VIEWS: 6 PAGES: 31 POSTED ON: 8/31/2012 Public Domain
First 3 minutes Having read Anglesea Cabins and Humboldt Oysters case consider the following common questions. What • is the marginal upside profit for a unit? • is the marginal downside cost of a unit? • things can you control? • things can’t you control? • concepts/elements of the course are applicable? Theme: Coping with Uncertain Demand Anglesea Cabins Humboldt Oysters Upside Downside Control Uncontrolled technique Theme: Coping with Uncertain Demand Topics Covered Today • Anglesea Cabins Case • Normal distribution AWZ 6.2 • Humboldt Oysters Case Anglesea Cabins The problem. Cnx They call up I decide Uncertain profit of $200 times x. Anglesea Cabins Current policy. • If C≤11 take n=C bookings • If C>11, take n=11 bookings • What is the chance of a “show”? • X is binomial n=11, p=0.8 Uncertain profit of $200 times x. Anglesea Cabins When they take 11 bookings: Profit =200 X X has mean value np=110.8=8.8 Mean Profit =200 8.8 = $1760 1760 20% loss 2200 What does the payoff table look like? Anglesea Cabins When they take 11 bookings: TAKE n=11 BOOKINGS Shows(x) Prob Profit 0 $0 1 $200 2 $400 3 $600 4 $800 5 $1,000 6 $1,200 7 $1,400 8 $1,600 9 $1,800 Bino(11,0.8) 10 $2,000 11 $2,200 Anglesea Cabins When they take 11 bookings: TAKE n=11 BOOKINGS Shows(x) Prob Profit 0 0.0000 $0 1 0.0000 $200 2 0.0000 $400 3 0.0002 $600 4 0.0017 $800 5 0.0097 $1,000 6 0.0388 $1,200 7 0.1107 $1,400 8 0.2215 $1,600 9 0.2953 $1,800 10 0.2362 $2,000 11 0.0859 $2,200 SIMULATE CASE Anglesea Cabins When they take 12 bookings: • What is the payoff table? • What is the mean profit? How does this compare to the previous profit? • What is the chance of being under/over? Have you gone far enough? 31% 1760 1899 2200 20% loss anglesea_inclass.xls Anglesea Cabins Why did I fix the number of calls C? What about low demand seasons? What if demand increases? What about loss of customers? What if Regal is full? Other issues? Normal Distribution The normal distribution • is used in market research, quality control (also in testing theory eg: GMAT) • describes error in many industrial processes • describes distribution of human features • is the basis of inferential statements based on regression output • is a continuous distribution What is the probability of being 180cm tall? Normal Distribution Continuous distributions described by a curve. Areas under curve represent probabilities. Normal Distribution The normal distribution defined by its mean μ – centre of the distribution standard deviation σ – spread of distribution Bell like shape calculus tables computer/XL Normal Distribution Any normal variable is within 1 σ of μ 68% of time 2 σ’s of μ 95% of time 3 σ’s of μ 99.75% of time calculus tables computer/XL Standard Normal Distribution The standard normal distribution is the normal distribution with mean 0 and std. deviation 1 Non-standard normal variable can be made standard normal variable by X Z Z measures how many std.dev’s above or below the mean you are. Standard Normal Distribution The standard normal distribution is the normal distribution with mean 0 and std. deviation 1 NORMSDIST(z) z Normal Distribution Computing Probabilities Step 1: Convert question about variable X into a question about standard normal variable Z. Step 2: Draw a diagram* of the area you require and express it in terms of areas to the left of z. Step 3: Use NORMSDIST to obtain these areas. Java Demo * The curve is symmetric about 0 and total area is 1. Normal Distribution Graduate students sitting GMAT have scores that are normally distributed with mean 570 and standard deviation 60. What is the chance someone scores over 700? Let X be the GMAT score. Normal (570,60) Z = (X-570)/60 is standard normal. X 700 Z 700 570 / 60 2.1666 Normal Distribution Graduate students sitting GMAT have scores that are normally distributed with mean 570 and standard deviation 60. What is the chance someone scores over 700? Let X be the GMAT score. Normal (570,60) Z = (X-570)/60 is standard normal. Pr( X 700) Pr( Z >2.166) Normal Distribution Graduate students sitting GMAT have scores that are normally distributed with mean 570 and standard deviation 60. What is the chance someone scores over 700? Let X be the GMAT score. Normal (570,60) Z = (X-570)/60 is standard normal. Normal Distribution Graduate students sitting GMAT have scores that are normally distributed with mean 570 and standard deviation 60. What is the chance someone scores over 700? Let X be the GMAT score. Normal (570,60) Z = (X-570)/60 is standard normal. Pr Z 2.166 1 NORMSDIST 2.166 1 0.9849 0.0151 Normal Distribution Graduate students sitting GMAT have scores that are normally distributed with mean 570 and standard deviation 60. What is the probability that someone scores between 500 and 700? X 500 Z 500 570 / 60 1.1666 Pr(500 X 700) Pr(1.167 Z 2.167) Normal Distribution Pr(500 X 700) Pr(1.167 Z 2.167) Pr(Z 2.167) Pr(Z 1.167) Normal Distribution Graduate students sitting GMAT have scores that are normally distributed with mean 570 and standard deviation 60. What is the probability that someone scores between 500 and 700? Pr 1.167 Z 2.167 Pr Z 2.167 Pr Z 1.167 NORMSDIST 2.167 NORMSDIST 1.167 0.9849 0.1216 0.8633. Humboldt Oysters • What is the distribution of unknown demand D? What does it mean in simple language? -$5.35 $2.45 Humboldt Oysters • What is the distribution of unknown demand D? What if I set n=12150 production? -$5.35 $2.45 Humboldt Oysters • What is the distribution of unknown demand D? What if I set n=12150 production? • What is probability that I sell it and make $2.45? Use Excel and link so that you can change the 12150 policy. • Calculate the mean profit on the last item. Outcome Chance Profit Sell $2.45 Don’t sell -$5.35 Class exercise Normal Distribution Graduate students sitting GMAT have scores that are normally distributed with mean 570 and standard deviation 60. The top 1% of students score over what GMAT score? Use 2.33 for 1% percentiles. Use 1.65 for 5% percentiles. Use 1.28 for 10% percentiles. Use 0.68 for 25% percentiles (quartiles). Class exercise Normal Distribution Graduate students sitting GMAT have scores that are normally distributed with mean 570 and standard deviation 60. The top 1% of students score over what GMAT score? Normal variable is 2.33 std.dev’s above mean with probability 1%. For GMAT, 2.33 std.dev’s above mean is 570+2.32660=709.6. ANSWER is 710. Humboldt Oysters Demand will exceed what value with probability 99%. What production level should I set to be 90% sure of selling everything? KEY TAKE AWAYS FROM CLASS •In judging the level of production, two key quantities are the profit of selling the last unit and the loss incurred in not selling it. •The normal distribution is a continuous distribution. • Problems can always be translated to one involving standard normal probabilities. • Excel: NORMSDIST(x) – prob less than x NORMSDIST(z) – for standard normal