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Risk Pooling OIS 5620
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Terms in this set (73)
____ forecasts are more accurate than disaggregate forecasts.
Aggegate
Under demand uncertainty we can measure forecast accuracy using the coefficient of variation which is given by?
Std/u
Explain location pooling
combining the inventory from multiple territories/ locations into a single location
Explain order-up-to-model
is used to manage the inventory at the pooled territory. The same aggressive target in-stock probability is used for the pooled territory as is used at the individual territories
If the poisson distribution represents demand at different territories then their combined demand has a poisoon distribution with a mean that ?
equals the sum of their means.
If susan shares inventory with 2 nearby sales representatives and they all have mean demand for the InSync pacemaker of 0.29 per day then how much total demand is there across the 3
3*.29 = .87
The order up to model assumes a lead time of ?
one day and a mean demand = to all other locations
Pooling 3 locations where expected inventory at the pooled location is 5.3 and the expected inventory at each individual location is 3.4 reduces expected inventory by how much
48%. 5.3 and 3.4 were found using the Poisson distribution table.
Expected inventory in days-of-demand =
Expected inventory in units/expected daily demand
If you have expected inventory of 3.4 and expected demand per day of .29 then what is the expected inventory in days of demand
3.4/0.29 = 11.7
You found reduction in inventory investment using units. Whats another way to find it?
Using days of demand.
Adding two more territories to a pool of six has a big impact on the inventory investment?
False. Has little impact
Adding two more territories to a pool of one has a dramatic impact in inventory?
True
Location pooling generally increases inventory?
False it decreases inventory.
How to find coefficient of variation?
ratio of standard deviation to the mean
How to measure demand variability?
Find the coefficient of variation
Coefficient of variation of poisson distribution = (3 ways to find)
standard deviation/ Mean = squroot(mean)/Mean = 1/Squroot(Mean)
As the mean of a poisson distribution increases, its coefficient of variation?
decreases, that is, the poisson distribution becomes less variable. Less variable leads to less inventory
Because the coefficient of variation decreases with the sqaure root of the mean, it ?
decreases at a decreasing rate.
Every incremental increase in the mean has a proportionally _____ impact on the coefficient of variation and hence on the expected inventory investment
smaller
Little's Law depends on ____, not _____
averages; variability.
Because pooling territories reduces the variability of demand, it reduces expected inventory in the field, but it has no impact on the ?
pipeline inventory
While we can exploit location pooling to reduce inventory while maintaining a service level, we also can use location pooling to?
increase our service level.
Because in stock probability is so high, it probably makes better sense to use location pooling to ?
reduce the inventory investment rather than to increase the service level. However there may be settings where it's more desirable to increase the service level especially if its low
Location gives us many options. We can choose too (3 things)
1. maintain the same service with less inventory
2. Maintain the same inventory with a higher service,
3. reduce inventory and increase service simultaneously
If demand in the dive market is independent of demand in the surf market, then the standard deviation for the universal hammer is? given that surf hammer std is 1,181
1,181 * squarrt(2) = 1670
Q =
u + std*z
Expected profit =
(Cu
expected sales) - (Co
Expected leftover inventory)
Therefore pooling the surf and dive hammers together can potentially increase profit by? See page 57
4.4%.
Expected pooled demand =
2 * u
Std of pooled demand =
squrt(2
(1+correlation))
std
Correlation has no impact on ___ ___ but it does influence the ___ ___
expected demand; standard deviation
Coefficient of variation of pooled/aggregate demand =
squrt(1/2
(1+correlation))
(std/u)
As the correlation increases, the coefficient of variation of pooled demand _____?
increases
With perfectly positive correlation there is absolutely no benefit from inventory pooling?
True
With perfectly negative correlation, the coefficient of variation of total hammer demand is ?
0
And that means the maximum profit is
achieved at 510,720
If the demands at two locations are negatively correlated, is location pooling more effective for that or if the demands were merely independent.
More effective if demands are negatively correlated
A key benefit of universal design is the?
Reduction in demand variability
If extra product variety merely divides a fixed customer base into smaller pieces, then the demand-supply mismatch cost for each product will?
increase
Both of these strategies use a form of risk pooling that we call lead time pooling
Consolidated Distribution and Delayed Differentiation
With an 8 week lead time and a mean demand of 0.5 unit per week, the expected demand over l + 1 periods is?
(8+1) * 0.5 = 4.5
Expected Inventory =
S - Expected demand over l + 1 periods + Expected back order
The total inventory among the 100 stores would then be?
Expected Inventory * 100
retail stores on average order 0.5 units. What is standard deviation
squrt(.5) = .707
With a poisson demand, the std equals the square root of the?
mean
If demand were independent across all 100 stores then the std of total demand would be. Given std of .707
.707 * squrt(100)
If there was a positive correlation across stores then the std would be ____. with negative it would be _____
higher; lower
Using Little's Law, that pipeline inventory equals ?
0.5
100
8 = 400
Allows the retailer to avoid the second gamble
Consolidated distribution model. The retailer only needs to bet on the amount of inventory needed for the central distribution center.
In the direct-delivery model, the retailer must commit to a unit's final destination?
True
The consolidated-distribution model exploits what is often called?
lead time pooling
What is lead time pooling
Where you combine lead times for multiple inventory locations. So rather than going straight from supplier to store you go from supplier to Retail DC and then to stores. That way you have a one week lead time to stores rather than an 8 week lead time. See page 64 if you don't understand
The greater the correlation, the ____ the standard deviation of demand at the distribution center.
higher
The direct delivery model may be more attractive if the lead time is short. In example on page 67 if lead time is 3 or less the Direct model is better?
True
a strategy that uses lead time pooling to provide some of the benefits of location pooling without moving inventory far away from customers?
Consolidated distribution
is the analogous strategy with respect to product pooling that is delayed differentiation hedges the uncertainty associated with product variety without taking the variety away from customers?
Delayed differentiation
Explain delayed differentiation
Where you change form of product when you know what demand is.
Delayed differentiation is an ideal strategy when
1. customers demand many versions, variety is important
2. less uncertainty with respect to total demand than there is for individual versions
3. variety is created late in the production process
4. variety can be added quickly and cheaply
5. the components needed to create variety are inexpensive relative to the generic component
Make-to-order is generally thought to apply to a situation in which the remaining products steps from components to a finished unit are more substantial therefore involving more than a trivial delay?
True
Having 20 links is like the same as having 100?
True
a group of plants and vehicles that are connected via links
chain
The effectiveness of that configuration can be explained by the concept of?
Chaining
With risk pooling strategies, risk pooling becomes more effective as demand becomes more ____ correlated?
negatively
Negative correlation is prefered, but it doesn't mean that two negative correlated products must be produced in the same plant. It is sufficient that two negatively correlated products are produced in the same chain ?
True
Flexibility is most valuable when ?
capacity and demand are approximately equal
Whats better out of Consolidated distribution and location pooling at reducing inventory.
Location pooling, but consolidated distribution keeps inventory near customers
can increase sales and capacity utilization, but requires flexible capacity, which is probably not free and may be quite expensive
Capacity pooling
Can only be reduced by moving the inventory through the system quicker.
Pipeline inventory
Risk pooling strategies are most effective when?
demands are negatively correlated because then the uncertainty with total demand is much less than the uncertainty with any individual item/location
Coefficient of variation for the aggregate demand with no correlation=
std/(sqrt(N) * u) < std/u
4 versions of risk pooling?
1. Location pooling
2. Product pooling
3. Delayed differentiation
4. Capacity pooling
flexibility is least valuable when capacity is?
very high or very low
;