory cost = ___________ [$/yr]

300 150 9 772,800

Given that purchasing cost C = $1 per can, unit holding cost h = $0.5 per can per year, and ordering cost R = $0.75 per order. Optimal Order Quantity = _________ [cans/order]. Under the Optimal EOQ quantity, annual ordering cost = ____________ [$/yr] Under the Optimal EOQ quantity, annual holding cost = __________ [$/yr] Annual purchasing cost = ____ Annual total inventory cost (excluding purchasing cost) = ___________ [$/yr]

33 8.18 8.25 360 16.44

Development Time: How long does it take for an average technology from winning a patent to start the development process? _______ months (Keep 2 decimal places.)

33.25

Cranston Cranberry Cooperative (CCC) processes cranberries that are harvested in the local area. Barrels of cranberries arrive on trucks to CCC's facility at a rate of 150 barrels per hour and are processed continuously at a rate of 100 barrels per hour. Trucks arrive at a uniform rate over 8 hours, from 6:00 a.m. until 2:00 p.m. What is the maximum number of barrels of cranberries that are waiting on the trucks at any given time?

400 (8*50)

For 113 consecutive days, a process engineer has measured the temperature of champagne bottles as they are made ready for serving. Each day, she took a sample of 10 bottles. The average across all 1,130 bottles (113 days, 10 bottles per day) was 44 degrees Fahrenheit. The standard deviation across all bottles was .6 degree Fahrenheit. When constructing an X-bar chart, what would be the center line?

44 degrees The center line would be given by the average across all 1,130 bottles,

Find a Doctor is a small startup that helps people find a physician that best meets their needs (location, insurance accepted, etc.). During a "slow" time for them, they have 6 staff members taking calls from customers. On average, one call arrives every 6 minutes. On average, each staff member spends 19 minutes with each customer.. What is the probability that one of their staff members is busy?

52.8% Given processing time (p = 19 min), interarrival time (a = 6 min), and number of servers (m = 6 staff members), the utilization equals 19 / (6 × 6) = 52.8%

A jeweler purchases silver for use in its products. The firm uses 200 grams of silver per week and purchases silver for $3 per gram from a supplier. The cost to hold one gram of silver in inventory for one year is $0.6. Each time the firm orders silver from the supplier, the firm must pay a $10 order processing charge. What is the optimal order quantity (in grams)?

589 Annual demand = 52 weeks × 200 grams per week = 10,400 grams per year. EOQ = √(2 × 10,400 × 10/0.6) = 588.78 -> 589 grams per order.

Max Stamp approves study abroad documents for the university. Students must wait in line with their forms outside Max's office. One student at a time is allowed in his office and Max takes precisely 20 minutes to evaluate each student's set of documents. On average, 3 students per hour go to his office and they spend, on average, 155 minutes trying to get their forms approved (time waiting in queue plus time in Max's office having him evaluate their documents). How many students are waiting outside of Max's?

6.8 Time in queue = 155 − 20 = 135 min. Interarrival time = 20 min. The average number of customers waiting in the queue = Time in queue / Interarrival time = 135 / 20 = 6.8.

Camille owns Crunch Code, a company that provides quick programming solutions. Clients send projects to Crunch via their web page and a programmer develops the needed code as quickly as possible. Camille has five programmers, who do all of the coding. On average, a project arrives once every 4.8 hours, with a standard deviation of 6.00 hours. Each project is assigned to one programmer and that programmer takes on average 19.2 hours to complete each project with a standard deviation of 19.2 hours.How many uncompleted projects does Crunch Code have in the system on average at any given time?

6.96

A firm purchases and resells widgets. Holding one widget in inventory for one year costs the firm $8. The firm purchases widgets in lots of 48. Demand for widgets is 6 per week. Each time the firm orders widgets from the supplier, there is a $12 charge for transportation. What is the total transportation cost incurred by the firm over one year (52 weeks)?

78 The firm will sell 52 × 6 = 312 widgets each year. The firm will place 312/48 = 6.5 orders per year. Each order incurs a transportation cost of $12, so the firm will spend 6.5 × $12 = $78 on transportation each year.

Market Life: How many years of patent life are left for an average product launched to the market? _____ years. (Keep 2 decimal places.)

