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Questions tagged [sensitivity-analysis]

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1 answer
925 views

How to obtain reduced cost in the graphical sensitivity analysis?

According to some tables in the book Operations Research by Hamdy Taha(7th edition), it seems that for a variable whose optimal value is zero, reduced cost can be evaluated by the following formulas: ...
2 votes
1 answer
152 views

Sensitivity Analysis

In an Operations Research Problem: "A beverage company wants to produce a new juice with a mixed flavor, using only orange and pineapple flavors. Orange flavor contains 5% of vitamin A and 2% of ...
1 vote
1 answer
92 views

Pyomo sensitivity report access

I have been learning pyomo with glpk for a week now and I would like to know if pyomo team has developed a way to access "allowable increase" and "allowable decrease" values of the ...
7 votes
1 answer
1k views

Negative reduced cost for basic variable

I am observing something unusual : after solving a linear program, some basic variables have negative reduced costs (instead of $0$) : ...
2 votes
0 answers
81 views

Does the value function of a quadratic program stay convex when adding constraints?

I am interested in the value function of a quadratic program of the form $$ v(y)=\min_x \frac{1}{2} x^\top Q(y) x, $$ subject to a linear equality constraint $$ E(y)x=d(y), $$ and a linear inequality ...
2 votes
0 answers
76 views

When do two integer linear programs yield the same solution?

This question is cross-posted from math stack exchange An illustrative example Consider an integer linear program $\min -2x_1 + x_2$ subject to $x_1 - x_2 \leq 3$ and $x_1 + x_2 \leq 10$ and integer $...
6 votes
1 answer
6k views

Interpretation of Reduced Costs

I am looking for an answer to a question I can't quite get behind. (continuation of Linear Programming: Integer and non-integer decision variables) I am given the following mathematical optimization ...
2 votes
1 answer
287 views

LP Sensitivity Analysis with multiple simultaneous changes

TLDR: When doing sensitivity analysis (specifically the objective coefficients), there maximum allowable increase and decrease before the solution changes is only valid when a single coefficient ...
1 vote
1 answer
120 views

Sensitivity analysis for decision vectors in convex programming

Can we perform sensitivity analysis on the decision variables for the perturbed right-hand side of the constraints in a convex/nonlinear program? I know a basic result regarding the sensitivity of the ...
4 votes
1 answer
1k views

Can sensitivity analysis and limits report be done on an BILP problem?

I am not that experienced with Operations Research yet. I have become familiar with what Sensitivity Analysis and Limits Reports are in general and through the use of Excel. I know that they can only ...
5 votes
1 answer
761 views

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

One can solve the linear programs using google or-tools with GLOP solver. I wonder if there is a way to print the sensitivity report (like shadow prices etc.).
3 votes
1 answer
194 views

Sensitivity analysis for specific sets of constraints on DoCplex

I am working on DoCplex to run a large model with several variables and constraints. I used the following link from sensitivity analysis in python + Docplex to run the sensitivity analysis. In that ...
10 votes
1 answer
459 views

Sensitivity analysis of QP

Given a quadratic program $$ f^* \equiv x^\top Q x + b^\top x \\ x \geq 0 \\ A^\top x = d \\ x \in \mathbb{R}^n $$ I would like to analyze the sensitivity of the solution $x^*$ to perturbations in $Q$ ...
3 votes
1 answer
86 views

Determining constraint relevance in crew scheduling problem

I am working on a crew scheduling problem formulated as a MIP binary optimization where each employee is represented by a binary variable $X_{ids}$ s.t. $i \in I$ is $i$th employee, $d \in D$ is the ...
2 votes
1 answer
171 views

Sensitivity Analysis for Traveling Salesman

I am trying to understand how the idea of Sensitivity Analysis would apply to the Traveling Salesman Problem. For instance, suppose my optimization algorithm returned the following path as the ...
4 votes
1 answer
282 views

"Sensitivity Analysis" vs. "Machine Learning"

I have the following question that compares how "Sensitivity Analysis" is perceived in the field of Optimization compared to that of Machine Learning. Sensitivity Analysis in Machine ...
0 votes
2 answers
428 views

sensitivity analysis in python + Docplex

I want to do a sensitivity analysis for the following problem. I know how to add new variables or constraints, but I do not know how I can change the right-hand side (RHS) of the constraint. ...
4 votes
1 answer
1k views

Why are the final value and reduced cost 0 in excel sensitivity report for multiple variables even though there exists a unique optimal solution?

In solving a linear program (in specific a network optimization problem of the shortest path type) with the Excel solver, I noticed two things after running a sensitivity report on the solution ...
1 vote
1 answer
84 views

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

I have a problem as: $$ \begin{align} \begin{array}{cl} \underset{x \in \mathbb{R}^n_+}{\min} & c^\top x \\ \mathrm{s.t.} & Ax \leq \mathbf{1} \cdot b , \end{array} \end{align} $$ where $A \in ...
2 votes
0 answers
335 views

Reading MPS file for linear programming and reconstructing the Optimization model

Are you aware of any tutorial that can help me learn on how to reconstruct the objective function and constraints from a MPS file once it's loaded in MATLAB. I can load the mps file given to me and ...
2 votes
1 answer
169 views

How to obtain the sensitivity analysis of correlated data?

A company should supply 2 products namely A and B. The company can buy A and B in advance or in real-time, however at different prices. The demand is uncertain and prices are considered to be ...
2 votes
2 answers
355 views

Waiting time in M/M/n queue

I was able to numerically "show" that an M/M/n queue is concave increasing in the number for $n$ servers, which makes intuitive sense. However is there a formal analytical proof for it? Where can I ...
3 votes
1 answer
981 views

Linear programming sensitivity analysis using Matlab

I have a linear program in the MPS file format listing all the rows, columns, right-hand sides, etc. I can read that in Matlab and solve it using linprog. However, it seems there is no easy way to do ...
10 votes
1 answer
161 views

Variable Sensitivity Analysis

I am working with the following MIP : \begin{alignat}2\min&\quad\sum_{j\in J} c_j x_j\\\text{s.t.}&\quad l_j \le f(x_j,t_j) \le u_j \quad &\forall j \in J \\&\quad x_j \in \mathbb{N} \...
9 votes
2 answers
297 views

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

Suppose I have an optimal solution and I want to know how the solution would (likely) change if one of the coefficients in the objective function changes, or if I add a constraint that forces $x_i$ ...