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0answers
2 views

Are fuzzy sets appreciated by OR community?

I may not be correct but it seems that the leading operations research and management science journals (Informs OR and MS) do not publish any works on fuzzy logic or fuzzy sets. I could find only ...
4
votes
0answers
13 views

Difficulties with finding equivalent problem on literature

I'm working with a sort of pickup delivery problem right now. We need to assign vehicles to routes and requests to those vehicles. Each request has its due date, client and may be delivered in one of ...
5
votes
0answers
25 views

CVRP With Variable Fleet Size: Upper Bound on Optimal Fleet Size

Given a CVRP where the number of trucks is a decision variable, is there an upper bound on the number of trucks used in an optimal solution in terms of number of customers, some distances, capacities, ...
5
votes
1answer
87 views

Excel Solver linear programming - Is it possible to use average of values as a constraint without #DIV/0! errors or sacrificing linearity?

I'm trying to create an assignment optimization model where the areas are assigned to either the south or north school districts so that the total distance is minimized. Each school must have at least ...
5
votes
1answer
29 views

The departure process of an $\rm M/M/\infty$ queue

Burke's theorem says that the output process of an $\rm M/M/1$, an $\rm M/M/C$, and a $\rm M/M/\infty$ queue with arrival rate $\lambda$ and service rate $\mu$ follows a Poisson with parameter $\...
5
votes
0answers
24 views

Solutions to a parametrized optimization problem

I have the following maximization program \begin{align} \max\limits_{\{q_i\}}&\quad\sum\limits_{i=1}^nq_i \\ \text{s.t.}&\quad\begin{cases} k_j \geq \sum\limits_{i=1}^n q_i^{1 \over \...
6
votes
2answers
75 views

Is the “reverse search” algorithm of David Avis the state-of-the-art method for finding discrete solutions to a system of linear inequalities?

Is the "reverse search" algorithm of David Avis the state-of-the-art method for finding discrete solutions to a system of linear inequalities? If it is not, then what is? For $m$ inequalities in $d$ ...
6
votes
0answers
37 views

What are the top three applications (in terms of number of citations) of the “reverse search” algorithm of David Avis?

I can see that this algorithm is quite popular, and that one of the original papers now has 820 citations on Google Scholar. However, what are the most highly cited applications of it? If in Google ...
7
votes
1answer
77 views

I've formulated my optimization model; now what?

I've formulated my linear/nonlinear/integer/mixed-integer optimization problem in algebraic form (possibly with the help of the folks on this site). Now what? How do I solve it?
9
votes
1answer
109 views

Vehicle routing benchmark instances

I recently started working on the classical split delivery vehicle routing problem (SDVRP). I appreciate if someone could let me know where to download benchmark instances for this problem? I am also ...
3
votes
1answer
52 views

XOR constraint representation

In an scheduling optimization problem, for job $l$, $\xi_l$ is binary variable that $\xi_l=1$ shows job $l$ is selected. $t_{r,l}$ and $t_{e,l}$ are registration time and time that job is completed. ...
12
votes
3answers
776 views

Can an integer optimization problem be convex?

I'm trying to wrap my head around an apparent paradox that I've come across while trying to learn more about optimization algorithms: On one hand several sources state that convex optimization is ...
8
votes
2answers
64 views

When should I use a solver for IP and MIP and can I just use a library from Python, R, Matlab, etc…?

Are there any rules of thumb for figuring out when you need to use a solver like Gurobi or CPLEX, and when you can just solve you problems directly with a Python, R, or Matlab package? Is it just a ...
3
votes
1answer
88 views

Scheduling Optimization Problem

I want to solve below optimization problem. This is scheduling problem where I seek to complete as many of the jobs $\xi_l$ (objective function and constraint 1), with $T_C$ being the last time until ...
6
votes
4answers
1k views

Why is there not a feasible solution for a MIP?

Is there a way to see why a solver (OR-Tools, CPLEX, Gurobi) cannot find a feasible solution when solving a MIP? By that I mean, is there a possibility to show at which constraint and exact indices ...
10
votes
3answers
1k views

Allocating credit card points

I’m interested in the idea behind this in general, so I thought this would be the best place to post, though I have a practical and semi-urgent need of allocating the points on my credit card towards ...
4
votes
0answers
44 views

Pyomo: Is this triple summation objective function formatted correctly?

