Questions tagged [optimization]

For questions involving mathematical problems that aim to minimize or maximize some objective function, possibly subject to one or more constraints.

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37 views

Solving transportation problem by the Network Simplex

I am trying to solve the following problem using Network Simplex method. But I have questions. My attempt: Basis Matrix$(B)$ Rows: 1, 2, 3, 4, 5 Column: (1,3) (1,4) (1,5) (2,3) (2,4) (2,5) $$ \...
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47 views

CPU time on Linux with Gurobi

I am solving a MILP model in C++ using Gurobi 10.1. I retrieve the CPU time of my C++ program under Linux via the following commands: ...
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0answers
86 views

Prove Non-Homogeneous Farkas' Lemma

Let $A\in\mathbb{R}^{m \times n}, c\in\mathbb{R}^{n}, b\in\mathbb{R}^{m}, d\in\mathbb{R}$. Suppose that there exists $y\geq0$ such that $A^Ty=c$. Question: prove that exactly one of the following is ...
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55 views

Node ordering in Graph optimization

I'm solving a network optimization problem which is modeled as a graph $G=(V,E)$. Solving this problem using Pulp and NetworkX in Python and ordering the graph's nodes in a certain order (i.e. (1,2,3,...
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26 views

MILP formualtion for Two-level minimum dominating set (MDS) problem?

I'm working on an optimization problem which is kind of finding the minimum dominating set (MDS) or the minimum vertex set (MVS) in an undirected graph. given the MILP formulation for both problems, I ...
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53 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
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0answers
25 views

MDP model for a unique system

Let's assume that we have a system where there are two exogenous factors, name $a$ and $b$, that can affect the system state. At each decision epoch either $a$ or $b$ occurs and it is not possible ...
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0answers
34 views

Interger programming using gray encoding

Could anyone suggest me a tool or library which takes an integer programming problem written in DOCPLEX or CVXPY as input and outputs the equivalent problem using Gray binary encoding? I am happy to ...
2
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0answers
33 views

Optimization of strongly convex functions with approximate evaluations of gradient and Hessian

Suppose I want to find the minimum of a differentiable, strongly convex function $f:\mathbb{R}^n\to\mathbb{R}$ with constant $\mu>0$. That is, for all $x,y\in\mathbb{R}^n$, I have that: $$f(y) \geq ...
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143 views

Operation hours optimization for circular schedule

Here is my problem. A store has X = 15 electical devices with the ability to work non-stop, fully charged, up to 8 hours. Their battery charge lasts 2 hours and the operating hours of the store differ ...
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0answers
42 views

Decision-making algorithm for dynamic load balancing

I'm researching a subject of balancing the load between two black-box systems (with some twists). I thought that I could record latest response time log from each of those systems and process such a ...
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62 views

Density Optimization by Fitting an Circle to a Field - Monte Carlo Method

Given: I have 2D non-parametric formula that provides instantaneous intensity at certain (x,y) location. Required: I want to en-circle a region where the density is high via optimization. In other ...
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55 views

Weapon Target Assignment Problem + Time Windows

So I am very familiar with the WTAP it the static case. What I am wondering, is there a formulation that has "time windows" as well? Let's say you have some weapons and some targets, you know the ...
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61 views

How to solve an LPP with summation

Up until this point I have only solved simple LPP problems with maybe 2 to 3 variables that looked like this, using pen and paper. I need to solve This Problem using Simplex, Dual Simplex, Big M and ...
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0answers
60 views

Problem classification: optimal weights for Weighted Arithmetic Mean

I want to write an optimisation problem then solve it, to get optimised weights to compute a final score using a weighted arithmetic mean. The problem is as follows. I have an entity (an input vector ...
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0answers
65 views

How to find minimum number of locomotives to cover maximum miles in a network?

I have a freight train dataset with details like locomotive type, substations it passes through, trip date, travel miles, etc. There are 5 locomotive types in the dataset, and each type has 20-30 ...
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2answers
193 views

Hard to soft constraint

What are all necessary changes to the below model so that constraint set $(2)$ becomes soft? Give the new full model. $\alpha_{ij}$ are parameters. Eqn. $(1)$ refers to an already existing function of ...
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1answer
620 views

How to describe the traveling salesman problem with an integer programming model?