8.23

Products under development: On average how many patented products are undergoing development or waiting to be developed? (Keep 2 decimal places.)

9.05

The control limits, calculated as three standard deviations from the long-term sample mean, imply that _________ of the sample points are expected to fall between the upper and lower control limits.

99.7%

Suppose processing times and the coefficients of variation of interarrival times and processing times are held constant. If utilization is increased from 80 percent to 90 percent, which of the following systems experiences the largest increase in the average waiting time in queue? A queue with 1 server. A queue with 10 servers. A queue with 100 servers. All of the above three queues experience the same increase.

A 1 server Queues with more servers experience less change in average waiting time for the same increase in utilization as compared to queues with fewer servers.

Queuing system A has a utilization of 80 percent, and queuing system B has a utilization of 90 percent. Both have a single server. Say the utilization of both systems increases by 5 percent; that is, A increases from 80 percent to 85 percent while B increases from 90 percent to 95 percent. Which system is likely to experience the bigger change in the average time in queue? System A. System B. Time in queue for each system will increase by the same amount. More information is needed to determine which has a bigger change in average time in queue.

B Time in queue increases at a faster and faster rate as the utilization is increased. So a 5% increase in utilization has a larger effect from 90% to 95% than from 80% to 85%.

A defect occurs only because of abnormal variations in input variables.

False

Eliminating variations is always possible.

False

You harvest 50 tomatoes. You notice that the tomatoes vary in size and weight. If some of the tomatoes were exposed to extra sunshine or irrigation, this would be a common cause variation.

False

YourNurse (YN) Inc. uses certified nurses to answer medical queries from customers over the phone. When patients call into YN, they are first asked to provide their zip code, which then allows YN to route their call to the call center nearest to the patient (it operates 10 across the country). Which single suggestion in the following list (and explanation) is most likely to reduce the average time callers wait before speaking with a nurse? Run an advertising campaign to increase demand and to better utilize its nurses.Train its nurses so that they spend more time answering the patients' questions. Instead of using callers' zip codes, route calls to the call center with the fewest callers to help prevent situations in which there are idle nurses at the same time that there are callers on hold. Play a recording of useful medical information while callers are on hold so as to decrease their perception of how long they are waiting. None of the above.

C Running the advertisement campaign would increase demand but not capacity, so it increases waiting time. Training nurses decreases capacity, so it increases waiting time. Playing a recording might change the perception of waiting time, but it doesn't change the actual waiting time.

If the order quantity doubles, what happens to the frequency of orders (i.e., the number of orders submitted per unit of time)? multiple choiceDecreases by more than 50 percent.Decreases by 50 percent. CorrectRemains unchanged.Increases by 100 percent or doubles.Increases by more than 50 percent.

Decreases by 50 percent The number of orders per unit of time is R / Q, where R is the flow rate and Q is the order quantity. So if Q doubles, then the number of orders per unit of time decreases by 50%.

You consider to see a doctor at one of the two local clinics - Walgreen Clinics (WC) and CSV Clinics (CC). During busy periods, a new customer walks into WC every 20 minutes (with a standard deviation of 20 minutes). At CC, a customer walks in 30 minutes (with a standard deviation of 0.5 hour). WC has a staff of 2 doctors, while CC has 1 doctor. A typical service time at either clinic lasts 20 minutes (with a standard deviation of 20 minutes). Answer the following questions. Round your answers to TWO decimal places when necessary. In WC, the average amount of time a patient waits in line before he/she can see a doctor equals In CC, the total time a patient needs to spend to see a doctor equals When the arrival rate for WC changes to 5 [patients/hr], the new waiting time at WC becomes

