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Sensitivity analysis of QP

The sensitivity analysis of optimization problems is called parametric programming or sometimes "post-optimal analysis". The short version is that you describe the variability of your ...
Richard's user avatar
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7 votes

Partial derivative of LP solution $(x_1 , \ldots, x_n)$ w.r.t. $x_i$ or $a_i$

As Larry Snyder mentioned in his comment, almost all of the Operations Research books include a chapter dedicated to answering your question which is about "Sensitivity Analysis". A good(short and ...
Oguz Toragay's user avatar
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6 votes
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Interpretation of Reduced Costs

The reduced costs (or marginal costs), tell you by how much the objective function will increase (or decrease), if the corresponding variable increases by one unit. So if you are minimizing, the ...
Kuifje's user avatar
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6 votes

Partial derivative of LP solution $(x_1 , \ldots, x_n)$ w.r.t. $x_i$ or $a_i$

The solution to an LP is given directly by its active set, $I = \{i_1,i_2,...,i_n\}$, which forms a system of equations that recovers the solution $x^*$. If your solution varies, then the question is ...
Richard's user avatar
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4 votes

Negative reduced cost for basic variable

My guess would be that the variable is not basic, it is non-basic but at the upper bound of 1.0. Modern solvers use the generalized simplex method which allows for lower and upper bounds on a ...
Philipp Christophel's user avatar
4 votes
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Variable Sensitivity Analysis

Having fixed the discrete decisions, you could start at the beginning and work forward through the task dependency graph, starting each task as early as possible; then work backward from the end, ...
prubin's user avatar
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4 votes
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Waiting time in M/M/n queue

Dyer and Proll (1977)1 showed that for an M/M/c queue, the mean waiting time is a strictly decreasing and convex function of c. Reference [1] Dyer, M. E., Proll, L. G. (1977). On the Validity of ...
TheSimpliFire's user avatar
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4 votes

Can I print the linear programming sensitivity analysis report using google or-tools?

Here is a straightforward conversion of Python PuLP code from https://machinelearninggeek.com/sensitivity-analysis-in-python/ into Google OR Tools: ...
asmaier's user avatar
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4 votes
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Sensitivity analysis for specific sets of constraints on DoCplex

You can filter the results you get from sensitivity.rhs : See small example out of the zoo example again: ...
Alex Fleischer's user avatar
3 votes
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Sensitivity analysis for decision vectors in convex programming

Suppose that $F: R^{n} \rightarrow R^{n}$, $F(x)=b$, and $F$ is differentiable at $x$ with non-singular Jacobian $J(x)$. Then to first order, we can use the Jacobian to find a change $\Delta x$ due ...
Brian Borchers's user avatar
3 votes
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Can sensitivity analysis and limits report be done on an BILP problem?

Parametric/sensitivity analysis of a right hand side coefficient in an optimization problem with integer variables can be done, but it is messy. See: Schrage, L, and L. Wolsey (1985), "...
LINDO Systems's user avatar
3 votes

Sensitivity Analysis for Traveling Salesman

You can certainly do sensitivity/parametric analysis on the objective function. If you are interested in the effect of changing a single coefficient in a linear objective function to be minimized, e.g....
LINDO Systems's user avatar
3 votes

"Sensitivity Analysis" vs. "Machine Learning"

Machine Learning: Firstly, sensitivity analysis on Machine Learning models goes way beyond the Bias-Variance tradeoff. Sensitivity analysis of a Machine Learning model is done mainly to see how the ...
Shibaprasad's user avatar
2 votes

LPs having a 'stable' objective value wrt changes in the constraint right-hand sides

The property that some infinitesimal change in one of the constraints impacts the objective is called "a constraint being active" or "a constraint being in conflict with the objective&...
worldsmithhelper's user avatar
2 votes

sensitivity analysis in python + Docplex

Also, besides the answer by @EhsanK, you can obtain the range of the parameters for sensitivity analysis as follows to know how much you should play around with those parameters: ...
A.Omidi's user avatar
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2 votes

sensitivity analysis in python + Docplex

There are several ways to do this: You already used left_expr that modified the left-hand side. You can do the same thing with ...
EhsanK's user avatar
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2 votes
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Why are the final value and reduced cost 0 in excel sensitivity report for multiple variables even though there exists a unique optimal solution?

Consider the following LP: \begin{align*} \max\,3x_{1}+5x_{2}\\ \textrm{s.t. }x_{1}+2x_{2} & +s_{1}=3\\ 2x_{1}+x_{2} & +s_{2}=3\\ x_{1}+x_{2} & +s_{3}=2\\ x,s & \ge0 \end{align*} ($s$ ...
prubin's user avatar
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2 votes

Sensitivity Analysis

If you are minimizing cost, then there is no advantage to producing more than the required 100 liters of juice. Using that, you can rewrite the model so that the 5% limit on vitamin C is part of a ...
prubin's user avatar
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2 votes
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Linear programming sensitivity analysis using Matlab

As documented at https://www.mathworks.com/help/optim/ug/linprog.html, linprog returns the Lagranage multipliers via the optional 5th output argument, lambda. What are called Lagrange Multipliers by ...
Mark L. Stone's user avatar
1 vote

Pyomo sensitivity report access

Here is a simple example of how one can access the suffix needed for printing the dual information of the constraints and also the reduced cost of the variables: ...
A.Omidi's user avatar
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1 vote
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LP Sensitivity Analysis with multiple simultaneous changes

For either changes to the objective or changes to the right hand side values, the sensitivity results hold for multiple changes as long as the sum of the fraction of the allowed change used by each ...
prubin's user avatar
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1 vote

How to obtain reduced cost in the graphical sensitivity analysis?

As I understand suppose $z= 6x+2y-1$ then max of z would be at $x,y=(6,0)$ for x bounded by $[0,6]$ and $y=[0,3]$. Imagine z is the negative sloping line or contour in x-y plane. Slope of contour z is ...
Sutanu Majumdar's user avatar
1 vote
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Determining constraint relevance in crew scheduling problem

This is tricky for a variety of reasons, including the fact that relaxing a constraint that is nonbinding at the optimal solution could cause the optimum to improve. I don't think the duals of the LP ...
prubin's user avatar
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1 vote

How to obtain the sensitivity analysis of correlated data?

Disclaimer: I did my PhD on the topic below and was the author of one of the toolboxes I mention below. This sounds a lot like you are interested in multi-parametric programming, i.e. solving your ...
Richard's user avatar
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1 vote

Waiting time in M/M/n queue

You can derive them from the balance equations. If you check Taha's or Lieberman's Introduction to OR books, you can find the proofs.
Evren Guney's user avatar

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