Questions tagged [modeling]

For questions related to the process of converting a real-world problem into a mathematical model. Can include questions related to linearization, logical constraints, tightness of formulations, and so on.

80 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
7 votes
0 answers
102 views

MIP formulation for graph planarity test

In this question, it was asked wether a MIP formulation exists to test for a graph's planarity. The inputs are the graph's nodes and edges, and the output would be a certificate which guarantees that ...
Kuifje's user avatar
  • 13.3k
7 votes
0 answers
118 views

What distuingishes a model-and-run framework solver from a programmatic solver?

I am looking for examples to understand what kind of benefits a model-and-run framework solver offers that a more programmatic solver doesn't do or doesn't do as well. What distinguishes a model-and-...
Geoffrey De Smet's user avatar
7 votes
0 answers
151 views

Modeling traffic in a city

I am trying to model traffic in a city, $(i,j)$ represents a road in a city. There are $H$ vehicles in a city they have some prescheduled set of destinations to visit, $A_{j,h}$ denotes arrival time ...
ooo's user avatar
  • 1,589
7 votes
0 answers
153 views

Why does PuLP call copy for addition and how can I avoid it?

Using a for loop to append terms to an expression seems to be much faster than summing a group of terms all at once. Constructing the expression using a for loop uses __iadd__, which does not include ...
Charles Fox's user avatar
7 votes
0 answers
81 views

Modelling a simple ordering problem to have balanced delivery days

Assuming that I should buy 50 items from 25 different vendors with pre-known delivery duration between 2-7 day for each, which day of a week should I place each order so that the delivery days be even ...
Sean's user avatar
  • 159
6 votes
0 answers
88 views

Issue of Dense columns in the formulation

I'm working on a price-selection model where we need to identify price point for each time-period (could be day/week). Objective of the model is to figure out optimal price-point for each time-point ...
anjikum's user avatar
  • 984
6 votes
0 answers
225 views

Airline revenue management re-solving problem

I am considering a bid prices (shadow price of the capacity constraint) problem (from Chen, L. and Homem-de Mello, T. (2009)., page 14) where the acceptable classes for booking requests for ...
SimonCello94's user avatar
6 votes
0 answers
100 views

Estimating multistop routing costs

In many OR problems, it is sometimes a good idea (or necessary) to relax routing constraints. An example of this occurs in the classical facility location problem, where a warehouse can send out a ...
Kuifje's user avatar
  • 13.3k
6 votes
0 answers
90 views

Data Formulation for Mixed-Integer-Programming Models

Until now, I have used the Gurobi, CPLEX and OR-Tools (GCO) interface to formulate mixed-integer-programming models. Recently, I have discovered MiniZinc and want to utilize it to formulate big ...
Georgios's user avatar
  • 1,193
6 votes
0 answers
124 views

Help in solving resource allocation optimization problem

I've been pondering on this question for some work optimization, and I need some help in being directed to the right direction. I have multiple customers that require an amount of $X$, $Y$ and $Z$ ...
Sylicas's user avatar
  • 61
4 votes
1 answer
135 views

Need help understanding robust optimization formulation

I am reading these notes from Stanford called "Optimization with uncertain data". In section 2.2, Example 2 (page 7), the author mentions the following portfolio problem $(P)$: $$ \max \; t $...
Kuifje's user avatar
  • 13.3k
4 votes
0 answers
81 views

Is this weighted feedback concept a known, solved, problem?

Imagine a fairly standard Thumbs Up/Down feedback system. For each piece of content they consume, every user has the ability to give a binary positive/negative feedback that piece of content. They're ...
Brondahl's user avatar
  • 171
4 votes
0 answers
121 views

Modeling question on continuous variable that dependens on binary variables

Given a model with a binary variable $b_s$ that describes whether taking an item $s$ from a set $S$ or not. Consider that some other constraint in the model depends upon whether all items of the set ...
Andreas's user avatar
  • 313
4 votes
0 answers
103 views

Can this problem be modelled with a transformation from a known TSP with profits?

The profitable tour problem (PTP) is defined on a graph $G=(V,E)$ with $|V|=n$, where each vertex $i \in V$ has an associated prize $m_i \geq 0$ and each edge $e \in E$ has an associated cost $c_e \...
Alberto Santini's user avatar
4 votes
0 answers
77 views

Adding redundant inequality to a model

The following relationship is part of my optimization model ($W_k$ denotes a binary variable) $$W_{1} \le \cdots \le W_{k-1} \le W_{k} \le W_{k+1} \le \cdots \le W_{k^{\max}}$$ My question is, do ...
Clement's user avatar
  • 2,252
4 votes
0 answers
106 views

