# 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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### Setting up a community Server for OR-enthusiasts [migrated]

It is more a suggestion than a question. I am thinking it would be a great idea to set up a OR-Discord-Server for people who are studying or working with the methods for operations research. I myself ...
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### Circular reference in states of the Bellman equation

I want to formulate a game of darts as a dynamic program. The goal is to minimize the number of darts thrown while reaching checkout. A dart player has a score s. If his score is s = ...
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### How to interpret this problem of multicriteria decision

I am trying to optimise a cost function that consists of three parameters (A,B,C) using weighted sum approach for the selection of optimal technique out of three techniques. Parameter A unit is in ...
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### Mosek Fusion APIs

Does anyone know if there is a list of available function APIs for Mosek Fusion APIs? Namely, what functions are available, their arguments list and meaning, what they do. Something similar to UNIX ...
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### How to get professional help in OR

I would like to hire a consultant at OR to do a formulation of a mathematical optimization problem. Which website is reliable for it?
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### Harvest planning problem

I need to model the following problem: For a planning horizon of $P$ equal periods, one has $N$ harvesting locations and $K$ contractors who can harvest at those locations ($K < N$). Each ...
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### Multi-product distribution modeling : too many constraints

I have received many helps to model the problem, thank's for that ! I just edited the post to make clear what my actuel problem is. The following model is giving me amazing results with few products (...
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### Resource Optimization For Cargo Handling

I have to work on some real world data and come up with an optimization technique to handle cargo. To make thing simpler let's assume that there are 2 types of resources Manpower (150 ton / 8 hour) ...
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### From a performance/speed perspective, does the programming language matter if the solver used is the same?

Perhaps a silly question, I know... But just wondering if the programming language has an impact here if the solver used is the same? For instance, the same model formulation being solved using Gurobi ...
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### What is the best open source solver for large scale LP optimization in pyomo?

I have used Gurobi and cplex for solving large scale LP problems with Pyomo. However, I do need to use open source solver. Any advise? glpk and cbc seems to be very slow in solving the problem (with ...
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### Bin Packing with CP Solver

[ [0,5], [0,4], [1,6], [2,4], [3,6], [3,2], [4,5], [5,5], [6,4], [7,3], [8,2], [8,3], [9,5], [10,3]] ...
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### Are short-sell allowed in conic formulation of Markowitz optimization?

Sorry to ask a question about the basic Markowitz portfolio optimization. The example is from Mosek's example book. The basic Markowitz portfolio optimization is formulated as: The book mentioned we ...
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### How to set solver options in Pyomo with GAMS Python API?

Did anyone have experiences with Pyomo and GAMS as solver? I had looked into the pyomo documentation (GAMSShell Solver) and in the CPLEX Manuals, but doesnt find the correct syntax. My Code looks like:...
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### Optimization Problem: Recommending Service Providers to Clients

I am new to optimization, not sure if the problem described below is trivial. Any guidance on solution or nudge in the right direction would be very helpful. Problem: There are two groups – clients ...
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### Tuning the coefficients of an objective function of LP

I want to solve a problem that results in this general objective function which I want to maximize: $$a\cdot x_1+b\cdot x_2-c\cdot x_3-d\cdot x_4+e\cdot x_5$$ When I write out in full this objective ...
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I'm trying to explore OR problems and wanted to know what algorithm fits here. Consider fuel stations with lithium ion battery that service replacing battery at each refuel ( you replace your batters ...
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### How to calculate the complexity order of an optimisation model?