I am writing a Pyomo model and trying to code the following mathematical constraint: $$ \sum_{i=1}^I\sum_{j=1}^J\sum_{t=1}^T 5I_{ijt} + 10L_{ijt}I_{ijt} $$ where $L_{ijt}$ is binary. However, I am ...
6
votes
2answers
80 views

What Exactly Is A Warm Start? [duplicate]

I am fairly new to optimization modelling but I am encountering a situation in which I supply initial values to my problem and then after I run my optimization those initial values change. This seems ...
8
votes
4answers
2k views

What do solvers like Gurobi and CPLEX do when they run into hard instances of MIP

MIP is NP-Hard, so it is possible that an instance is very difficult and has multiple local minima that the search can get stuck in. With a Metaheuristic Algorithm, the stochastic and approximate ...
9
votes
2answers
174 views

Could reserving a hotel room potentially lead to a suboptimal allocation of rooms?

Suppose you have a standard hotel with a set of rooms. If you have booked a room for a fixed period of time, would allocating a specific room in advance potentially cause a conflict when trying to ...
9
votes
1answer
101 views

Rules of thumb for using classic methods (e.g. branch and bound) vs. meta-heuristics (G.A, S.A, etc..) for non-convex problems?

Are there any rules of thumb for when to use classical methods like branch and bound, branch and cut, etc...for non-convex problems, vs using meta-heuristic methods like genetic algorithms, ...
23
votes
5answers
732 views

Statistical tests for benchmark comparison

Suppose that you have two algorithms for solving an optimization model, and you want to benchmark their performance over a large set of instances (with only one performance metric, for example, the ...
4
votes
1answer
95 views

Machine Allocation & optimal Utilization using python

Problem statement: Meet the demand which can be met across 2 facilities each having multiple machines where several components are made. The objective is to find the optimal solution to meet the ...
8
votes
0answers
78 views

Ill-conditioned LP in Bender's decomposition

I have implemented a Bender's decomposition for a constrained network flow but the LP solver (Gurobi) warns me of the ill-conditioning of the slave dual LP. As you can see below, the coefficients seem ...
10
votes
2answers
425 views

Is using gradient descent for MIP a good idea?

I'm researching ways of solving constrained optimization problems on a cloud platform. I stumbled across this: https://cloud.google.com/blog/products/data-analytics/distributed-optimization-with-...
7
votes
1answer
132 views

Specific filter on the set using Python

I'm trying to write an optimization model using an open-source solver's Python API. I'm new to use Python. The model objective function is as follows: \begin{equation} \sum_{k=1}^{K} \sum_{j=1}^{n}\...
12
votes
2answers
128 views

Linearisation techniques for MINLPs

I am wondering what kinds of linearisations people do for MINLPs outside my field of expertise. I work in global optimisation, so by "linearisation" we would typically mean one of the following: ...
8
votes
1answer
74 views

Binary variable to count appearances

Let $x \in \mathbb{R}^n$ be an optimization variable. Now, at a constraint, I would like to count how many times a value, say $2$, appears in $x$ decision. I think we can have a binary variable $y_i$...
9
votes
1answer
87 views

Approaches for choosing a “risk” factor in an Inventory Optimization problem?

I'm working on an Inventory Optimization (Allocation) problem. The decision variable is the amount of inventory budget to allocate for each product, from a set of products. My objective is to ...
13
votes
7answers
158 views

Might you know any simple puzzles similar to $n$ queens? Anything parametized worth running to a constraint solver

In the $n$ queens puzzle, we have to put $n$ queens on an $n \times n$ chessboard, without any $2$ queens being able to attack each other. Finding a single feasible solution is not NP-complete. It's ...
13
votes
1answer
122 views

Convexity of Variance Minimization

$X$ is a discrete random variable taking value $x_n$ with probability $1/N$ for $n=1, \ldots,N$. I would like to set the $x_n$ values in an optimization problem. My objective is to minimize the ...
9
votes
2answers
98 views

Integer Decision Variables Always Forced to Zero in Minimization Problem (MINLP)

I am trying to write out a MINLP problem of optimal control for an invasive species and the code that I have for my PYOMO model is below. Some of the initialization values take from an Excel ...
14
votes
4answers
121 views

Model conversion as fast as gurobipy and solved by open source solvers

Gurobipy is a fast solver and can convert a mathematical programming model to its underneath language very fast compared to some open source wrappers (e.g., PuLP, OR-tools, etc.). However, a ...
7
votes
2answers
80 views

CP Framework/Solver for .Net Core

First I want to say that I'm very new to this field. As far as I understand it, there are two different ways to use a Constraint Programming (CP) Solver: Using the API from the Solver itself. For ...
8
votes
3answers
108 views

Difference between “Optimization” and “Constrained Optimization”?

