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Chapter 4: Q. 9OQ (page 545)

Sally鈥檚 Silk Screening produces specialty T-shirts that are primarily sold at special events. She is trying to decide how many to produce for an upcoming event. During the event, Sally can sell T-shirts for \(20 apiece. However, when the event ends, any unsold T-shirts are sold for \)4 apiece. It costs Sally $8 to make a specialty T-shirt. Sally鈥檚 estimate of demand is the following:

Demand

Probability

300

.05

400

.10

500

.40

600

.30

700

.10

800

.05

a. What is the service rate (or optimal fractile)?

Short Answer

Expert verified

The profit function and the optimal fractile formula The conventional newsvendor profit function is where is a random variable with a probability distribution indicating demand, each unit is sold and purchased for a price, is the number of units supplied, and is the expectation operator.

Step by step solution

01

Step 1:Calculation of Service rate (or Optimalfractile)

Given,

The selling price of a T shirt is $20 each

Cost price for making a specialty T shirt is $ 4

Unsold T shirts are sold for $ 4 each

Costofunderstocking=$20-$8=$12Costofoverstocking=$8-$4=$4

Service rate=Cost of under stockingCost of understocking + Cost of overstocking=1212+4=0.75

So, the service rate or optimal fractile is 0.75

02

Calculation of number of T-shirts that should be produced for an upcoming event

Demand

Probability

Cumulative Probability

300

0.05

0.05 =0.05

400

0.10

0.05+.010 = 0.15




500

0.40

0.05+.010+0.40 = 0.55

600

0.30

0.05+.010+0.40+0.30 = 0.85

700

0.10

0.05+.010+0.40+0.30+0.10 =0.95

800

0.05

0.05+.010+0.40+0.30+0.10+0.05 = 1

So, the number of T-shirts that should be produced for the upcoming eventis 600.

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Most popular questions from this chapter

Prepare an aggregate plan for the coming year, assuming that the sales forecast is perfect. Use the spreadsheet 鈥淏radford Manufacturing.鈥� In the spreadsheet, an area has been designated for your aggregate plan solution. Supply the number of packaging lines to run and the number of overtime hours for each quarter. You will need to set up the cost calculations in the spreadsheet. You may want to try using the Excel Solver to find a solution. Remember that your final solution needs an integer number of lines and an integer number of overtime hours for each quarter. (Solutions that require 8.9134 lines and 1.256 hours of overtime are not feasible.)

CU, Incorporated, (CUI) produces copper contacts that it uses in switches and relays. CUI needs to determine the order quantity, Q, to meet the annual demand at the lowest cost. The price of copper depends on the quantity ordered. Here are price-break and other data for the problem:

Price of copper

\(0.82 per pound up to 2,499 pounds

\)0.81 per pound for orders between 2,500 and 5,000 pounds \(0.80 per pound for orders greater than 5,000 pounds

Annual demand

50,000 pounds per year

Holding cost

20 percent per unit per year of the price of the copper

Ordering cost

\)30

Which quantity should be ordered?

Historical demand for a product is:

Month

Demand

January

12

February

11

March

15

April

12

May

16

June

15

a. Using a weighted moving average with weights of 0.60, 0.30, and 0.10, find the July forecast.

b. Using a simple three-month moving average, find the July forecast.

c. Using single exponential smoothing witha= 0.2 and a June forecast =13, find the July forecast. Make whatever assumptions you wish.

d. using simple linear regression analysis, calculate the regression equation for the preceding demand data.

e. using the regression equation in d, calculate the forecast for July.

Gentle Ben鈥檚 Bar and Restaurant uses 5,000-quart bottles of imported wine each year. The effervescent wine costs \(3 per bottle and is served only in whole bottles because it loses its bubbles quickly. Ben FIgures that it costs \)10 each time an order is placed, and holding costs are 20 percent of the purchase price. It takes three weeks for an order to arrive. Weekly demand is 100 bottles (closed two weeks per year) with a standard deviation of 30 bottles. Ben would like to use an inventory system that minimizes inventory cost and will provide a 95 percent service probability.

a. What is the economic quantity for Ben to order?

b. At what inventory level should he place an order?

Not all the items in your office supply store are evenly distributed as far as demand is concerned, so you decide to forecast demand to help plan your stock. Past data for legal-sized yellow tablets for August are

Week 1

300

Week 2

400

Week 3

600

Week 4

700

  1. Using a three-week moving average, what would you forecast the next week to be?
  2. Using exponential smoothing witha =0.20, if the exponential forecast for week 3 was estimated as the average of the first two weeks [(300 + 400)/2 = 350], what would you forecast week 5 to be?
See all solutions

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