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.

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2answers
403 views

Modeling a constraint such that a set of binary decision variables do not equate to 1 simultaneously

I would like to seek some advice on modeling the following logical condition: I would like to ensure that a group of binary variables do not equate to 1 simultaneously, i.e., $\omega_{1}=1, \omega_{2}=...
3
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2answers
126 views

A relaxed version of job shop scheduling

I am working on a formulation for a problem that seems similar to the bin packing problem. My problem variables include items that are to be placed in bins, special events that are conditionally ...
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1answer
99 views

Why some decision variables don't get values in Cplex?

I use this code in the cplex and don't know why some decision variables don't get value, I attach my code below. I don't know my model is wrong or my code? I haven't error in the code but have some ...
5
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2answers
604 views

How to transform this logical if-then constraint?

Consider the binary variables $x, y, z \in \{0,1\}$. I'd like to formulate the two if-then constraints: $$ x + y \geq 2 \implies z = 0, \tag{1} $$ $$ x + y \leq 1 \implies z = 1. \tag{2} $$ Constraint ...
1
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1answer
90 views

Solving general minimum cost flow problems using only one demand and one supply node

This is a practice in using reduction. Suppose I have a solver that only allows input to a MCF that specifies only one demand and one supply node. How could I use this solver to solve general MCF ...
2
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0answers
31 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 ...
2
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1answer
68 views

Which is better to minimize w.r.t a lower bound or an upper bound of an objective function?

Suppose there is a optimization problem that aims at minimizing an objective function $X$ but we can't develop a mathematical model for minimizing $X$. However, there are two objective functions $Y$ ...
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0answers
40 views

The different behavior of the solvers to dial with MINLP problem

I have tried to solve an optimization problem (an MINLP) to minimize the number of items which need to be stored. The objective function is as follows: $$\min \quad z = \sum_{i=1}^{n} \, \color{blue} {...
5
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1answer
146 views

ILP Constraint to ensure exactly one constraint from a set of constraints is satisfied

Consider several Integer (0/1) ILP variables, i.e., Boolean variables, $x_i$'s. Consider an ILP constraint $x_1 + x_2 + x_3 \geq 1$ and another constraint $x_4 + x_5 + x_6 \geq 1$. I would like to ...
2
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0answers
21 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. ...
2
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1answer
40 views

Logical equivalencies to modeling an indicator decision variable in transportation problem

I am formulating a model that seeks to minimize the cost of shipping goods from factories to warehouses, where the cost of shipping is independent of the type or amount of goods being shipped (except ...
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0answers
50 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 ...
6
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1answer
127 views

Formulating two non-negative variables without binary and/or big-M

There are two non-negative integer variables $q$ and $p$, where only one of them can take a positive value. To impose this relation, I write: \begin{align} q &\leq M(1 - y) \tag1 \\ p &\leq M(...
2
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1answer
141 views

Working with large models

I am working with a variant of TSP, number of nodes that I need to test are in between 2500 to 3000 nodes, I am using docplex for modelling, I have a 8 gb Ram but it gets filled with only 400 nodes. ...
3
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2answers
174 views

Modeling in integer programming vs modeling in constraint programming

I have some experience with linear and integer programming modeling (I read Model Building In Mathematical Programming by Williams). Now I am trying to learn how to model with constraint programming. ...
2
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0answers
60 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 ...
2
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1answer
67 views

How to model these constraints correctly

$W$ is a vector of $N$ complex elements. $D$ is a binary variable The requirements are: when $D==1$, $L_{\min}\le ||W||_2^2\le L_{\max}$ and when $D==0$, $||W||_2^2=0$ I have formulated the following ...
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1answer
50 views

Priority Constraint

Suppose I have the following set of binary variables: $X_i$: $I$ ranges from {1,..,4} Highest priority among the three variables $X$ , $Y$ and $Z$ $Y_j$: $J$ ranges from {1,..,3} $Z_k$: $K$ ranges ...
5
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1answer
107 views

How to check whether two formulations are equivalent?

I am given two formulations, that is, two integer programs $ (IP1)\quad \min \{c^tx \mid Ax\geq a, x\in Z^n\} $ and $ (IP2)\quad \min \{d^ty \mid By\geq b, y\in Z^m\} $ and I wish to check whether ...
2
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1answer
106 views

How can I perform discrete optimisation of a variable over a data set

This question relates directly to a dataset I've generated for Fantasy Premier League, but I'm also curious how I can apply this to a more general case. Data I have a list of premier league players, ...
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0answers
55 views

Modeling the multiplication of two binary decision variables in undirected graph in python

In an undirected graph, I'm trying to model a constraint that forcing the optimizer to set an edge $(u,v)$ between two nodes to only exist (= $1$) if the two nodes have been selected to be $1$. The ...
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2answers
116 views

Modeling the product of two variables

Suppose we have two continuous nonnegative variables $X_{1}$ and $X_{2}$ both bounded by the number $M$ from above. I would like to model the following: If $X_{1} > 0$ then $X_{2} = 0$ If $X_{2} &...
3
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1answer
78 views

What type of model is this

I was trying to find a name for the following model; is it mathematical programming, constraint programming, convex optimization, but as I can see, none of them has a continuous parameter $t$ like in ...
3
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1answer
91 views

What are the flow based formulations?

What are the flow-based formulations? For what optimization problems are they applied, and in which form? Which are the specificities of such a formulation? Also, the same question for the time staged ...
6
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2answers
410 views

How to model bicycle sharing scheme?