(Another OR noob question) As I'm trying to learn about OR and Optimization methods for work, I'm having a hard time understanding the difference between "Optimization" and "Constrained Optimization"...
15
votes
5answers
2k views

Linear Programming with additional “if-then”/“Default to zero” constraints?

What approaches can I use for a Linear Programming problem with the additional constraint that if a decision variable falls below a certain threshold, then it should just be forced to 0. I'm ...
6
votes
1answer
72 views

Common structures in Gurobi - Python

I'm new to Gurobi in Python and I was wondering if someone knows how to code some common structures of linear constraints. Punctually, I'm trying to understand how you'll code something like the ...
11
votes
3answers
1k views

What is the purpose of libraries like Pyomo and Google OR tools?

I'm new to the OR world, and trying to learn the various tools available. I originally thought that Pyomo and Google OR tools were open source alternatives to commercial solvers like Gurobi or CPLEX. ...
8
votes
2answers
313 views

What is the standard practice in Constraint Programming modeling?

I know some general concepts regarding Constraint Programming (e.g., the ones explained in this answer). I am interested in learning how to formulate a combinatorial optimisation problem as a ...
11
votes
2answers
138 views

Paging operations research people: how is the field evolving?

I am interested in applying to some OR faculty positions this academic cycle and I am hoping to get a better understanding of the field. For context, I come from an (electrical) engineering background,...
8
votes
1answer
258 views

How to resolve this issue in multi-objective optimization?

I have the following multiobjective optimization problem. The objectives are non-conflicting. The Optimization Problem: $$\underset{\large{a^{(l)}_{c,u},f^{(l)}_{c,u},z_{l,t},l\in\mathcal{L}}}{\max}...
12
votes
3answers
1k views

Number of aircraft to operate in an airline company

Suppose that an airline company has X planes, in general the companies keep a number of these aircraft (say 80% of X) in reserve in case of hazards. My question is how the airline companies compute ...
15
votes
4answers
532 views

How to progress with CPLEX/Gurobi

I've been learning and playing with CPLEX/Gurobi for a year using C++/Python API. I know some basic stuff like writing a model, callbacks, basic playing with solvers' parameters. I am wondering what ...
13
votes
3answers
413 views

Online Education for OR and Developing Decision Support Systems

I am looking for educational programmes which can be conducted online, such as full MSc., degree certificates, postgraduate courses/modules, MOOCs. Topics I am looking for are on advanced ...
9
votes
2answers
125 views

Valid Inequalities and Strong Inequalities

Consider the following mixed-integer set: \begin{equation} P(A, b ; S) \stackrel{\text { def }}{=}\left\{x \in \mathbb{R}^{n} : A x \leq b, x_{j} \in \mathbb{Z} \text { for } j \in S\right\} \end{...
16
votes
6answers
4k views

Are programming languages necessary/useful for operations research practitioner?

This semester I will start teaching Programming in Python to Master students in Supply Chain Management. I would like to start the first lesson with "Why learning programming languages will be useful ...
12
votes
2answers
131 views

Convex vs Strictly Quasiconvex Functions in Optimization

I have read/heard quite a few time that in the old days, it was considered that linear programs constitute the class of optimization problems that can be solved efficiently in practice (as a rule of ...
-3
votes
0answers
35 views

how to identify hard and soft constraint [duplicate]

I was being asked few questions on hard and soft constraints in an interview. Question 1. Which among following questions are hard or soft constraint ? Question 2. In these examples, How to convert ...
7
votes
1answer
43 views

Get a MPS file using NEOS/GAMS web interface

I'm trying to use Neos/GAMS to solve an optimization problem. I will need to get a MPS file from the model. With using GAMS IDE it is easy to use an option file to get it but, it needs a licence file ...
9
votes
3answers
185 views

To which area does constraint programming belong?

The problem I solved is a flow-shop scheduling problem with parallel machines. I solved it with the IBM ILOG CPLEX Optimization framework. There I used the constraint programming (CP). The question ...

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