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.
494
questions
3
votes
2
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338
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How to model a binary variable?
I am trying to find a constraint for the following relationship, but am failing a bit at it right now. I want to find a linear constraint that does the following. The binary variable $switch_{ot}$ is ...
- 31
2
votes
1
answer
90
views
Find the minimum number of equipment required for a service period
I'm starting to learn operations research and trying to get my head around this problem that I have.
Problem statement: Find the minimum number of equipment needed to run a service schedule.
There are ...
- 21
0
votes
2
answers
97
views
Is there a comprehensive list of problems in OR?
I was trying to search for different types of problems in OR and couldn't find a exhaustive list of problems. So far I have,
Travelling salesman problem
Cutting Stock problem
Shortest path problem
...
- 57
0
votes
1
answer
74
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Mixed Integer Programming - How to model a term in objective function with a constant multiplied by (1-Decision Variable)
I am solving an optimization problem, where I want to minimize the objective function
$$Z = \sum_q \left(D_q \text{fare}_q - \sum_{p \ne q} \Delta D^p_q \text{fare}_q \right) (1-Z_q)$$
Each $q$ is an ...
1
vote
1
answer
59
views
Workforce scheduling MIP formulation
I am working on a large scale workforce scheduling problem with a large number of hard and soft constraints. The soft constraints are modeled as objectives with penalties for violating them. So my ...
5
votes
4
answers
829
views
Rewriting if-then constraints of binary summations
Suppose both $x_{i,j}^{ab}$ and $y_{i,j}^a$ are binaries. Then how can I rewrite the following if-then in linear form?
$\sum_b x_{i,j}^{ab} \ge 1 \implies \sum_{i,j} y_{i,j}^a = 0$
I was thinking of ...
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1
vote
2
answers
146
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how to satisfy time constraints with meeting points?
I have a specific pickup and delivery problem to work on and am thinking how to incorporate time windows effectively. The problem has some driver with some time window [$a_d, b_d$] which is the start ...
- 11
2
votes
2
answers
206
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Model Complexity and Constraints in Mathematical Modeling
I have a few questions about mathematical modeling (MILPs mainly). My understanding is that the complexity of a model is primarily determined by the number of decision variables, rather than the ...
- 41
6
votes
0
answers
89
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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 ...
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4
votes
1
answer
200
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MIP Model with relaxed integer constraints takes longer to solve than normal model, why?
I am currently working on my undergrad thesis which is a mathematical optimization problem of the territory design family of problems. I am using the mathematical formulation of the problem to solve ...
1
vote
1
answer
49
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Assistance in formulating implication constraints for inequalities
I would like to seek some advice on modeling the following logical implications, where $\delta$ is a binary variable, $D_{j}$ and $A_{j}$ are nonnegative discrete variables, and $p_{j}$ are ...
- 707
1
vote
1
answer
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Traffic lights optimization (part 2)
This is a follow up question of this thread, in which it is asked how to model a circular layout of a given set of cliques of a graph, which represent simultaneous movements at an intersection.
@...
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1
vote
2
answers
113
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Is there a way to obtain coefficient matrix A and RHS b of constraints equation from cplex or guribi in python?
I have a non-linear program, minimizing sum of concave functions subject to linear constraints. Hence I'm using a different solver(in Julia). However, that solver assumes we have constraints in $Ax \...
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4
votes
3
answers
480
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How can I formulate this 'if-then' constraint problem?
I have five integer variables, and I need to write some constraints on them:
$x_0$ , $[x_1, x_2, x_3, x_4 ]$. $1 \leq x_i \leq 3$
if $x_0 =1$ then no constraint on $[x_1, x_2, x_3, x_4 ]$
if $x_0 =...
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2
votes
1
answer
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A tighter relaxation of the mix logical constraints
Suppose the following logical form there exists.
$$Iff: (x_{j,m} \land x_{k,m}) \implies ((C_{j} \leq S_{k}) \lor (C_{k} \leq S_{j}))$$
This is well-known as a no_overlap_constraint in the parallel ...
- 7,559
1
vote
3
answers
61
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PuLP ensure first and last choice
I have an assignment problem where I have $N$ locations and $M$ dates for each location, and the goal is to choose $K$ location-date pairs that maximize revenue. There are a number of constraints, for ...