Modelling issue with rcpsp and boolean expressions

I'm trying to solve an RCPSPDc problem in OR-Tools with CP-SAT solver. In my RCPSPDc model (with discount rate) i want to set this objective: $$\max_{s}\sum_{j\in J}\text{profit}_{j}\cdot \frac{1}{(1+...
Diego R. Troncoso's user avatar
4 votes
0 answers
171 views

Publishing paper that uses LP solver to solve equation

I was reading this paper by Cerna et al. (2018)1. In the paper there are only CPLEX-solvable equations given by the authors and the results. How valuable is this paper, and what is its quality? Can ...
ooo's user avatar
  • 1,589
4 votes
0 answers
242 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 $$\max\...
KGM's user avatar
  • 2,265
4 votes
1 answer
92 views

Nurse Rostering constraints - LP

I am fairly new to linear programming since I came across this topic at university this semester. We mainly focus on nurse rostering. In the lecture, we created a very basic rostering model with an ...
nflgreaternba's user avatar
3 votes
0 answers
87 views

Minimize total cost to buy unique products over timespan

I am looking for some guidance on how to better state my problem formally and practically (e.g., relevant Python libraries). Let's assume I have a set of $X$ unique products to buy. I have $Y$ days in ...
M2FKXY's user avatar
  • 31
3 votes
0 answers
90 views

How to compute the time required to transport one unit of flow on a given path?

My question is related to freight transportation, but I am stuck on the logic. So, I am considering a path between two points $(a, b)$ where I am sending $n$ trucks where the capacity/truck is $k$. ...
Bree's user avatar
  • 115
3 votes
0 answers
101 views

What is the general name (e.g. facility location problem) for this problem (if any)?

I would like to know if there is a general name for the following problem: We will open several facilities. Each facility has an associated facility type. There exists a given number of facility ...
Displayed_Name's user avatar
3 votes
0 answers
190 views

Good book to get familiar with the key concepts of Operations Research for a person which didn't enjoy a good math education in university?

I am currently reading research papers on optimization problems in logistics and struggle to understand the math notation. Any good beginner friendly books you would recommend? This is the paper I ...
Eddiee's user avatar
  • 533
3 votes
0 answers
123 views

How to approach this Truck Utilisation problem?

The problem statement currently I have is very broad (or you can say very vague at the same time): I have a number of dropping locations (Customer locations) I have the location of the HUB I have a ...
Shibaprasad's user avatar
3 votes
0 answers
67 views

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 ...
Dylan Solms's user avatar
3 votes
0 answers
183 views

How to linearize a max min objective function?

Let us suppose that I have a $\max \min$ objective function that only depends on one set of variables: $\underset{x}\max \underset{y}\min dy$ Associated with the linear set of constraints and right ...
JKHA's user avatar
  • 679
3 votes
0 answers
53 views

How to formulate a storage component?

Let’s say I have a drink for several customers, and I know their demand. Besides, I also have a storage tank for the drink during times when demand exceeds supply. The storage tank's size is not yet ...
Snowflake's user avatar
  • 517
3 votes
0 answers
233 views

How to model non-zero minimum constraint?

I found following way to model a minimum constraint but in my case I need a non-zero minimum value. So in this figure, if any value of x_i is 0 then answer is 0 (assume x_i >=0) but I need non-zero ...
Vinod Kumar Chauhan's user avatar
3 votes
1 answer
73 views

Are there standard symbols to describe discrete event simulations (DES)

I just wonder, whether there is a good reference for the symbols used in a flow chart to describe a DES process. I am looking for something like Kendall notation but with a reference to the symbols. I ...
Christoph's user avatar
  • 131
3 votes
0 answers
83 views

Where I can study some job shop scheduling by course (video )?

I am seeking the help to know where I can study the job shop scheduling Heuristics or using solver by some course/video as I see some of books and papers hard to understand . It is hoped that the ...
Yue Chao's user avatar
3 votes
0 answers
110 views

Production planning for a video game economy

I'm a software developer who likes to play a video game that has a complex economy. I realized that the type of problem I'm trying to solve mimics real life operations research problems, and I am ...
0x1F602's user avatar
  • 139
3 votes
0 answers
68 views

Discrete optimization in transport economics

I was working on a problem in transport economics where the optimal number of trips in a given duration of time is to be found out. The profit is a function of the price vector $p$ and time cost $c$ ...
Ishan Kashyap Hazarika's user avatar
3 votes
1 answer
103 views

Modelling Question

Let $W^C_t$, $W_t$ be binary variables and $p$ an integer variable with $1 \leq p \leq 3$ The variables are related through the following equation: $$W^C_t = \sum_{\theta=1}^{p} W_{t-\theta}$$ I can ...
Clement's user avatar
  • 2,252
3 votes
1 answer
162 views