In WC, how long does a patient wait in line before he/she can see a doctor? CVa for WC=20/20=1 CVp=20/20=1 m=2 Service time p=20 min. Arrival rate for WC=3 patients/hour. Total service rate (60/20)*2 = 6 patients/hour. Thus, utilization = 3/6 = 0.5. Tq = 20/2 * 0.5^(sqrt(2*(2+1))-1) / (1-0.5) * (1^2 + 1^2)/2 = 7.32 min. In CC, what is the total time a patient needs to spend to see a doctor? CVa for CC=30/30=1 CVp=1 m=1 (use single-server formula) Arrival rate=2 patients/hour; service time p=20min; service rate = 3 patients/hr. Thus, utilization U=arr rate/ser rate=2/3=0.67, and Tq = 20/1 * 0.67^(sqrt(2*(1+1))-1) / (1-0.67) * (1^2 + 1^2)/2 = 40 min. T=Tq+p=40+20=60 min When the arrival rate for WC changes to 5 patients/hour, what is the new waiting time at WC? Assume that the coefficient of variation of customer inter-arrival times is still 1, and WC still staffs 2 doctors in total. New arrival rate = 5 patients/hour, and total service rate is still (60/20)*2 = 6 patients/hour. Thus, utilization = 5/6 = 0.8333. Tq = 20/2 * 0.8333^(sqrt(2*(2+1))-1) / (1-0.8333) * (1^2 + 1^2)/2 = 46.07 min.

Which of the following control charts indicates that the process is in control?

In between lines on top and bottom. not touching, completely in between

Which of the following is NOT an assumption of the EOQ model?

It is possible to receive a purchase discount if the order quantity is sufficiently large The EOQ assumes there are no purchase quantity discounts.

You measure the exact size of 100 ping pong balls from manufacturer A and then another 100 balls from manufacturer B. The balls of manufacturer B have a much larger variation. Means and specification limits for the two manufacturers are identical. Which of the two manufacturers has a higher process capability index?

Manufacturer A

Consider a product meeting newsvendor assumptions. The unit purchase cost is $140. For each sold unit, you earn a profit of $60. For each leftover, you lose $20. The demand distribution is shown in the table below. Demand 20 40 60 80 100 120 Prob. 0.1 0.15 0.22 0.2 0.25 0.08 We apply the newsvendor model to solve the following questions. The selling price is The salvage value is The newsvendor critical ratio equals Calculate the cumulative probability and then find the optimal order quantity Q* as (If there is no Q* with the cumulative probability matching exactly with the critical ratio, round up and find the first quantity such that its cumulative probability exceeds the critical ratio.) If you order Q=80 units, the expected profit Do not use the Q* you get from (b) If the critical ratio becomes 90% and assumine that the purchase cost and salvage value does not change, the selling price change to 320 The new optimal order quantity Q* under this ratio is (Samee as in b, if there is no Q* with the cumulative probability matching exactly with the critial ratio, round up and find the first quantity such that its cumulative probability exceeds the critial ratio.)

Purchasing cost C = 140, per unit profit = 60 = selling price - C. So selling price = 200. C - salvage value = 20. So salvage value = 120. Critical ratio = (200 - 140) / (200 - 120) = 0.75. The cumulative probability is filled in the last row of the table below. From the table, 0.92 is the smallest number that is larger than the ratio=0.75. Thus, Q* = 100 units. Demand 20 40 60 80 100 120 Prob. 0.1 0.15 0.22 0.2 0.25 0.08 Cum. Prob. 0.1 0.25 0.47 0.67 0.92 1 Expected Sales = 0.1 * 20 + 0.15 * 40 + 0.22 * 60 + (0.2+0.25+0.08) * 80 = 63.6 Expected Leftover = 80 - 63.6 = 16.4 Expected Profit = 60 * 63.6 - 20 * 16.4 = 3816 - 328 = $3488 Denote the selling price as R. We have that (R - 140) / (R - 120) = 0.9. So, R - 140 =(R - 120) * 0.9 = 0.9R - 108. This gives 0.1R = 32, or R = $320. The optimal quantity is still 100 units since the cumative probability for Q=100 is 0.92, which is the first number that exceeds the critical ratio of 0.9.

