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7
votes
3answers
204 views

Matlab fmincon for a problem with many nonlinear constraints

Using Matlab to solve a problem which has linear objective function and many nonlinear constraints, I am trying to generate the inequality nonlinear constraints by a function and pass it to fmincon ...
9
votes
1answer
60 views

Using Spatial Multi Criteria Analysis for simultaneously locating various facilities?

Is it possible to use SMCA (Spatial Multi Criteria Analysis) for determining simultaneously where to locate various facilities? Suppose, for example, I'm planing to build a new city and everything ...
8
votes
1answer
49 views

Understanding the AMPL Solver LIbrary within Pyomo

For anyone familiar with the Pyomo book, it occasionally makes reference to the AMPL Solver Library, and to my understanding, if you can manage to hook up to the solver library then you are able to ...
7
votes
2answers
251 views

Finding an Objective Function for Assigning Employees to Sequence Dates

I am using a mixed-integer-program to schedule employees to projects. These projects can have a time window to get completed from a few weeks to a few months. At the moment I am working in a ...
10
votes
1answer
79 views

DOCplex adding columns

When using DOCplex to implement column generation, is it possible to add columns as an object, as opposed to creating a variable and then modifying the coefficients in the constraints? Edit: In ...
6
votes
1answer
56 views

Problems Installing APOPT in Pyomo

I am trying to install the solver "APOPT" in Pyomo by following the guidelines laid out below: *Instructions for usage: Place apopt.py in an appropriate folder in the system path (e.g. Linux, /usr/...
9
votes
1answer
70 views

How to model 24 hours demand into a daily shift schedule?

I am working on a weekly staff scheduling optimization problem with 24/7 demand. The binary decision variable is: $X_{\text{staff},\,\text{day},\,\text{shift}}$ whether to assign the staff $s$ to day ...
14
votes
1answer
341 views

How to formulate a problem to prove/disprove convexity?

Given a general non-linear problem: \begin{align}P:\qquad&\min_{x\in X} f(x)\\\text{s.t.}\qquad&g(x)\leq 0\end{align} where $f$ is a non-linear function, $g$ is a vector of non-linear ...
15
votes
4answers
406 views

Case Studies and Real Problems for Teaching Optimization and Modelling

It is that dreadful time of the year when I am prepping classes and over the last few terms I came to the realization that I need to significantly beef up the practice-oriented content of my lectures. ...
-4
votes
2answers
294 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?
4
votes
0answers
166 views

How can I formulate this multi-objective optimization problem?

Now, for each system $X$ $(X=A,B,C,E)$, my objective is $$\max\min\frac{s_{x_u}}{d_{x_u}}$$ here, $x=a$ for system A, $x=b$ for system B and follows... and for the whole system, my objective is $$\...
15
votes
3answers
914 views

How does the search space affect the speed of an ILP solver?

Let us suppose we have an optimization problem which we have modeled as an ILP. Suppose we solve this problem using some set of constraints which restricts the search space. Let us suppose we model ...
7
votes
1answer
491 views

Why is the Ellipsoid Method of polynomial complexity?

We know that the ellipsoid method is proven to be of polynomial complexity. However, as far as I can tell we may need to add exponentially many feasibility cuts in order to solve the LP (or prove no ...
11
votes
1answer
109 views

How to solve the Cumulative Traveling Salesman Problem using or-tools in python?

The objective of the Cumulative Traveling Salesman Problem (CTSP) is to minimize the sum of arrival times at customers, instead of the total travelling time. This is different than minimizing the ...
9
votes
1answer
98 views

Profit Maximization vs Cost Minimization for Employee Scheduling

I wanted to write two objective functions for an employee scheduling problem (MIP) until it occurred to me, that one objective function may be redundant. Is there a difference between the cost ...
10
votes
2answers
190 views

How to determine the convexity of my problem and categorize it?

My problem is: \begin{align}\min\limits_{x_{ij}}\qquad&{\sum_{i\in N}\sum_{j\in M}\frac{x_{ij}}{C_j-\sum\limits_{i\in N} x_{ij}a_i}}\\\text{s.t.}\qquad&0<C_j-\sum_{i\in N} x_{ij}a_i\\\qquad&...
12
votes
3answers
560 views

What is a “hard problem” in the context of Mixed-integer programming?

