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14
votes
1answer
155 views

How to Speed Up the subgradient optimization procedure in a Lagrangian Relaxation Scheme

I'm currently working on the following problem (a variant of maximal k-covering problem): \begin{align} \max&\quad z =\sum\limits_{\omega\in \Omega}x_{\omega} \label{imbip3a} \\ \text{s.t.}&\...
3
votes
0answers
31 views

Extract binary value from continuous variable [duplicate]

I have a continuous variable $c$ which has value in between $[-R, +R]$. I want to create a boolean variable $x$ and, $x = 1$ when $c = 1.0$ otherwise $x = 0$ In more general form: $x = 1$ when $c \...
6
votes
0answers
62 views

Benefits of removing slack variables during presolve

I was reading Tobias Achterberg's thesis, and on page 138 he mentions the following presolving technique for linear equations (I'm slightly paraphrasing Example 10.2): Consider the equation $4x_1+...
11
votes
1answer
315 views

When using column generation, can a sub-problem be ignored once and for all once it fails to generate a new column?

Suppose you are solving a minimization problem with a column generation procedure, and that you have $2$ sub-problems. At some point, one of the $2$ sub-problems is no longer able to generate a column ...
9
votes
2answers
406 views

Modelling an if-then-else logic in MIP

I was hoping to get some help in modelling the following logic as an MIP Constraint If $X_{ij}=1$ and $\text{SDV}_{ikj}=1$ for a particular index $i$, then $\text{SOC}^L_i=100$, else $\text{SOC}^L_i$...
8
votes
3answers
356 views

CPLEX, number of threads and solving time

Using CPLEX via its Python API, I encountered a "weird" behavior. For some instances, with a limited number of threads (10 in my tests), the instances cannot be solved after 10 days (afterwards, the ...
8
votes
1answer
52 views

Check which constraints are violated (Concert - Cplex Studio 12.10 - C++)

Currently, I am working on the implementation of a formulation for an optimization problem, at the moment I already have the MIP formulation implemented in C++ using Cplex studio 12.10 with the ...
9
votes
4answers
273 views

Open Source MILP software for Python with user-friendly API to define the optimization problem

Following the accepted answer to Assignment problem where assignments must be done sequentially I would like to write a Python script which can solve the problem defined there. It's a Mixed Integer ...
4
votes
0answers
59 views

Continue on “Is there a known MILP to schedule routes after routes are made”

I have made some progress on my previous question (Is there a known MILP to schedule routes after routes are made). I have derived the sets of the problem, which are: 1) Itineraries of vehicle: $i \in ...
7
votes
0answers
52 views

Can demand be modeled by a limited amount of probability distributions?

In stochastic inventory control, it is very important to model the demand appropriate to set e.g. order levels. Demand can be fit to a certain probability distribution via many means (e.g. a goodness ...
1
vote
0answers
58 views

Converting Nonlinear Program into an LP

I have a problem with a nonlinear objective function which is \begin{align}\min&\quad Z_j\cdot(N_j)^{0.5}\end{align} where $j$ is the index. I want to know how can I turn it into a linear ...
6
votes
1answer
137 views

How to propagate time using linear inequalities?

I have an adjacency matrix $G_{i,j}$ that tells the distance between $i$ to $j$ (between 0 to 1) if there is no edge between $i$ to $j$ I am putting a large integer $100$. This is my previous ...
6
votes
1answer
82 views

How to write a constraint for a directed graph?

I'm working on an optimization problem regarding a directed acyclic graph. The constraint looks in pyomo like this: ...
6
votes
2answers
130 views

Assignment problem where assignments must be done sequentially

I have a weird planning problem. I think it falls under the assignment category, but I'm not sure because I'm not familiar with assignment problems, and also because there is a "temporal" angle to it, ...
7
votes
1answer
128 views

Is Dantzig-Wolfe decomposition finite if variables are unbounded?