Optimization model testing tooling: likes, dislikes, and wishes

We’re [1] in the thick of building out a testing suite for decision models, starting with a focus on route optimization. There are several angles we care about [2] and are considering: unit testing, ...
Ryan O'Neil's user avatar
2 votes
0 answers
60 views

System Stability constraints formulation

I am working with a system having a massless 2D plane and on that plane there is a rigid object with some mass placed on it. I want to support the plane with wooden sticks such that the system is ...
Ken Adams's user avatar
2 votes
0 answers
61 views

Resources on the soft aspects of modelling

Usually, the modeling involves those steps : Fuzzy Description ----(1)----> Clearer Description -----(2)-----> Mathematical model. Of course, it's not linear and a lot of iteration and re-...
BloodyOrange's user avatar
2 votes
0 answers
223 views

OR constraint in Gurobi - Python

I'm new to Gurobi in Python and I am wondering if there is way to code the following constraints: 1- $\sum x_i =0$ for all $i\in A$ OR for all $i \in B$ where A and B are distinch sets of integers ...
M.Badaoui's user avatar
  • 185
2 votes
0 answers
66 views

Assignment/scheduling how to formulate considering job time and job cost

I have the following problem that I do not know how to formulate. There are a fixed number of workers $w_i \in W$ for $i \in [1…N]$. Also, there are a fixed number of jobs that must be assigned to ...
Daniel Baquero's user avatar
2 votes
0 answers
57 views

How to construct a restriction for a blending problem that has 2 inputs that are blended, and as result we get 2 outputs?

THE PROBLEM A refinery has 10 million barrels of type A crude and 6 million barrels of Type B crude oil. The refinery has 3 plants to produce Gasoline (it makes a profit of 2 USD / barrel) and Naphtha ...
ergch24's user avatar
  • 67
2 votes
0 answers
109 views

Recommendations on Operations Statistics/Analytics Approaches/Materials

I'm an operations data analyst. I was wondering if I can get recommendations on books/videos on statistical models specific to optimizing business operations through analytics and statistical modeling....
luckee.13's user avatar
2 votes
0 answers
140 views

How to use NEOS without using Pyomo

I am new to modelling language and specifically NEOS server. I aim to solve MINLP using Baron, through the NEOS server. So, far I have been able to write model file, data file and command file as ...
user avatar
2 votes
0 answers
42 views

Hardness Reduction for assigning Users to Servers

Suppose there are $x$ servers, and $y$ users. The $y$ users are to be assigned to the $x$ servers similar to classic scheduling problems. The cost of using servers is given by $c(|x|)$ which is an ...
ephemeral's user avatar
  • 897
2 votes
0 answers
84 views

Dynamic Programming problem of affecting equipment with budget constraint

I have a problem that I must formulate as a DP problem and solve. A hospital is split up into 4 sections, each section has 1 or 2 or 3 backup generators. We have to maximize the likelihood that no ...
ndrb's user avatar
  • 21
2 votes
0 answers
80 views

Analysis model vs. executable implementation of model?

In my post-graduate research and subsequent career in operational analysis, the difference between following seems to have become clearer with the years: (1) a model of a problem or operations in the ...
user2153235's user avatar
2 votes
0 answers
70 views

What are the efficient ways to model this scheduling problem and ways to improve running time

There are $N - \{1 \ldots N\}$ jobs, each with processing time $p_j$, to be scheduled on $M - \{1 \ldots M\}$ machines over span of $D - \{1 \ldots D\}$ days and while working $T - \{1 \ldots E \ldots ...
Amogh Bhosekar's user avatar
2 votes
0 answers
110 views

Efficient way to do user rescaling of variable in Gurobi

Is there a better way than the code below to the rescaling of variable in a model after the model has been build with Gurobi? Like some build in function or a direct manipulation of the column object? ...
user3680510's user avatar
  • 3,655
2 votes
0 answers
135 views

Montoya et al. 2017 benchmark Results

I am testing Montoya et al. 2017 dataset and trying to replicate the Result from this paper The electric vehicle routing problem with capacitated charging stations. I am unable to replicate the exact ...
ooo's user avatar
  • 1,589
2 votes
0 answers
170 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 ...
HABIL BHAGAT's user avatar
2 votes
0 answers
90 views

Problem classification: optimal weights for Weighted Arithmetic Mean

I want to write an optimization problem then solve it, to get optimized weights to compute a final score using a weighted arithmetic mean. The problem is as follows. I have an entity (an input vector $...
Betty's user avatar
  • 544
2 votes
2 answers
117 views

constraint set for a scheduling problem with machine availability

I have a set of tasks $I$ with processing times $p_i, \forall i \in I$. There exists a set of machines $M$ and each machine has availability time ranges in a given time horizon. For instance, given a ...
ball_jan's user avatar
  • 157