As a practical (real-world problems) point of view, it's important we could solve optimization problems as quickly as possible (for instance, to release a daily schedule). Maybe a problem with many ...
10
votes
5answers
657 views

What is the following VRP?

I am researching a Vehicle Routing Problem for a safety insurance company that provides roadside assistance. The company does not have a depot, as in classical VRP, and has a set of heterogeneous ...
11
votes
1answer
74 views

Model or State Uncertainty in Queueing Model due to uncertain arrival rate

Introduction I am currently modelling a scenario where two queues need to be served by a single server in a non preemptive discipline. I am quite sorted on generating the optimal policy via Value or ...
6
votes
1answer
67 views

Alternative definition for the value of stochastic solution

I have a two-stage stochastic programming problem in which the expected-value solution results in a quite different first-stage solution than the recourse problem. Although the value of VSS (defined ...
10
votes
1answer
111 views

Difficulties with Finding a Proper Penalty Value for the Progressive Hedging Algorithm

Recently, I've been working on some two-stage stochastic programming problems. Due to the presence of integer second-stage variables in the model, I've preferred to use the Progressive Hedging ...
19
votes
3answers
1k views

Find feasible point in polynomial time in linear programming

Background A while ago my team was implementing an interior point LP solver and we came across the following conundrum: Is there a polynomial-time algorithm to find a feasible starting point in ...
9
votes
2answers
226 views

Expressing an implication as ILP where each implication term comprises a chain of boolean ORs

Consider an implication of the form $A \implies B$ where both $A, B$ comprises a chain of Boolean OR variables. For example, $(a_1 \lor a_2 \lor a_3) \implies (b_1 \lor b_2 \lor b_3)$. How can this ...
10
votes
1answer
279 views

Simulation in Python

What is the most common package for discrete-event simulation in the OR community? I have found SimPy package.
13
votes
1answer
120 views

Are there any real-world problems where quadratization helps to solve something that couldn't have been solved without quadratization?

The closest thing I know is the computer vision problem, in which an image is de-blurred and/or de-noised by quadratizing a quartic problem into a quadratic optimization problem (QUBO) and then the ...
6
votes
1answer
79 views

Obtaining the intermediate solutions in AMPL

I know that for some solvers, for example, the constraint programming solver in Google OR-Tools, it is possible to see all the intermediate solutions that the solver finds while it searches for an ...
14
votes
2answers
167 views

Divisibility constraints in integer programming

In the study of a certain pure mathematical problem (related to infinite-dimensional Lie algebras) I found myself in a situation where it would be very desirable to be able to solve an integer ...
9
votes
1answer
104 views

Comparison of Algebraic modelling languages and general programming languages

Some optimization software/frameworks (commercial or open-source) such as AMPL, GAMS, Cplex, ... have a specific Algebraic modelling language. Some of them have another type of programming that uses ...
9
votes
1answer
77 views

Extreme rays in polymake

I am trying to find extreme rays of a polyhedral cone using polymake. My understanding is that in a cone, every feasible solution is also a ray and an extreme ray is a ray that cannot be written as ...
14
votes
3answers
147 views

Dataset human solutions for OR problems

I would like to compare human solutions for OR-problems to optimal solutions. Therefore, I am looking for a dataset with the manual solutions computed by a human. I do not have a specific problem in ...
13
votes
2answers
429 views

State-of-the-art algorithms for solving linear programs

Průša and Werner (2019) show that the general linear programming problem reduces in nearly linear time to the LP relaxations of many classical NP-hard problems (assuming sparse encoding of instances)....
8
votes
1answer
81 views

Workforce Scheduling problem - Modelling to minimize resources

I am working on a scheduling program for a service desk. I want to decide the number of people required to come in at each shift. The data I have is: There are 4 overlapping shifts Arrival pattern at ...
8
votes
1answer
117 views

Strategy for filling a table only slightly dependant on the number of columns

I'm using the OR-Tools CP-SAT solver to fill a table with integers, with various constraints, as illustrated by the x in the following figure. ...
6
votes
5answers
2k views

Algorithms vs LP or MIP

Is there a way of writing an algorithm with if-, while-statements to find an optimal solution without using linear-programming (LP)/MIP? If so, what would the benefits be against the LP/MIP? Is it ...
18
votes
1answer
102 views

Optimality in a simultaneous column and row generation procedure

What is the optimality argument in a simultaneous column and row generation procedure? By column and row generation procedure I mean a procedure in which every time a column in generated, several ...
11
votes
1answer
125 views

Quadratic programming using CPLEX: how to check whether candidate is an extreme point?

