Distributionally robust stochastic programs with side information based on trimmings
This is a research paper whose authors are Adrián Esteban-Pérez and Juan M. Morales.
Abstract:
- We look at stochastic programmes that are conditional on some covariate information, where the only knowledge of the possible relationship between the unknown parameters and the covariates is a limited data sample of their joint distribution. We build a data-driven Distributionally Robust Optimization (DRO) framework to hedge the decision against the inherent error in the process of inferring conditional information from limited joint data by leveraging the close relationship between the notion of trimmings of a probability measure and the partial mass transportation problem.
- We demonstrate that our technique is computationally as tractable as the usual (no side information) Wasserstein-metric-based DRO and provides performance guarantees. Furthermore, our DRO framework may be easily applied to data-driven decision-making issues involving tainted samples. Finally, using a single-item newsvendor problem and a portfolio allocation problem with side information, the theoretical findings are presented.
Conclusions:
- We used the relationship between probability reductions and partial mass transit in this study to give a straightforward, yet powerful and creative technique to expand the usual Wasserstein-metric-based DRO to the situation of conditional stochastic programming. In the process of inferring the conditional probability measure of the random parameters from a limited sample drawn from the genuine joint data-generating distribution, our technique generates judgments that are distributionally resilient to uncertainty. In a series of numerical tests based on the single-item newsvendor issue and a portfolio allocation problem, we proved that our strategy achieves much higher out-of-sample performance than several current options. We backed up these actual findings with theoretical analysis, demonstrating that our strategy had appealing performance guarantees.
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First, we need to know how much profit in dollar value by this method
profit = percentage × whole price
Plug in the numbers to the formula above
profit = percentage × whole price
profit = 40% × 25
profit = 0.40 × 25
profit = 10
The profit Daniel gets is $10
Second, add the original price and the profit together and you'll find the new price.
new price = original price + profit
new price = $25 + $10
new price = $35
Daniel sold the computer game for $35
First, convert 3 tons to ounces.
3 tons = 96,000 ounces. Divide this by 12 ounces.
96,000/12 = 8000
So, 8000 boxes can be filled each week!
Hope this helps!!
Answer:
c
Step-by-step explanation:
next
The value of integration of y=16-
from x=-1 to x=1 is 94/3.
Given the equation y=16- and the limit of the integral be x=-1,x=1.
We are required to find the value of integration of y=16- from x=-1 to x=1.
Equation is relationship between two or more variables that are expressed in equal to form.Equation of two variables look like ax+by=c.It may be linear equation, quadratic equation, or many more depending on the power of variable.
Integration is basically opposite of differentiation.
y=16-
Find the integration of 16-.
=16x-
Now find the value of integration from x=-1 to x=1.
=16(1)-
-16(-1)-
=16(1)-1/3+16-1/3
=32-2/3
=(96-2)/3
=94/3
Hence the value of integration of y=16- from x=-1 to x=1 is 94/3.
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