Consider the same newsvendor setting as in Problem 1. That is, the unit purchase cost is $140. For each sold unit, you earn a profit of $60. For each leftover, you lose $20. However, the demand now follows a normal distribution with mean 75 and standard deviation 30. The newsvendor critical ratio equals 0.75 The optimal order quantity Q* under this normal demand distribution is If you order Q=100 units, the expected profit

Purchasing cost C = 140, per unit profit = 60 = selling price - C. So selling price = 200. C - salvage value = 20. So salvage value = 120. Critical ratio = (200 - 140) / (200 - 120) = 0.75. The z-value for the critical ratio is 0.68. Q*= mean + Zratio * std = 75+0.68*30=95.4 ~96 [units] c. Note that Q changes to 100 units here, and we need to use this new Q to re-calculate the corresponding z value, that is, z = (Q - mean)/std = (100-75)/30 = 0.83. (This is from transforming the formula Q = mean + z ratio*std.) L(Zratio) = L(0.83) = 0.1140 (you can use the loss function table I provided to you. ) E[loss sale]= 30*0.1140= 3.42 Expected Sales = Mean demand - E[loss sale] = 75- 3.42 = 71.58 Expected Leftover = 100 - 71.58 = 28.42 Expected Profit = 60 * 71.58 - 20 * 28.42 = $3726.4

Sarah is a buyer for a department store. A supplier offers her a 5 percent discount if she triples her usual order quantity. Which of the following best explains why Sarah should take the deal?

Sarah knows that even though she may triple her order quantity, this would increase her operating costs by far less than a factor of three Choice A suggests that the store would lose money on the deal, which is not a good justification for the deal. Choice B is too speculative. Choice D is incorrect - even if operating costs (inventory holding and ordering costs) are small relative to the purchase cost, they should not be ignored. Choice C is correct - large changes in the order quantity generally do not create large changes in operating costs.

A new backpack that has a zipper which is broken due to a supplier problem is indicative of a quality problem resulting from assignable cause variations.

True

A process capability index of 2 means that the upper and lower specification limits of the process are six standard deviations above and below the mean respectively.

True A process capability index of 2 means that the upper (lower) specification limit is six standard deviations above (below) the mean

Consider the following call center with one agent. The parameters of this call center is given in the above chart. "a" stands for the average inter-arrival time, and "p" stands for the mean service time of the agent in this call center. CVa and CVp are estimated from data and are provided to you. a= 5min/cust 1/a = 12 cust/hr CVa = 1 (given) p= 4.5min/cust 1/0= 13.33 cust/hr CVp = 1.39 (given)

Utilization = 90% (4.5/5) Waiting time in queue (Tq) = 59.38 Inventory in queue = 11.88 Total Inventory = 12.78

John is a newly minted quality engineer at MakeStuff Inc. His boss tells him to increase the process capability index of their main product. John is somewhat lazy and does not want to tackle the variation in the process, so he decides to simply increase the upper specification limit and reduce the lower specification limit. Does this increase the process capability index?

Yes, it does, though one might question if the underlying process is really better.

Millennium Liquors is a wholesaler of sparkling wines. Its most popular product is the French Bete Noire, which is shipped directly from France. Weekly demand is 40 cases. Millennium purchases each case for $110, there is a $350 fixed cost for each order (independent of the quantity ordered), and its annual holding cost is 25 percent. What order quantity minimizes Millennium's annual ordering and holding costs?2 b.If Millennium chooses to order 300 cases each time, what is the sum of its annual ordering and holding costs? c.If Millennium chooses to order 75 cases each time, what is the sum of the ordering and holding costs incurred by each case sold? d.If Millennium is restricted to ordering in multiples of 50 cases (e.g., 50, 100, 150, etc.), how many cases should it order to minimize its annual ordering and holding costs? e.Millennium is offered a 5.00 percent discount if it purchases at least 1,000 cases. If it decides to take advantage of this discount, what is the sum of its annual ordering and holding costs?

a. 230. Sqrt (2 × 350 × 2,080) / (110 × 0.25) = 230 b. 6,551.67. Orders per year = 2,080 annual cases / 300 = 6.93 orders. Annual order cost = 6.93 × $350 = $2,426.67. Annual holding cost = 0.5 (300 × 110 × 0.25) = $4,125.00.Annual order + holding costs = 2,426.67 + 4,125.00 = $6,551.67. c. 5.16. Orders per year = 2,080 annual cases / 75 = 27.73 orders. Annual order cost = 27.73 × $350 = $9,706.67. Annual holding cost = 0.5 (75 × 110 × 0.25) = $1,031.25.Annual order + holding costs = 9,706.67 + 1,031.25 = $10,737.92. Annual order + holding costs per case = $10,737.92 / 2,080 cases = $5.16 d. 250. The order size of 250 is the quantity that is the multiple of 50 that leads to the lowest cost. e. $13,790.50. Orders per year = 2,080 annual cases / 1,000.00 = 2.08 orders. Annual order cost = 2.08 × $350 = $728.00. Annual holding cost = 0.5 (1,000.00 × 104.50 × 0.25) = $13,062.50.Annual order + holding costs = 728.00 + 13,062.50 = $13,790.50.