I am currently solving an indefinite quadratic program with linear constraints using CPLEX. Moreover, I am trying to determine whether the candidate point CPLEX is feeding my callback function is an ...
10
votes
2answers
149 views

Decoding a Deep Neural Network as an Analytical Expression for Optimization Purpose

This post is not really about a specific question but rather a topic I am curious about to know more. We know that when it comes to integrate machine/statistical learning with optimization for the ...
11
votes
0answers
113 views

Modeling an assignment/scheduling problem to minimize total wait

I have an assignment type problem in which there is a set of students, $S$, and a set of training classes $T$. Each training has a fixed start and end day and can accommodate at most 1 student. In ...
10
votes
1answer
175 views

Expressing a chain of boolean ORs using ILP involving different variables

How can I express a chain of OR operations in an ILP, given that each operand is an inequality between two binary variables? I have asked a similar question here: Chain of Boolean ORs. In that ...
20
votes
6answers
1k views

How to compare two different formulations of a problem?

I somewhat know how to compare two MILP formulations of a problem that both use the same set of decision variables (as in the classical MTZ vs DFJ formulations of the TSP). I was wondering how two ...
5
votes
2answers
256 views

Linear and Integer programming materials

I was wondering if you could refer me to some online video/text resources to learn linear and integer programming. I am intending to work in the field of data science. I greatly appreciate your kind ...
15
votes
4answers
512 views

Best model for precedence constraints within scheduling problem

Suppose I'm modeling a problem where I want to compute the start time bucket for some jobs. All time buckets have equal duration. There are some additional constraints involved but I also have to ...
12
votes
2answers
226 views

How to choose an architecture for an OR web app and how to learn the tech stack associated?

After carefully reading the answers to my previous post I decided to opt for developing and deploying an app as a web service. I watched a talk on optimization apps. It suggests using the following ...
11
votes
1answer
129 views

Representing an indicator function: binary variables and “indicator constraints”

I want to represent the indicator function: $$ \mathbb{1}_{(y=j)}$$ where $y$ is a non negative, integer variable. My attempt is as follows: define a binary variable: $$ z_j =\begin{cases} 1 \qquad\...
35
votes
9answers
3k views

Are there any OR challenges that are similar to kaggle's competitions?

I am looking for previous OR challenges. My goal is : Applying my knowledge while solving problems suggested in those competitions; and/or If possible, reading solutions posted by participants. I ...
12
votes
2answers
380 views

Expressing a chain of boolean ORs using ILP

How to express a chain of OR operations in an ILP in which each expression is a less than or equal constraint and the left hand side variable in all inequalities is always the same? All the variables ...
9
votes
1answer
102 views

Real world demand dataset

I am looking for a publicly available real world demand data to compare the performance of some algorithms. The dataset should include some products with data of a sufficiently long period of time. I ...
9
votes
2answers
197 views

Generating all extreme rays

I am trying to understand a problem and would like to generate all extreme rays for a given set of linear constraints. With the Python interface of CPLEX, I was able to generate a single ray (not sure ...
5
votes
2answers
189 views

Bridge the gap between theory and practice in Integer Programming

I've finished Wolsey's book on Integer programming. It's a theoretic book. I aim to learn how the ideas presented in the book can be applied to solve real-world non-academic problems. I am looking ...
13
votes
2answers
341 views

Simulation optimisation: Monte carlo simulation, regression, optimise within regression model?

Can you help me identify if this technique has a standard name to help me explore the literature? Suppose I have a black-box stochastic simulation parameterised by $X=[x_1,...,x_p]$ with some single ...

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