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.
474
questions
3
votes
2
answers
279
views
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
297
views
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-
$$
x_{1}^i \geq x_{2}^i \quad and \quad x_{3}^i \geq x_{4}^i \quad {(1)}
$$
$$
x_{1}^i \...
- 65
3
votes
3
answers
160
views
Quantifying a measure of standard deviation in MILP
I am trying to set up a MILP for production scheduling. The specific details I'm not sure are important but in general a plant has M machines running N parts, each part requiring W workers. The model ...
- 33
1
vote
1
answer
56
views
how to minimize the distance to the final points with incomplete information?
Suppose we have a transportation problem similar to pickup and delivery problems. So, we have a set of drivers and a set of passengers. each passenger has predefined origins and destinations. I'd ...
- 113
1
vote
1
answer
20
views
Array of string in OPL
how to make 2d array of strings in Cplex
//indics
{string} cluster=...;
setof(string) darkstore =...;
setof(string)demandpoint =...;
//data
cluster={chav,sree};
demandpoint=[{tsnami,adholokam,...
1
vote
0
answers
38
views
Identifying problem category of balancing resources in transport networks
I'm new to OR, and I'm in the process of categorizing a problem I'm working with.
The attached picture is an example of a transport network. Note that s2, s5, and s8 are shared stops.
Every stop in ...
4
votes
2
answers
272
views
The linearization of the (Iff-and-only-Iff) expression
I am trying to linearize the following expression without using the Big-M formulation, but I cannot convert it. I am willing to know if there exists an efficient way to do that?
$$ Iff \quad (w=1) \...
- 43
1
vote
3
answers
111
views
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
56
views
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 $b_z$ ...
- 927
3
votes
2
answers
120
views
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 ...
- 131
0
votes
1
answer
66
views
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 ...
- 429
1
vote
1
answer
171
views
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, ...
- 123
2
votes
2
answers
79
views
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
...
- 485
6
votes
3
answers
430
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, \...
- 1,001
3
votes
3
answers
543
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 ...
- 181
2
votes
2
answers
99
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 ...
- 158
3
votes
1
answer
101
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 ...
- 2,028
3
votes
3
answers
262
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: ...
- 33
1
vote
1
answer
85
views
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 ...
- 11
1
vote
1
answer
75
views
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&...
- 2,179
6
votes
2
answers
231
views
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 ...
- 11.8k
5
votes
2
answers
375
views
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
136
views
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\...
- 2,179
3
votes
1
answer
136
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, ...
- 39
5
votes
3
answers
382
views
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 ...
- 51
4
votes
1
answer
316
views
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$...
- 43
1
vote
1
answer
151
views
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. ...
- 79
5
votes
1
answer
198
views
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 ...
- 53
2
votes
1
answer
103
views
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 ...
- 2,179
-2
votes
2
answers
56
views
How to model the following "if, then" constraint
There are two matrices:
Matrix $S^{v\times v} \in \{0,1\}$ this is a know parameter.
Matrix $X^{v\times p} \in \mathbb{N}$. Elements of $X$ are the variables.
I want to model:
$$\textrm{if }s_{v v'} =...
- 169
5
votes
3
answers
183
views
MIP constraint with sum of decision variables having certain value : $\sum_{i=1}^nx_i = 2 \implies \delta = 1$
I want to formulate a MIP constraint such that :
$$\sum_{i=1}^nx_i = 2 \implies \delta = 1$$
$x_i, \delta \in \{0, 1\}$.
My problem is that delta should be one when this sum is exactly 2 and not ...
- 235
2
votes
1
answer
381
views
If/then constraint formulation
Let's assume we have event $i=1,2,\cdots,k$, denoted as $\text{event}_i$. We know for a fact that $\text{event}_i$ is smaller then $\text{event}_{i+1}$ i.e., $\text{event}_i \leq \text{event}_{i+1}$. ...
2
votes
1
answer
104
views
Conditional constraint for binary
Could you please check where I might be wrong?
Task is:
If $z=1$, then either $x=1$ or $y=1$
My approach:
If $z=1$, then $x+y=1$
$\implies x+y\le1$
$\implies x+y\ge1$
If $z=0$, then $x+y\ge0 - M\cdot(...
2
votes
1
answer
44
views
Automatic Reformulation Tools For AML Programs
Are there any tools to transform programs written in an algebraic modeling language like GAMS,AMPL,... into a different formulation.
E.g. there is a quadratic constraint $\sum_j b_i b_j = N, b \in \...
- 153
2
votes
3
answers
497
views
How to find the index of the item, the first time appears?