Most descriptions of the Dantzig-Wolfe decomposition, I have seen end up with subproblems like this: $$\min_{x_j \in \mathbb{R}^n} \{ (\pi A_j - c_j)x_j \mid x_j \in P_j \}$$ They argue that $P_j$ ...
6
votes
0answers
101 views

Modelling issue with precedence constraint in OR-Tools

I'm trying to solve an RCPSPDc model It is infeasible, although Ilog Cplex solves it, so I think I have a modelling issue. I have more constraints but the precedence is the one that makes it ...
11
votes
1answer
261 views

Job Shop Scheduling: what objectives are harder?

It is well known that job shop scheduling problems are notoriously hard from a computational point of view. Many papers exist for the makespan objective, and some report on min sum objectives (like ...
3
votes
1answer
61 views

ValidateModel or tools in c++ and proto problems

I'm trying to validate my model, this is the relevant part of my code: ...
12
votes
1answer
80 views

Improving cuts from sub-problem with problem-specific hierarchical information

I'm solving an assignment-alike problem with a Logic-based Benders decomposition-alike (LBBD) method. The master problem provides an assignment, which is checked in the sub-problem. Define the set of ...
10
votes
0answers
73 views

Is there a known MILP to schedule routes after routes are made

I am trying to create a mixed integer model that has as an objective to schedule routes for a single vehicle within its timeline. Let me try to elaborate. Let's say we have a single vehicle vrp and ...
8
votes
2answers
113 views

Bounding arrival time at a node in a resource-constrained shortest path problem

Given a city map (a graph) $G$, $b_{i,j}$ is a Boolean variable for whether or not edge $i$,$j$ is allocated, $d_{i,j}$ denotes the distance between $i$,$j$. The objective is to move from $s$ to $e$ ...
10
votes
2answers
395 views

Solving multiple easy ILP instances

I have an application where I am solving millions of ILP instances that differ from each other only on one constraint. The instances, of course, are relatively easy to solve or otherwise this would be ...
5
votes
0answers
54 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+...
4
votes
0answers
41 views
6
votes
1answer
64 views

Linearizing objective function with absolute differences

I want to turn this objective function $$\max \sum_{i=1}^{N-1} \sum_{j=i+1}^N |TX_i^T - TX_j^T|$$ where $T$ is just a vector with increasing integers (e.g $[1 \ 2]$) and $X_i$ is a vector ...
5
votes
0answers
76 views

Convexity of the projection of a convex set

Question: A set $S \subset \mathbb{R}^m \times \mathbb{R}^n$ is convex. Using the fact that affine maps preserves convexity prove that $S(y) = \{x \in \mathbb{R}^m\mid (x,y)\in S \}$ and $\hat{S} = ...
9
votes
1answer
64 views

Queuing Theory with Learning Perspective

I am willing to work on queuing models but in classical queuing models, it is assumed the probability distributions of arrival and service are known or at least the rate is known. However, I am ...
7
votes
1answer
51 views

Expressing a chain of boolean if-then with logical ANDs using MIP

How to express a chain of boolean If-then as MIP such as: If $(x_{10} \ge b_1$ and $x_{11} \le b_1)$ AND $(x_{20} \ge b_2$ and $x_{21} \le b_2)$... AND... then $y_1 = 1$ else $y_1 = 0$. So basically,...
12
votes
2answers
918 views

How fair is limit solver threads when publishing?

Reading gurobi reference manual I found this: We have also found that certain classes of MIP models benefit from reducing the thread count, often all the way down to one thread. Starting multiple ...
5
votes
1answer
100 views

Cumulative Constraint OR-Tools

I'm trying to solve an rcpsp model. I can't find documentation for the AddCumulative function of OR-Tools. How should this function be used? I want to write this ...
6
votes
1answer
86 views

Precedence Constraint in OR-Tools

I'm trying to write this constraint in C++ and add it to my model (addLessOrEqual): $$\text{start}_{i}+\text{duration}_{i}\le\text{start}_{j}$$ for an $(i,j)$ arc ...
11
votes
2answers
2k views

Operations Research books by world-famous authors made available on the web, despite not being “completed”

Are there any books on Operations Research subjects by world-famous authors which have been made available for free access on the web, despite never having been "completed" to the standard to which ...
5
votes
1answer
138 views

How to model shipment size constraint?

