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SCMA 331 – Fall 2020 Homework 3 Teamwork: Homework Can Be Prepared By A Team Of Two Students

. Each team should submit only one report. Provide team member names in alphabetical order at the top of the submitted report.

 

Submissions: Homework report must be submitted via Canvas as a single electronic file in formats such as pdf, word, etc. You can submit the pdf scan of a hand-written document. (Do not submit the pictures of your homework report as multiple separate jpeg files. Make sure to merge all your pages in a single file).  Make sure your document is clear and legible. LATE submissions will NOT be graded. Make sure you submit the correct file. Any update/re-submission/change after the deadline will NOT be accepted. 

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Question 1 (35 pts): Daily demand for ground coffee at a Whole Foods store is normally distributed with a mean of 100 pounds (lbs) and a standard deviation of 50 pounds. Store manager continuously monitors the inventory of coffee and currently orders 1,000 lbs of coffee each time the inventory drops to 410 lbs. Whole Foods’s coffee supplier BlackBean takes 4 days to fill an order (every time 4 days, no variation).

 

1. (5 pts): How much safety inventory does the store carry with the current inventory policy?
2. (10 pts): What service level does the store achieve with the current policy?
3. (5 pts): On average, how many pounds of ground coffee are there in the store? 
4. (5 pts): On average, how many days does a pound of coffee sit in the store before being sold? 
5. (10 pts): If the store would like to have a 99% service level, what should the reorder point be?

 

 

 

 

 

 

 

 

 

 

 

Question 2 (35 pts): Joe Brown is the owner of Smiling Flowers shop in downtown Lincoln. Joe needs to decide on the number of roses to order from his supplier before the Valentine’s Day.   Joe buys each rose from the supplier at $4 per a rose and sells a rose at a price of $9 per rose. At this price, the anticipated demand is normally distributed with a mean of µ = 100 roses and a standard deviation of σ = 40 roses. Any leftover rose at the end of Valentine’s Day will be sold at a discounted price of $1 per rose. Assume that each customer demands one rose.

 

Note: The questions in sections (a)  to (e) below are independent. That is, in each section use the information given above unless otherwise is stated in that specific section. For instance, in section (b) demand information is given as uniform distribution. In this section use this uniform distribution info. However in the remaining sections, use the demand information of normal distribution as given in the original question above.

 

1. (7 pts): Given the information above, how many roses should Joe order before the Valentine’s Day?

 

 

2. (7 pts): If the anticipated demand had a uniform distribution between 100 and 200, how many roses would Joe order before the Valentine’s Day?

 

 

3. (7 pts): Suppose a customer who is unable to purchase a rose (due to stock out at Smiling Flowers), settles for buying a daisy bouquet. A bouquet sells for $10 and costs Smiling Flowers $8 each. Smiling Flowers never runs out of bouquets. In this case, how many roses would Joe Brown order before the Valentine’s Day?

 

 

4. (7 pts): Suppose it costs $1 to hold a rose in the inventory for the selling season. This holding cost is incurred only for the roses that are not sold by the end of Valentine’s Day. In this case, how many roses would Joe Brown order before the Valentine’s Day?

 

 

5. (7 pts): If Joe Brown orders 180 roses at the beginning of the selling season, what is the probability that Smiling Flowers will sell all the roses by the end of Valentine’s Day?

 

 

 

 

 

 

 

 

 

 

 

Question 3 (30 pts): Wilson Inc. manufactures tennis balls using an automated machine. To monitor the diameter of the tennis balls it produces, 6 samples were taken with 10 balls in each sample. Table below reports the diameter measurements in centimeters (cm) on the samples taken:

 

	Sample 1	Sample 2	Sample 3	Sample 4	Sample 5	Sample 6
Ball 1	7.525	8.340	6.803	8.759	7.234	7.947
Ball 2	7.888	8.573	8.896	7.314	7.527	8.467
Ball 3	8.405	10.064	8.787	8.940	9.268	7.278
Ball 4	8.783	7.140	8.074	8.548	9.447	8.299
Ball 5	8.563	8.175	6.829	9.066	7.578	8.689
Ball 6	8.205	8.003	6.931	8.442	7.243	8.720
Ball 7	8.737	6.010	7.764	6.264	8.101	8.536
Ball 8	8.022	10.132	6.985	8.894	7.257	8.711
Ball 9	7.422	8.633	7.671	7.924	8.880	8.176
Ball 10	7.563	7.607	6.475	7.589	7.066	6.477

 

Note: Table above is also provided in excel format on Canvas with file name Homework 3 - ExcelData 

 

1. (10 pts): Construct the appropriate three sigma control chart to monitor the average diameter in centimeters. (Report center line and controls limits. Draw the control chart and plot your sample information on the control chart. In your analysis use a precision level of 3 digits in decimal points).

Hint: To obtain sample average, ?????????, you can use excel’s =AVERAGE(.) function. To obtain sample standard deviation, s, you can use excel’s =STDEV.S() function.

 

2. (7 pts): What would be the probability of making a type I error if the control limits were set as 8.305 and 7.749?

 

3. (6 pts): Studies on the machine indicate that the diameter of the tennis balls it produces has an average of 8 centimeters (cm) and a standard deviation of 1 cm, following a normal distribution. Management determined the diameter specifications of a tennis ball as 6 cm to 11 cm. Is the machine capable of meeting these specifications?

 

4. (7 pts): Not all of the tennis balls pass the final quality control inspection. Over a period of 8 days, 100 tennis balls were sampled each day.  The table below shows the number of defective balls found in each of these samples. Construct the appropriate three-sigma control chart to monitor the proportion of the defective balls using the data given in the table below. (Find the center line and control limits – no need for the plot this time).

               Sample #            1            2            3            4            5            6            7               8

 

               # of defects        4            8            5            7            1            4            0               3