Operations Research Stack Exchange
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Rewriting if-then constraints of binary summations

Suppose both $x_{i,j}^{ab}$ and $y_{i,j}^a$ are binaries. Then how can I rewrite the following if-then in linear form? $\sum_b x_{i,j}^{ab} \ge 1 \implies \sum_{i,j} y_{i,j}^a = 0$ I was thinking of considering an indicator. But is there a better…
linkho
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OR applications in medicine

Read this article on potential application of Markov Decision Process in decision making process of patient evaluation schedule. Does anyone know or have experience in application of such OR techniques in medicine? I am aware of application of…
Sutanu Majumdar
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Separating violated cover inequalities

Consider a knapsack problem with binary variables and a standard knapsack constraint $\sum_{j\in N}a_jx_j\leq b$. A set $C\subseteq N$ is a cover if $\sum_{j\in C}a_j >b$ If $C\subseteq N$ is a cover, then we can state a cover inequality (CI):…
Joris Kinable
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What are my options for exact linear programming solvers in python3 that work as of April 2023?

So a while back I had asked this question: Is there a Linear Programming Library that natively supports fractions instead of floating point arithmetic? And basically the overwhelming consensus was that the best libraries for exact linear programming…
Sidharth Ghoshal
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Discrete optimization for a simulation objective

I am looking for a list of solution methodologies that solves a discrete optimization problem, except that the objective function evaluated at any feasible point can only be obtained by performing a simulation. In other words, for any $(\bar{x},…
batwing
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Software for optimization problem

I want to solve the following optimization problem min $\|x\|_{\infty}$ such that $Ax \ge b, x \ge 0$ where $A$ is a matrix with integer coefficients and $b$ is a vector with integer coefficients. Here $\|x\|_{\infty} =…
user1868607
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The study of directional derivatives for functions that are minimums of convex functions

Has there been any research on the topic of directional derivatives of functions that are minimums of convex functions?
Samira Fallah
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Multithreading vs DPCC SYCL Programming for OR computational implementations

While well-known IP/LP solvers such as CPLEX and Gurobi have capabilities to run their solver on multiple threads, is there any tool that helps exploit the availability of not only multiple threads on a single CPU, but also increasingly, the…
Tryer
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Understanding reduced costs and dual values

I have a headache regarding calculating the reduced costs of a linear program. I am using Pulp for modelling and CBC for solving. What I do is, I model a linear programming problem based on a rhs vector $b$, a constraint matrix $A$ and a cost vector…
Djames
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Determining the optimize lambda in Multi-Objective Optimization

I have a convex optimization problem: Maximize obj1 Minimize obj2 Some constraint Now to solve this problem, I used lambda to make it one problem: Maximize lambda * obj1 - (1-lambda) * obj2 For my problem, I considered lambda to be 0.8,…
Soroosh Noorzad
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how to ensure minimum output of a generator (else zero output) in linear programming?

I want to ensure, that a generator (in my case a heat generator, for example a boiler) first starts to output thermal energy, when a certain minimum output can be realized. Otherwise the output should be zero. For example, the boiler should not run…
Andre
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How to approximate an uncertain constraint?

Suppose $\theta$ is the uncertain vector of parameters and it varies within the interval $\Theta$. We have the following uncertain constraint. $$ \sum_{i} f_i(x,\theta) \ge \sum_{j} g_j(x,\theta) \quad \theta \in \Theta $$ To find the robust…
Amin
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Alternative way to restrict an employee to work on multiple jobs

Suppose I have a set of employee $E$ and set of jobs $J$ in a given time horizon $T$. I would like to make sure that no employee works on multiple jobs where each job $e\in E$ takes a certain amount of time presented as $\delta_e$. Let $X_{ejt}$ be…
ball_jan
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How to solve a "nearly" linear program

Given a positive integer $n$, a constant $k=2/3$, and $7$ variables $x_1, x_2, x_3, x_{12}, x_{13}, x_{23}, x_{123}$ (non-negative reals or integers) I would like to find: $$\min \binom{x_1}2$$ subject to: $$\binom{x_1}2 \ge \binom{x_2}2 \ge…
Fabius Wiesner
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How to get paid for operations research skills?

Maybe this is a weird question for Operations Research SE, but I seek to get paid for my operations research skills while working remotely. I already have accounts on freelancing websites. However, I exert a lot of effort in refusing to do students'…
OR Junior
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