I am working on an LP problem where I have to model a constraint as: "The total number of units of product A and B should be shipped in multiples of $1200$" e.g. $700\text{(product A)} + 500\text{(...
8
votes
2answers
120 views

Convex Optimization: Separation of Cones

I am trying to solve Exercise 2.39 at Boyd and Vandenberghe's Convex Optimization book. In one source, the answer is given as: 2.39 Separation of cones. Let $K$ and $\tilde K$ be two convex cones ...
6
votes
1answer
91 views

Gurobi stuck at start - 16GB RAM exhausted

I'm solving a large instance using Gurobi 7.0, 64-bit version on machine with 16GB of RAM. Gurobi is stuck at the start and all the memory is exhausted. Here is the output: ...
6
votes
0answers
56 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 ...
12
votes
2answers
164 views

Restoring a list from differences

Given a list of (absolute valued) pair differences ordered and with duplicates removed, how can we recover/reconstruct the list that generated these differences? We do not know anything about the ...
10
votes
0answers
60 views

Column generation for TSP

For teaching purposes, I would like to solve the Travelling Salesman Problem with a column generation approach. In the academic literature, an approach is proposed (for example here), where columns ...
4
votes
0answers
155 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 ...
5
votes
4answers
186 views

MIP for similar production percentages in production planning

As a task, I want to produce three products $x,y,z$ in different quantities $a,b,c>0$ respectively. It is not always possible to produce the full amount of each product, because of a lack of ...
5
votes
2answers
78 views

What is the technique of branch-and-bound used in Knitro to solve MINLP?

I am using Knitro to solve an MINLP using branch-and-bound and I want to know about the reference or technique they are adopting to code their algorithm. I know that there are many applications of ...
6
votes
0answers
41 views

Demonstrating a given solution is basic for a MCFP?

Given a minimum-cost flow problem, how could I go about demonstrating that a specific solution (as sets of basic and non-basic (!) arcs that build a rooted spanning tree for a given graph) is basic ...
7
votes
1answer
141 views

Custom Nurse Rostering Problem

I've asked this question also on Math Stack Exchange. It's a custom nurse rostering problem: $N$ is a set of nurses; $S$ is the set of shift-type (morning, afternoon, night, rest) $n_\mathrm{...
7
votes
1answer
140 views

Why is there a constant in the objective function of the *best subset selection problem*?

This article presents the following formulation of the best subset selection problem $$\min_{\|\beta\|_0\leq k}\frac{1}{2}\|y-X\beta\|^2_2$$ I wonder where the $1/2$ comes from. Help appreciated.
5
votes
1answer
178 views

How to express this constraint?

I have the constraint \begin{align}\max&\quad\gamma\\\text{s.t.}&\quad a\ge\gamma b\\&\quad\gamma\le 1\end{align} where $\gamma$ is an optimization variable and $a$ is a function of some ...
3
votes
0answers
78 views

Power of variable or tools

I'm working with OR Tools in Python and I need to define the objective function an expression of the variables. In particular, the objective function is $$\frac{c_j}{1.7^{s_j}}$$ with $c_j$ ...
11
votes
1answer
82 views

CPLEX allows manually inserted solutions to violate lazy constraints

I am using CPLEX 12.9 to solve a mixed integer linear programming problem. Some of my constraints are enforced through a legacy LazyConstraintCallback. Heuristic solutions are inserted through a ...
7
votes
1answer
157 views

Floating points in ORtools

I'm trying to solve an RCPSPDc model (maximizing the net present value instead of a makespan). The objective function is: $\sum\limits_{j \in \text{Tasks}} e^{-\theta\cdot s_{j}}\cdot p_{j}$, where $...
10
votes
2answers
302 views

Current Issues of Interest

What are some current issue of interest in Operations Research? I am interested in current topics that experts in the field are interested in researching.
6
votes
1answer
101 views

GUROBI Re-optimize a model

(For Linear Programming) I am aware of CPLEX's reoptimize methods. If I am not wrong, if you solve a problem and after that you add a new constraint, then you can call the reoptimize method for not to ...

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