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exam 3 - chapter 12
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Terms in this set (27)
newsvendor model implementation steps
1.
2.
3.
4.
1. generate demand model
-distribution function that reflects possible demand outcomes
2. gather economic inputs
-selling price/ production costs/ salvage value
3. choose objective
-profit/in-stock probability
4. choose quantity to order
demand model definition
possible demand outcomes
possibility of those outcomes
which type of distribution is easier to work with gamma or normal?
normal
-easily manipulated
when do we use poisson distributions?
slow moving units
only stays positive
difference between density function and distribution function
density
- probability of specific/exact outcome occurring
distribution
- probability of outcome at particular value OR SMALLER
why do we prefer distribution functions over density functions?
1.
2.
3.
1. usually we don't want to isolate singe values when looking at probabilities
2. density functions can take all kinds of shapes
-but we want bell curves
3. distribution functions ALWAYS start low and increase towards zero
draw the two graphs (one for distribution, one for density) that show two ways to describe the same demand model (look at bookmark)
...
All normal distributions are related to the standard normal that has mean = ? and standard deviation = ?.
All normal distributions are related to the standard normal that has mean = 0 and standard deviation = 1.
example problem:
Let Q be some quantity, and (m, s) the parameters of the normal distribution used to model demand.
Prob{demand is Q or lower} = ???
Prob{the outcome of a standard normal is z or lower}, where
z = Q - u(mean) / SD
OR
Q = U(mean) + z * SD
how to find z in excel?
normsdist(z)
How to start with a quantity and find the corresponding probability?
Q: What is the probability the outcome of a standard normalwill be z = 0.28 or smaller?
Look for the intersection row with the header 0.2 and the column with the header 0.08 (0.2+0.08 = 0.28), which is the z value.
A: The answer is 0.6103, which can also be written as 61.03%
How to start with a probability and find the corresponding quantity?
Q: For what z is there a 70.19% chance that the outcome of a standard normal will be that z or smaller?
Find the probability inside the table.Add the row and column headers for that probability
A: the answer is z = 0.53
newsvendor model: develop a demand model
given forecast, actual demand, error, and A/F ratio;
-how do you calculate error
-how do you calculate A/F ratio
-what does it mean if error is negative
-what does it mean if error is positive
-what does it mean if A/F ratio > 1
-what does it mean if A/F ratio < 1
-what does it mean if A/F ratio = 1
error = forecast - actual demand
A/F ratio = actual demand / error
negative error = underforcasted
positive error = over-forecasted
A/F > 1 --> under-forcasted
A/F < 1 --> over-forecasted
A/F = 1 --> perfect forecast and actual demand line
newsvendor model: develop a demand model
-steps to choose normal distribution for demand model
1.
1. use initial forecast given for product
2. evaluate A/F ratios of historical data
-get the average and standard deviation
3. set the mean of the normal distribution = expected actual demand = average A/F ratio x initial forecast amount
4. set standard deviation of normal distrubtion
standard deviation of actual demand = SD of A/F ratio x initial forecast amount
newsvendor model: order quantity that maximizes expected profit
Co = ?
-give definition as well
Cu = ?
-give definition
balancing the risk and benefit of ordering a unit
- as more units are ordered, what is the relationship between expected benefit of ordering one more vs. expected loss of ordering one more?
Co = overage cost (cost - salvage value)
-increase in profit enjoyed if ordered one fewer unit
Cu = underage cost (price - cost)
-increase in profit enjoyed if ordered one more unit
as more units are ordered, the expected benefit from ordering one unit decreases while the expected loss of ordering one more unit increases
newsvendor model: order quantity that maximizes expected profit
to maximize expected profit:
-what equation do we use?
we want the expected loss on Qth unit = expected gain on Qth unit
Co x F(Q) = Cu x (1 - F(Q))
F(Q) = Cu / (Co + Cu) --> critical ratio
newsvendor model: order quantity that maximizes expected profit
once we get the critical ratio, what do we do?
1.
2.
hint: round-up rule
1. given critical ratio, use the Stndrd Normal Distribution Function table to find the z-statistic
round-up rule: if the ratio falls between two z values, chose the greater one
2. convert z-statistic into order quantity
Q (quantity) = mean + z-stat * standard deviation
The Newsvendor Model: Performance Measures
In-stock probability:
Stockout probability:
In-stock probability: Probability all demand is satisfied
Stockout probability: Probability some demand is lost
In-stock probability
-All demand is satisfied if demand is ??
the order quantity, Q, or smaller.
If Q = 3000, then to satisfy all demand, demand must be 3000 or fewer.
Evaluate the in-stock probability
What is the in-stock probability if given order quantity / mean / SD?
find the z-statistic
look up z-stat on table --> find correct percentage
Evaluate the stockout probability
Some demand is not satisfied if ??
Stockout probability =
demand exceeds the order quantity
1 - F(Q) (already solved for in in-stock)
Choose Q subject to a minimum in-stock probability
Suppose we wish to find the order quantity for the Hammer 3/2 that minimizes left over inventory while generating at least a 99% in-stock probability.
steps?
1.
2.
Step 1: Find the z-statistic that yields the target in-stock probability (which is given as 99%)
Choose z = 2.33 to satisfy our in-stock probability constraint
Step 2: Convert the z-statistic into an order quantity for the actual demand distribution.
use the equation Q = u + z * SD --> answer
Other measures of service performance
two definitions of fill-rate
fill-rate is not the same as .......
if 99% of demand is satisfied (___________) then the probability all demand is satisfied (__________)need not be 99%
fraction of demand that can purchase a unit
probability a randomly chosen customer can purchase a unit
in-stock probability
if 99% of demand is satisfied (the fill rate --> after sales probability value) then the probability all demand is satisfied (the in-stock --> prior to sales probability) need not be 99%
The Newsvendor Model: Performance Measures
Expected lost sales:
Expected sales:
Expected left over inventory:
expected number of units by which demand will exceed the order quantity
expected number of units sold
expected number of units left over after demand (but before salvaging)
calculate expected lost sales given Q
1.
2.
3.
1. normalize the order quantity to find its z-statistic
use the z-stat equation: Q - u / SD
2. look up z-stat in Standard Normal LOSS Table to find L(z) value
3. pull values into expected lost sales equation
= sd * L(z)
given expected lost sales, you can calculate the rest
ie. expected sales
expected left over inventory
expected profit
--we can use same steps if we already found out max order quantity Q--
...
Newsvendor model summary
model can be applied to settings in which
1.
2.
Firm must have a demand model that includes
1.
2.
With the normal distribution, uncertainty in demand is captured with ??
At the order quantity that maximizes expected profit the probability that demand is less than the order quantity equals ??
1. demand uncertain
2. too much too little challenge
1. expected demand
2. uncertainty in that demand
the standard deviation parameter.
critical ratio
-The expected profit maximizing order quantity balances the "too much-too little" costs.
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