In some optimisation problem it is stated that the complexity is ${\cal O}(n)$ or ${\cal O}(n^2)$. How is this calculated? Any example will be very helpful.
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### Convex Optimization Problem with norm inequality constraint

Consider the following optimization problem: \begin{align} \inf_{x,y}&\quad(x-x_0)^\top A(x-x_0) + (y-y_0)^\top B(y-y_0) \\\text{s.t.}&\quad x^\top a\geq0,\\ & \quad y^\top b\geq0, \\& ...
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### Constraintlist with two Options Pyomo

I recently started with Pyomo and I have the following Problem: I want to construct a ConstraintList with an if statement. I already learned, that it's not possible. But the problem still exists... My ...
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### Maximizing sum of step functions under single linear constraint

I am trying to efficiently solve the following optimization problem: \begin{align}\max_{b \in \mathbb{R}_+^D}&\quad\sum_{n=1}^{N}\operatorname H(b^T w^{(n)} - c^{(n)}) \\\text{s.t.}&\quad\sum_{...
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### What industries and applications are chronically underoptimized?

What are examples of industries or applications, which would greatly benefit from using OR, but it is not standard or common to use these technologies there?
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### Minimising average holding cost per unit time is equivalent to minimising average delay per customer in queue

This question was originally asked on Math Stack Exchange. It is probably better suited here. Introduction When one thinks about a queue, it is natural to want to find a policy that minimises the ...
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### Does it make sense to use strict equality constraints in optimization?

Once I learned from some post that the strict equality constraint in an optimization problem does not make much sense. We should always use $\le$ constraint. How much truth is in this? If I must have ...
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### Optimization When True Costs Are Unknown

here is a problem I thought of: Suppose there is a car repair shop and 5 mechanics work there. Everyday, new cars arrive at the shop and each mechanic has to choose 3 cars to work on. In short, the ...
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### Lower bound very bad. How to improve?

I have the following MILP: \begin{alignat}{2} \nonumber \mbox{minimize } \quad & \phi = \sum_{i=1}^{m-1} \sum_{f=1}^{F} \sum_{\underset{\bar{f} \neq f}{\bar{f}=1}}^F \sum_{h \in H} \left( D_{f \...
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### How to compute the minimum number of vehicles required

I am trying to solve the following problem: I have a set of $N$ requests that must be processed by vehicles. I do not know the locations of these requests. Requests can be processed by a same vehicle, ...
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### Multiple Depot/Crew Office Bus Driver Scheduling Modelling

I'm working on Bus Driver Schedule with multiple add-on constraints that are complex and hence trying to figure out how this can be achieved. Reference of Bus Driver Scheduling using OR-Tools:- https:/...
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### Subtracting Values from a Positive semidefinite Matrix in a Semidefinite Program

I'm trying to construct an SDP relaxation for a non-convex quadratic program ($x^{\intercal}\mathbf{H}x$) with the following objective function: x_{11}y_{11} + x_{12}y_{12} + x_{21}y_{...
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### Violation of specific constraint in Pulp

I have successfully implemented a program where I allocate N truck drivers to M gathering hubs for each one of the days of the ...
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### Optimisation Multiple Constraints

I am trying to solve a linear algebra problem: an optimisation problem and I am using CVXOPT. I've split the problem into 3 components In its simplest form, The general formulation for CVXOPT is \...
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### How to run MOSEK solver in CVXOPT

I have written a small code to do a simple min variance optimisation using CVXOPT, you can see the whole code below By using solvers.qp(P, q, G, h, A, b) in CVXOPT ...
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### Prove NP Hardness for non-convex multi-objective optimization

The multi-objective optimization problem in my case is non-linear as it consists of three objective function of which two are nonlinear function and the third is a linear function. Lets say objective ...
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### How to simplify the following constraints as I'm using MIP optimization solver in python?

Following is the initial snippet of the code: ...
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### Excel Solver is not performing as desired

I have a simple optimization problem and would like to solve it using Microsoft Solver. However, the solver does not do what it is supposed to. Briefly to the background: In the problem the gross ...
The multi-objective optimization problem in my case is defined below: Objective 1: Minimize $f_1(X_1,X_2)=C_1X_1+C_2X_2+C_3X_1^2+C_4X_2^2+C_5X_1^2X_2^2$ Objective 2: Minimize \$f_2(X_1,X_2)=D_1X_1+...