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7
votes
2
answers
307
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Traffic lights optimization
I am interested in the following problem dealing with the optimization of traffic lights on the intersection illustrated below:
The goal is maximize the duration during which each movement $m\in M=\{...
- 12.3k
1
vote
0
answers
31
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Auxiliary parameters for two uncertain parameters Robust Optimization
I have the following constraint for robust counterpart formulation, where two uncertain parameters appear at the same time;
$\sum{QG_{ij}}$*${\theta}$+$\sum_{}\sum{QD_{ij}}*p $ * ${\theta}$
where;
${...
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1
vote
2
answers
56
views
Is it possible to route based only upon shortest path?
I have a routing problem and am wondering if it is even possible to only use the $k^{th}$ shortest path?
There are a set of people with cars and a set of other people with no cars, each has its own ...
- 41
3
votes
2
answers
635
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Writing a constraint of an integer programming in a linear form
I modeled an optimization problem in an integer programming format. The main constraint I came up with is now nonconvex. I would like to see if there is another equivalent formulation in which the ...
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3
votes
2
answers
326
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How to model C1 = C2 implies b1 = b2
Suppose $C_1 \ge 0$, $C_2 \ge 0$ are continuous variables and $b_1$, $b_2$ are binary variables.
How could I model the following?
$C_1 = C_2 \implies b_1 = b_2$, the opposite does not hold.
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3
votes
2
answers
330
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How to model this binary constraint?
I have an optimization problem that has a variable in the matrix form. The variable is a binary matrix. It has size $M \times N = 10 \times 50$ where $M$ is the number of machines and $N$ is the ...
2
votes
2
answers
349
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Representing "and"/"or" relationships into constraints
How do I represent the following constraints in terms of equations?
For each i, either (1) holds or (2) holds-
$$
x_{1}^i \geq x_{2}^i \quad and \quad x_{3}^i \geq x_{4}^i \quad {(1)}
$$
$$
x_{1}^i \...
- 77
3
votes
3
answers
189
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Quantifying a measure of standard deviation in MILP
I am trying to set up a MILP for production scheduling. The specific details I'm not sure are important but in general a plant has M machines running N parts, each part requiring W workers. The model ...
- 33
1
vote
1
answer
64
views
how to minimize the distance to the final points with incomplete information?
Suppose we have a transportation problem similar to pickup and delivery problems. So, we have a set of drivers and a set of passengers. each passenger has predefined origins and destinations. I'd ...
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0
votes
1
answer
35
views
Array of string in OPL
how to make 2d array of strings in Cplex
//indics
{string} cluster=...;
setof(string) darkstore =...;
setof(string)demandpoint =...;
//data
cluster={chav,sree};
demandpoint=[{tsnami,adholokam,...
4
votes
2
answers
283
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The linearization of the (Iff-and-only-Iff) expression
I am trying to linearize the following expression without using the Big-M formulation, but I cannot convert it. I am willing to know if there exists an efficient way to do that?
$$ Iff \quad (w=1) \...
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1
vote
3
answers
120
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Optimization solver that satisfies variable values within set membership
Is there a solver that can handle an AMPL model of this sort:
...
0
votes
1
answer
57
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Maximization problem with preferences on variables
Consider the following trivial, theoretical model:
$$
\max x+2y+3z \qquad s.t.
$$
$$
x \leq b_x
$$
$$
y \leq b_y
$$
$$
z \leq b_z
$$
$$
x+y+z = 1
$$
$$
x,y,z \in \{0, 1\}
$$
and $b_x$, $b_y$ and $b_z$ ...
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3
votes
2
answers
148
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How to find the maximizing number of expected delivered units of a probabilistic minimum cost flow problem?
I am a Bitcoin / Lightning Network open source developer and researcher and new here but very active on the sister site. In the context of my research I discovered the field of operations research ...
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0
votes
1
answer
75
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To maintain safe order level from a customer
A telecommunication company (CALLME TEL Co., Ltd) receives and processes customers’ orders.
Orange Co., Ltd is an important customer, who mostly places orders every 2 months. Medium quantity of ...
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1
vote
1
answer
238
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multi-commodity flow vs integer programming
A theater center needs to select which shows to broadcast in one of its rooms for a given day. There are three options available: short films that last about 1 hour, movies that last about 2 hours, ...
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2
votes
3
answers
107
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Efficient formulation of flexible job-shop scheduling constraints
I am working on a flexible job-shop scheduling problem, where indices are as follows:
$i$: Index of operations
$j$: Index of jobs
$m$: Index of machines
$p$: Index of operation sequences on a machine
...