I'm trying to describe the travelling salesman problem as an integer programming model. I'm interested in the asymmetric version of the problem. The problem can be summarized as finding the optimal ...
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2answers
357 views

Solving a (Non-)Linear Programming Problem

Apologies for my basic question, but I am kinda new to optimization methods, and I am bumping into the optimization problem below: $\min_{x} (c_1 \cdot u_1 + c_2 \cdot u_2)\\ \mbox{subject to:}\\ ...
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1answer
212 views

How to allow multiple assignments for jobs in Hungarian Algorithm?

In the Hungarian Algorithm, the assignment for a bipartite graph considers the restriction of assigning a single job to a single person for example. Can this restriction be relaxed? I would like to ...
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1answer
36 views

Enforcing discontinuous range for a variable

I want to enforce the following ranges for a set of variables, where the ranges for each variable are discontinuous. For example, I have two sets of ranges for each variable, \begin{align}\sf LB_1 &...
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1answer
81 views

How to prove this convex-optimization problem?

I am struggling with the following optimization problems. Problem 1 \begin{align}\max_{\alpha, s_1, s_2}&\quad s_1 + s_2 - \gamma (s_1 (K_1 +c_1 + s_1) + s_2 (K_2+ c_2 + s_2) + 2\alpha K) +C\\\...
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1answer
90 views

How can I have minimum amount of resources wasted in this resource allocation problem?

I have a demand, $d$ I also have supply from 1000 sources. The supplies from those $N$ (for example, $N=1000$) sources are given by $s_1,s_2,s_3,\cdots,s_N$. So,the total supply is : $s_1+s_2+\cdots+...
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1answer
104 views

How to balance the workload of teachers in OR-Tools (maximization of the minimum)

I am very new to optimization and OR-Tools. I am trying to solve a very simple question. Let's assume that we have $n$ students. Each student needs to be assigned to only one teacher as a supervisor. ...
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2answers
202 views

Pulp: slack variable to identify & measure extent infeasible in supply problem

I am currently modelling a supply problem that attempts to optimise a rail schedule which moves products from a production plant, to a warehouse to satisfy sales. The model is working fine (thanks in ...
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1answer
50 views

Formulating “more complicated” objectives in Python Gurobi

I am currently learning how to use Gurobi for Python using their official tutorial found here. In this example, they appear to formulate the objective by simply specifying a cost dictionary to the <...
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1answer
59 views

KKT for second order approximation of $f(x)$

Let $f: \mathbb{R}^n \rightarrow \mathbb{R}.$ Consider second order approximation $f(x) \approx f_0(x)$ where $$f_0(x) = f(x_0) + \nabla f(x_0)^T (x-x_0) + (\mathrm{H}f(x_0)(x - x_0))^T(x - x_0)$$ ...
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1answer
150 views

How do I solve this Optimization problem?

Optimization of a simple expansion problem minimise: $$ \sum_{t=1}^{5}\left[\sum_{i=1}^{2}x_{i,t}CC_i\left(\frac{1+EIC}{1+r}\right)^t+UE_t*C_{UE}\right] $$ subject to: $$ 0 \leq x_{i,t} \leq 5 \\ ...
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1answer
74 views

What kind of job shop scheduling problem is this and how do I solve it?

I have a production planning / scheduling problem, which I believe is a kind of job shop scheduling problem. But I would like to get some input on what kind of job shop scheduling problem it is and ...
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1answer
125 views

Pulp Python: How to formulate a time-based variable for shipping demurrage

I am working on a shipping optimisation problem that aims to minimise demurrage charges as a result of low/insufficient inventory. I have daily vessel requirement (sales) data in the format ...
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1answer
54 views

How to get detail about 'OptimizationStatus.ERROR' in MIP module in Python?

I am using MIP (Mixed Integer Programming) module in Python to solve one of my optimization problems. for some of the scenarios, model returns "ERROR" (OptimizationStatus.ERROR) status after ...
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0answers
31 views

How to start the Dantzig-Wolfe decomposition?