How to formulate this problem as MIP:
For example, we have the following vector of binary variables:
$$
x= [0, 0, 0, 1, 0, 1, 1]
$$
How to find out when the first "1" is recorded? For ...
- 391
4
votes
3
answers
407
views
How to transform a logical constraint with integer variables?
Consider the binary variables $x_1, x_2 \in \{0,1\}$ and the integer variable $y \in \mathbb{Z}$ with $0 \leq y \leq 3$.
I'd like to formulate the following logical constraint:
$$
x_1 = 1 \wedge y \...
- 385
2
votes
1
answer
155
views
Binary variable constraint for condition
I am trying to solve the following task:
If $x=1$ or $y=0$ then $z=0$
My approach:
If $z=0$ then $x+y \le 2 + Mz \implies x+y \le 2+2z \quad$
where $M = 2$
If $z=1$ then $x+y=1 \\
\implies
x+y \le 1, ...
0
votes
1
answer
44
views
Conditional constraint for binary variables
I would appreciate any help to solve the following task:
If $y=1$ then $x_i=1$ for at least $k$ of the possible indices $i\in\{1,\cdots,n\}$ where $k$ and $n$ are parameters, $x$ is a binary variable ...
5
votes
2
answers
213
views
Binary variable constraint
The task is to ensure that if $x_i = 1$ for at least $k$ of the possible indices $i$ in $\{1,...,n\}$ then $y = 1$, where $k$ and $n$ are parameters, $x$ is a binary variable vector with $n$ elements, ...
4
votes
1
answer
68
views
Another difficult constraint for an ILP
How can I add to this ILP with all binary variables (again related to this question):
$$\min \sum_{1\leq i<j\leq n-1-h} t_{i,j}$$
$$\sum_{i=1}^{n-1-h} a_{k,i} \ge \lfloor (n-1)/2\rfloor \qquad \...
- 393
5
votes
3
answers
591
views
Constraint for two binary vectors to be different
If I have a matrix $A$ of binary variables $a_{i,j}$, $1 \le i \le n$, $1 \le j \le m$, how can I enforce in an Integer Linear Program with binary variables, the condition that every two columns must ...
- 393
2
votes
1
answer
87
views
Modeling advice: scheduling problem with judged events and "blocks" of judging assignments
I am considering a scheduling problem in which the events are officiated, likely as a MILP problem. I'm getting hung up on how best to model a particular requirement of how the judged events are ...
- 123
4
votes
1
answer
180
views
Difficult linearization of a constraint
My previous question was about this ILP with all binary variables:
$$\min \sum_{1\leq i<j\leq n-1-h} t_{i,j}$$
$$\sum_{i=1}^{n-1-h} a_{k,i} = \lfloor (n-1)/2\rfloor \qquad \text{for }k\in[h];$$
$$...
- 393
2
votes
2
answers
114
views
How can I include a penalty to my (linear) model?
Is it possible in a linear model to include a penalty if both variables $x$ and $y$ are greater than zero? I would like to have no penalty, if $x$ OR $y$ is zero.
For example, I have a model:
$$
\...
- 79
3
votes
0
answers
85
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 ...
- 31
3
votes
3
answers
517
views
Gurobi - Python: is there a way to express "OR" in a constraint?
I'm new to Gurobi in Python and I am wondering if there is way to express/code "or" in the following constraint, where $x_i$ are binary variables:
$x_i-x_i*x_{i-1} =0$
OR
$x_i*x_{i+1} =1.$
...
- 185
1
vote
1
answer
68
views
Can I get value from a variable and use it on a specific index of a different variable?
This is a peculiar question but I have two variables $s_{ik}$ (integer) and $y_{it}$ (binary). What I want is the following relationship: If $s_{ik} = 8$, then $y_{i8} = 1$.
Basically, if $s_{ik}$ ...
3
votes
1
answer
74
views
Jump, Julia : How to add constraints with different indexes a.c.a $x_i \leq z_j, \; \forall i, j$
I am having a constraint in the form :
$$ x_i \leq z_j, \quad \forall i, j \in \{1, 2, .., n\}$$
I know that if the right part of the equation was a constant so something like $x_i \leq c[i]$ I could ...
- 235
3
votes
1
answer
120
views
Efficient modelling via Gurobi
I would like to model the following constraint set in gurobi-java.
\begin{equation}
t^n_{ij} \geq t^n_{(i-1)j}+S_{(i-1)j} - (1 - \sum_{\substack{m \in \mathcal{M} \\ G_{ijm} = 1}}\sum_{k \in \mathcal{...
- 485