Questions tagged [sensitivity-analysis]

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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 ...
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2 votes
1 answer
87 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 ...
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4 votes
1 answer
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"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 ...
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0 votes
2 answers
165 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. ...
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4 votes
1 answer
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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?

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 ...
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5 votes
1 answer
678 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 ...
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1 vote
1 answer
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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 ...
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2 votes
0 answers
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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 ...
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2 votes
1 answer
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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 ...
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1 vote
2 answers
145 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 ...
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3 votes
1 answer
581 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 ...
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7 votes
1 answer
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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 $0$) : ...
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10 votes
1 answer
106 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} \...
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9 votes
2 answers
188 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 $x_i$ ...
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