I have the following problem: \begin{align}\min&\quad3x_1+5x_2+3x_3-2x_4+3x_5\\\text{s.t.}&\quad x_1+x_2+x_3+x_4\geq3\\&\quad3x_1+x_2+5x_3+x_4-2x_5\geq6\\&\quad x_1+2x_3-x_4\geq2\\&...
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0answers
75 views

Linearization of constraints with square root

I am trying to solve an optimization programming model involving a non-linear constraint with a square root. It follows (in a simplified form): $X_i\ge\sqrt{A_i/B_i}$ where $X_i,A_i,B_i$ are positive ...
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0answers
93 views

How to develop a vehicle routing optimization package? [closed]

I would like to know how vehicle routing software optimizes routes? In demos of this software, they provide the optimal (or a good) route in just a few seconds or minutes with several nodes (maybe 50 ...
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0answers
44 views

$\nabla_y\nabla_vf(x^*)\geq0$ for any concave $f$ if and only if $y=-v$

$f:\mathbb R^3\to\mathbb R$ is an arbitrary concave function. $H$ is a plane. $v$ is a given vector on $H$. $x^*=\max_{x\in H} f(x)$ Prove that $\nabla_y\nabla_vf(x^*)\geq 0$ if and only if $y=-v$. I ...
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0answers
38 views

Find minimum cost problem

The problem below aims to find the minimum cost for the network architecture: We want to build a network where client terminals are connected to servers by cabling which is very expensive. The network ...
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0answers
80 views

Simplex - Network flow problem : Arc from 1 to P with infinite capacity

The Network - Maximum flow problem below aims to find the maximum flow using simplex method : With the LP as follow : LP : \begin{Bmatrix} Z(Max) = \sum_{i=1}^{m} fi \\ Af =0 \end{Bmatrix} ...
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0answers
66 views

Ways to improve lower bounds while solving MIPs

What are the ways to improve lower bounds while solving a minimization problem (MILP)?
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0answers
85 views

How do I find the extreme rays and points for a stochastic programming problem

I have the following 2 stage Stochastic Programming program: \begin{align}\min_x& \quad x+\sum_{s=1}^{3}p_sQ_s(x)\\\text{s.t.}&\quad x\in\Bbb R\\&\quad Q_s(x)=\min\left[\begin{pmatrix}1&...
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0answers
62 views

Combining Two Different Queues

I am trying to create an optimization model for a problem that involves two different types of queues. Given Poisson demand (for both), there is a queue with constant service time and another queue ...
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0answers
136 views

Optimal value exceeds actual value for a minimization problem [closed]

I am solving a nonlinear numerical optimization problem in Pyomo using Scip as a solver. The goal is to minimize a certain objective function. For certain input conditions, I notice that the solver ...
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2answers
197 views

How can I formulate this specific if-then constraint?

IF $\sum\limits_d X_{i,d}\ge6$ THEN $Y_i = 1$ (strictly) AND IF $\sum\limits_d X_{i,d}<6$ THEN $Y_i = 0$ (strictly) $X$ and $Y$ are binary variables. What I'm actually trying to do is to charge the ...
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1answer
74 views

How can I find the shortest path for all nodes in a graph from a source $s$?

This is the shortest path problem. I've used a model where we can find the shortest path between the source and a specified destination. The idea behind this model is that we assign a flow of 1 for ...
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1answer
38 views

Adding slack nodes to min cost network flows

I have the following question. I want to clarify couple of points. As you can see, total demand and total supply does not match, we do not have enough demand. What I want to ask is: Do we need to ...
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1answer
47 views

How to deal with the sub-problem with zero reduced cost in D-W decomposition

The specific linear programme has an optimal solution as $x_1 = 0.66$, $x_2 = 1.33$, $x_3 = 12.2$, $x_4 = 0.0$ and the objective value is $33.3$. While the problem is solved by D-W decomposition ...
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1answer
82 views

Does this objective function makes sense?

I am wondering if the objective function in the following problem makes sense. The question is posted in CrossValidated, stack exchange as well. I know there is a physical system having an underlying ...
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2answers
197 views

Some theories and laws of Operations Research? [closed]

Can I know some theories and laws of Operation Research which has being widely used nowadays?
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1answer
86 views

Geometric interpretation of a Linear problem with bounded variables

I have a question of how to make a geometric interpretation of this problem \begin{eqnarray} \mbox{max} & z = 3x_1+x_3 \\ s.a: & \\ & \begin{array}{cc} x_1+2x_2+x_3+x_4& =...
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2answers
408 views

Are there NP hard problems solved in P time?

Does anyone know of a problem previously believed to be NP hard, to be solved nowadays in polynomial time optimally?
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1answer
66 views

How to change a function from Min(F(x)) to -Max(-F(x))?

I have not a good knowledge in math field, I am working on multi objective functions, and I have two maximization functions, and one minimize function, where: Max (X,Y) = X+Y Max (L,M) = Sum (LC + MD)...

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