Millennium Liquors is a wholesaler of sparkling wines. Its most popular product is the French Bete Noire, which is shipped directly from France. Weekly demand is 40 cases. Millennium purchases each case for $110, there is a $350 fixed cost for each order (independent of the quantity ordered), and its annual holding cost is 25 percent. a.What order quantity minimizes Millennium's annual ordering and holding costs?230 b.If Millennium chooses to order 300 cases each time, what is the sum of its annual ordering and holding costs?$6,551.55 c.If Millennium chooses to order 75 cases each time, what is the sum of the ordering and holding costs incurred by each case sold?$5.16 d.If Millennium is restricted to ordering in multiples of 50 cases (e.g., 50, 100, 150, etc.), how many cases should it order to minimize its annual ordering and holding costs?250 e.Millennium is offered a 5.00 percent discount if it purchases at least 1,000 cases. If it decides to take advantage of this discount, what is the sum of its annual ordering and holding costs?

a. 230. Sqrt (2 × 350 × 2,080) / (110 × 0.25) = 230 b. 6,551.67. Orders per year = 2,080 annual cases / 300 = 6.93 orders. Annual order cost = 6.93 × $350 = $2,426.67. Annual holding cost = 0.5 (300 × 110 × 0.25) = $4,125.00.Annual order + holding costs = 2,426.67 + 4,125.00 = $6,551.67. c. 5.16. Orders per year = 2,080 annual cases / 75 = 27.73 orders. Annual order cost = 27.73 × $350 = $9,706.67. Annual holding cost = 0.5 (75 × 110 × 0.25) = $1,031.25.Annual order + holding costs = 9,706.67 + 1,031.25 = $10,737.92. Annual order + holding costs per case = $10,737.92 / 2,080 cases = $5.16 d. 250. The order size of 250 is the quantity that is the multiple of 50 that leads to the lowest cost. e. $13,790.50. Orders per year = 2,080 annual cases / 1,000.00 = 2.08 orders. Annual order cost = 2.08 × $350 = $728.00. Annual holding cost = 0.5 (1,000.00 × 104.50 × 0.25) = $13,062.50.Annual order + holding costs = 728.00 + 13,062.50 = $13,790.50.

Joe Birra needs to purchase malt for his microbrewery production. His supplier charges $35 per delivery (no matter how much is delivered) and $1.30 per gallon. Joe's annual holding cost per unit is 35 percent of the price per gallon. Joe uses 300 gallons of malt per week. Suppose Joe orders 1000 gallons each time. What is his average inventory (in gal)?500selected answer correctgallons b.Suppose Joe orders 2000 gallons each time. How many orders does he place with his supplier each year?7.80 c.How many gallons should Joe order from his supplier with each order to minimize the sum of the ordering and holding costs?1,549 d.Suppose Joe orders 2250 gallons each time he places an order with the supplier. What is the sum of the ordering and holding costs per gallon?$0.166 e.Suppose Joe orders the quantity from part (c) that minimizes the sum of the ordering and holding costs each time he places an order with the supplier. What is the annual cost of the EOQ expressed as a percentage of the annual purchase cost?3.48 f.If Joe's supplier only accepts orders that are an integer multiple of 1000 gallons, how much should Joe order to minimize ordering and holding costs per gallon?2,000 g.Joe's supplier offers a 3.00 percent discount if Joe is willing to purchase 8000 gallons or more. What would Joe's total annual cost (purchasing, ordering, and holding) be if he were to take advantage of the discount?