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6
votes
3
answers
442
views
How do we formulate a problem where the decision variable has an index that is also a decision variable?
I want to maximize the sum of a nonlinear function $f(.)$ w.r.t. $x$ that is convex in $x$:
$$\max \sum_{i=1}^N f(x_i), $$where $x_i$ is a continuous variable and $0 \le x_i < 1$ for $i = 1, 2, \...
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3
votes
3
answers
567
views
Modelling if elif else conditions as MIP
I have 4 variables. Xl6, Xs6, Pl6, Ps6. I have a constant C as well.
Xl6 and Xs6 are binary whereas Pl6 and Ps6 are integers. Also, all variables can take only positive values.
I have to implement ...
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2
votes
2
answers
100
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 ...
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3
votes
1
answer
102
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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 ...
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3
votes
3
answers
264
views
Set null the next set of N values
I'm dealing with a problem I already modelled by using linear programming. The already existing constraints set at 1 groups of contiguous variables (for ex: ...
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1
vote
1
answer
140
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variable use of nested blocks in pyomo
I'm using pyomo to model a system consisting of subsystems which themselves consist of subsystems. Therefore, I use nested Blocks. Every block is described in a separate file. I want to be able to ...
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1
vote
1
answer
77
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How to model this problem with multiple objectives?
This question is related to How to deal this L0 norm of a vector of L2 or L1 norms in objective?
I have an optimization variable denoted as ${\bf A\in\mathbb{C}^{100\times 5}}=\begin{bmatrix}{\bf a}_1&...
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votes
2
answers
241
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How to partition a giant tour into feasible routes?
In vehicle routing problems, the route first cluster second approach starts by computing a "giant" TSP tour (which typically does not satisfy all constraints of the problem), and then ...
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5
votes
2
answers
396
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Is this constraint with an indicator function nonlinear?
We have two variables $x\geq0$ and $y\in\mathbb{Z}^{0+}$.
We have this constraint in our model
$$x = \sum_{i = 0}c_i \mathbb{1}_{\{y=i\}}$$
where $c_i$ is a parameter and $\mathbb{1}_{A} = 1$ if $A$ ...
user10774
1
vote
1
answer
137
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How to model this constraint? [duplicate]
I have a system with $C$ machine and $U$ users.
The decision variables are $d_{u,c}$ and ${\bf f}_{u,c}$ with $c=1,2,\cdots,C$ and $u=1,2,\cdots,U$, where
$$d_{u,c}\in\{0,1\}$$
$${\bf f}_{u,c}\in\...
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3
votes
1
answer
146
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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, ...
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votes
3
answers
383
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Is this arc routing formulation correct?
Let $G=(V,E)$ be a graph. I would like to identify an eulerian cycle in $G$ with minimum cost, with an integer programing approach:
$x_{ij}$ are integer variables that denote the number of times that ...
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4
votes
1
answer
333
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How can I transform this logical if-then constraint? [duplicate]
I want to know how to transform this logical if-then constraint? If $B=1$,then $A \ge C$, else $A=0$, where $A$ and $B$ are decision variables and $C$ are constants. $B$ is binary variable and $A\ge 0$...
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1
vote
1
answer
162
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How to write this logical expression with Gurobi + Java, or express it as a big-m formulation
I am trying to write the following expression in Gurobi+Java or Gurobi+python, if it is more practical It could be expressed as a big-M formulation.
\begin{equation} \label{const4}
\text{D}_{uv} =
...
- 11
2
votes
2
answers
204
views
How to model not-met demand to next period?
I am trying to include to my model a demand shift. That is, I am having a fixed demand for each period (t), but because of capacity constraints I am not able to serve the whole demand for each period. ...
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5
votes
1
answer
207
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Summation of Binary Variables Pushing a Binary Variable
I'm modeling a problem where I have a set of binary decision variables $x_{ij}$ that has a value of 1 if the person $i$ is allocated to day $j$ or 0 otherwise.
I have another set of binary decision ...
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2
votes
1
answer
108
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How to mathematically model this multi-objective optimization problem?
I have a system of $M$ machines and $U$ users.
Each machine has a capacity in terms of number of resources.
Let, machine $m$ has $\zeta_m$ resources.
Each user has a service demand $d_u$ and there is ...
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