One of the problems I have recently considered is the problem of rebalancing bicycle stations for bike-sharing schemes all over the world. It is not a secret that the demand for bikes across the city ...
7
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0answers
129 views

OR-TOOLS : delivery node with multiple possible pickup nodes

I am using ortools to model a VRP with pickup and delivery constraints, where pickups can be done at different nodes. For example, if node A has a demand, it must be picked at node B or C. Here is how ...
3
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1answer
55 views

What is the difference between min- cut formulation and (bi) partitioning formulation?

I have a min-cut formulation and a bi-partitioning problem. The two problems focus on finding the minimal cut value separating the two partitions? So what are really the differences between the ...
3
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0answers
98 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 ...
1
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1answer
71 views

How to model this chain of logical implication II

I would like to seek some advice on modeling the following (chain of) logical implication: For instance $\omega_{xz}$ might indicate precedence, i.e., $x$, $z$ being the nodes $x$ and $z$, ...
2
votes
1answer
65 views

Maximum bipartite matching with breakpoints in edge weight function

I am looking for an analogy to the problem I am facing or better yet a paper or even code. I have: Nodes from set A and B. Edges are from a single A to many B. I am framing a max bipartite matching ...
6
votes
1answer
170 views

OR-TOOLS : is it possible to partially fulfill a demand?

I am working on a vehicle routing problem with or-tools. Is it possible to partially fulfill a demand? I know it is possible to drop nodes with the disjunction constraints. But in this case, a node is ...
1
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1answer
59 views

How to model this chain of logical implication

I would like to seek some advice on modeling the following (chain of) logical implication: For instance $\omega_{xy}$ might indicate precedence, i.e., $x$, $y$ being the nodes $x$ and $y$, ...
2
votes
1answer
56 views

How to build a GAMS model in python

I looked at the GAMS python API but the documentation only describing already predefined models (run .gms with some tweaking options). My question is now: Can I somehow build a gams model from scratch ...
6
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0answers
56 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 ...
7
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1answer
126 views

MILP formulation for minimum set Vertex cover problem

I’m sorry to bother you with this simple question. I would like to model a simple model of the minimum cover vertex set problem. I believe that the original problem is such as $$ \min \quad \sum_{v\in ...
4
votes
1answer
87 views

How to linearize $f(x,y) = (ax+by)/(x+y)$?

I have a problem which is mainly linear but it has a non-linear component. The objective function is obj = Linear_term + $c*f(x,y)$ where, $f(x,y) = (G_1 x_1 + G_2 x_2)/(x_1 + x_2)$. The decision ...
5
votes
3answers
608 views

How to determine if this problem is NP-HARD or NP-COMPLETE?

Suppose that I have a pool with N nodes and I have to move the nodes one by one to another pool. For each move, consider a value on the edge linking the two pools. The goal is to find a order of nodes ...
3
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1answer
82 views

Soft OR & Problem Structuring Methods - often the first steps on an OR journey should not be missed out on this site. So what are they?

Let's make a space for ALL of OR to be discussed. I'm particularly interested in the link between OR and design, I also co-chair the PSM SIG for the OR Society. Hopefully by putting in some tags we ...
6
votes
1answer
224 views

What is the performance improvement when using semi-continuous variables instead of binary + continuous variable pair?

I have a MILP model that solves a master production schedule including capacity decisions. In the model I have a production quantity that should either be 0 or at least the amount that can be produced ...
3
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2answers
101 views

Relaxation and complexity of two formulations

I have two different MILP formulations for the same scheduling problem with the same complexity but with different running times. Why it is recommended to compare the relaxed versions of each ...
1
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1answer
77 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 ...
3
votes
3answers
640 views

Does adding constraint to an optimization model make it solve faster?

Some say adding constraints cuts the feasible region smaller hence the same solver terminates faster due to the less search effort. Others say it adds more complexity to the problem and it may take ...
1
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1answer
103 views

Constraint programming and scheduling issues

I have a constraint problem that I need to resolve, but I did not how know to model the problem: I have 11 employees, I will name them from $a$ to $k$: $\{a,b,c,d,e,f,g,h,i,j,k\}$. I have a small ...
2
votes
1answer
307 views

Divisibility constraint in Integer programming

I have a simple question regarding the divisibility in integer programming suppose the objective function is $\text{max}\quad x_1 + x_2$ where the constraint is that the sum of $x_1$ and $x_2$ are ...
0
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1answer
100 views

Help with excel solver

Need help with the following exercise. I am unable to work out the objective function. After months of closure due to Covid-19, a food court is preparing to re-open for business. However, safe ...
5
votes
1answer
214 views

How to determine the size of a model?

I want to know about the number of variables and constraints of this formulation (exp: $o(n)$ variables and constraints or $o(n^2)$ ....). Is the number of variables $\mathcal O(n^3)$ because we have ...
2
votes
1answer
94 views

How to model a set of integer variables getting assigned different values than another set of integer variables

Assume we have variables $x_1, x_2, x_3, x_4$ that each can belong to $\{1,2,...,10\}$. How can we model a constraint that variables $x_1, x_2$ get assigned different values than $x_3, x_4$? Because ...
2
votes
3answers
271 views

How to model two variables to NOT to belong to the same set partition using Constraint Programming

Assume we have two variables $x,y \in S$ where $S=\{1,2, \dots, 1000\}$. Also, we are given a partition of set $S$ as: $S_1 = \{1,2, \dots, 249\}$ $,S_2 = \{250, \dots, 499\}$ $,S_3 = \{500, \dots, ...
3
votes
1answer
82 views

Which method to use to solve this multi-objective conflicting objectives

I have the following multiobjective problem. I need to minimize the user-perceived latency while doing so aggressively minimizing user-perceived latency generates large switching cost (Reconfiguration ...
1
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1answer
70 views

A discrete location problem

I have a discrete optimization problem in which there are some predetermined nodes in the set A. a vehicle must visit them as the traveling salesman problem. there are some other nodes in the set B ...

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