a. 500. Average inventory = 1000 × 0.5 = 500 b. 7.80. Orders = (300 per week × 52 weeks) / 2,000 = 7.80 c. 1,549. Order size = Sqrt (2 × 35 × 300 × 52) / (1.30 × 0.35) = 1549 d. $0.0484. (300 per week × 52 weeks) / 2,250 = 6.93 orders. Annual order cost = 6.93 × $35 = $242.67. Annual holding cost = 0.5 (2,250 × 1.30 × 0.35 ) = $511.88.Annual order + holding costs = 242.67 + 511.88 = $754.54. (Annual order + holding costs) / annual demand = cost per gallon. $754.54/ 15,600 = $0.0484 e. 3.48%. (300 per week × 52 weeks) / 1,549 = 10.07 orders. Annual order cost = 10.07 × $35 = $352.44. Annual holding cost = 0.5 ([1,549 × 1.30 × 0.35) = $352.44.Annual order + holding costs = 352.44 + 352.44 = $704.88. Annual purchase cost = $1.30 × 15,600 = $20,280. $704.88 Annual order + holding costs / $20,280 = 3.48% f. 2,000. From part c the EOQ = 1,549. For 1,000 order quantity, Annual order cost = 15.60 orders × $35 = $546.00. Annual holding cost = 0.5 (1,000 × 1.30 × 0.35) = $227.50.Annual order + holding costs = 546.00 + 227.50 = $773.50.For 2,000 order quantity, Annual order cost = 7.80 orders × $35 = $273.00. Annual holding cost = 0.5 (2,000 × 1.30 × 0.35) = $455.00.Annual order + holding costs = 273.00 + 455.00 = $728.00. An order size of 2,000 has the lowest annual order + holding costs. g. 21,505. For 8,000 order quantity, Annual order cost = (15,600 / 8,000) orders × $35 = $68.25. Annual holding cost = 0.5 (8,000 × 1.26 × 0.35) = $1,765.40.Annual order + holding costs + purchasing cost = 68.25 + 1,765.40 + 19,671.60 = $21,505.

Monsanto sells genetically modified seed to farmers. It needs to decide how much seed to put into a warehouse to serve demand for the next growing season. It will make one quantity decision. It costs Montanso $7 to make each kilogram (kg) of seed. It sells each kg for $46. If it has more seed than demanded by the local farmers, the remaining seed is sent overseas. Unfortunately, it only earns $3 per kg from the overseas market (but this is better than destroying the seed because it cannot be stored until next year). If demand exceeds its quantity, then the sales are lost—the farmers go to another supplier. As a forecast for demand, it will use a normal distribution with a mean of 325,000 and a standard deviation of 100,000. How many kilograms should Montanso place in the warehouse before the growing season? b.If Montanso put 375000 kgs in the warehouse, what is its expected revenue (include both domestic revenue and overseas revenue)? c.How many kilograms should Montanso place in the warehouse to minimize inventory while ensuring that the stockout probability is no greater than 5%? Use Table 13.4 and round-up rule. d.What is maximum profit for this seed?

a. We have Cu = 46 − 7 = 39 and Co = 7 − 3 = 4. This gives the critical ratio of 39 / (39 + 4) = 1. Using Table 13.4 and the round-up rule, this corresponds to z = 1. The optimal order quantity is 325,000 + 1 × 100,000 = 465,000. b. An order quantity of 375,000 corresponds to z = (375,000 − 325,000) / 100,000 = 0. Using Table 13.4, we have that the expected left-over inventory is 1 × 100,000 = 69,780. The expected sales are 375,000 − 69,780 = 305,220. So, the expected revenue is 46 × 305,220 + 3 × 69,780 = 14,249,460 c. A 5% stockout probability corresponds to a 1 in-stock probability. According to Table 13.4, this requires z = 2. This yields an order quantity of 325,000 + 2 × 100,000 = 495,000. d. The maximum profit is (46 − 7) × 325,000 = 12,675,000.

Additional capacity and time-to-market. Pharma Dev is considering leasing an additional development center to shorten the time to market of patented products. If this center is used in addition to the three centers, how will the total time-to-market (waiting time plus development time) of a patented product change?

decrerase

A firm evaluates its EOQ quantity to equal 180 cases, but it chooses an order quantity of 200 cases. Relative to the order quantity of 180 cases, the order quantity of 200 cases has

lower ordering cost and higher holding cost The ordering cost decreases with the order quantity and the holding cost increases with the order quantity.

An X⎯⎯⎯X¯ chart has __________ on the x-axis and _____________ on the y-axis.

time periods at which samples are taken, sample means