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16 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 $c$ ...
6
votes
1answer
149 views

How do OR researchers choose which journal to submit and what are the differences between them?

Hello every senior OR researchers and enthusiast, I am a PhD student now and I have been curious about this question since I was an undergraduate student. How do researchers choose which journals ...
4
votes
1answer
65 views

Linearizing the square root of binary summations

My question is similar to this one and almost identical with this. I am so confused due to indexing and could not make sure if I could apply the solution in here to this indexed version as shown below....
3
votes
1answer
27 views

Linearizing the square root of two binary summations

My question is similar to this one though a bit more complicated. Though my question also includes indices, I am removing them to ease readability. Let binary variables $x,y\in\{0,1\}$, non-negative ...
5
votes
0answers
41 views

Solver for Go Programming Laguage

Has anyone used MIP solvers (open source or commercial) with Go language https://golang.org/? I am looking for a solver for simple linear MIPs for network flows and set cover types of problems.
7
votes
1answer
52 views

Scheduling events in order to maximize preparation time

Problem statement I'm given a set of events $E$, and $\forall e \in E$ also: a set of plausible dates on which the event can happen $D_e$ importance (weight) $w_e$ ideal preparation time duration $...
7
votes
1answer
246 views

Creating a Continuous Decision Variable between 0 and 1 in Python-MIP Interface

This task appears to be harder than it seems to me. I want to create a continuous variable $x \in [0,1]$. To test this, I did use the open-source Python-MIP interface which uses the CBC-Solver out ...
6
votes
3answers
137 views

Constraint that checks for an undirected graph whether it is connected?

I would like to create a constraint with AMPL that checks whether I am able to reach from one node $v$ to all other nodes of a set but I don't really know how to formulate it (especially in AMPL (+...
5
votes
0answers
44 views

Sequential quadratic programming source

What are the good text books to learn SQP? Are there any online courses that you can suggest?
8
votes
0answers
82 views

How to classify and model this problem?

I was given the task to model the following problem and find a solution for it, but as I do not have any experience in this field, I already have trouble classifying it. There are a number of ...
8
votes
2answers
876 views

Linear programming: objective function with “buckets”

I had a linear programming problem with the following objective function $$f(x) = \sum_{j}x_jq_jp_j - \sum_{i}\left(\sum_{k}x_kq_kC_{ik} \right) c_i$$ Where $q, p, C, c$ are known. This problem was ...
7
votes
2answers
126 views

The general meaning of “constraint relaxation” in the context of the Shortest Path Problem

I've read that in the context of the Shortest Path Problem, the use of the term "relaxation" ("relaxing edges") [...][the use of the term "relaxation"] is historical. The outcome of a relaxation ...
3
votes
1answer
64 views

Gurobi C++: adding variables with vector

I am solving an LP by using GUROBI - C++ combo. Assume I have a variable $p \in \mathbb{R}^n$. I am adding this as a vector: ...
5
votes
0answers
88 views

All optimal solutions

I have a following problem: If I have some function $aX+bY+cZ+mD+nF$ and I want to maximize it and have some constraints, how can I find ALL solutions for this maximum value of the function? To sum ...
7
votes
1answer
56 views

An upper-bound on the value of $S$ in $(s,S)$ policy

I recently have come across a problem which can be categorized as a stochastic optimization. The problem seems simple, but I haven't been able to solve it yet. It has a major impact on algorithm ...
6
votes
1answer
90 views

Creating a Decision Variable in Python-MIP with Dictionaries

I have already seen in the Python-MIP documentation on how to implement a variable with multiple indices. In each example I read, this is done with the use of lists and integers as indices. This is ...
5
votes
3answers
84 views

No solution found from n MIP starts

Currently, I am working on the implementation of a MILP formulation with lazy constraints for an optimization problem, and I am using the MIP Start strategy. I am generating the integer feasible ...
6
votes
1answer
45 views

How to minimize a weighted sum of RMSE-like terms?

I am trying to solve the following problem: \begin{align} \min&\quad f(x) = \sum_{i=1}^{n}{a_ix_i} + \sum_{i=1}^{n}{b_i\sqrt{\sum_{j=1}^{m}{\left(y_{i,j}-x_i\right)^2}}}\\\text{s.t.}&\quad x_{...
7
votes
1answer
67 views

Ridge Regression lagrange duality

In every machine learning book we see that it is roughly mentioned that the ridge regression: $$p_1^* = \min\limits_{\beta} \ \left( \mathrm{RSS} + \lambda\sum_{j=1}^p \beta_j^2 \right)$$ is ...
3
votes
1answer
32 views

defining Mixed integer linear inequalities for a set of variables

The problem is described as follows: considering $n$ variables which are continuous and bounded such that $$L_i \le x_i \le U_i\quad \forall i=1,2,\dots,n.$$ How can i define a set of mixed integer ...
4
votes
0answers
92 views

How to solve this production problem?

I have a set $J$ of factories. Each factory $j$ can produce $P_j$ products. We may have $\bigcap\limits_{j \in J} P_j \neq \emptyset$. For each product $p \in P_j$, there is an output rate $\theta_{...
3
votes
1answer
46 views

How to model $A_i=B_i$ for only one $i$

I would like to model the following: Only one of the following equalities can hold. $$(A_1 = B_1)\quad\text{OR}\quad(A_2 = B_2)\quad\text{OR}\quad\dots\quad\text{OR}\quad(A_k = B_k)$$ I can ...
11
votes
2answers
3k views

Is it necessary to study rigorous math courses in OR?

I am a business student with engineering background and I am studying papers published in some journals like Management Science, Operations Research, Math of OR and they use some notations and ...
13
votes
2answers
582 views

What is the difference between optimization software APIs based on performance and speed?

The state-of-art solvers like CPLEX or Gurobi and some of the open-source solvers have had the different APIs (like Python, C/C++, Java, etc.) in which users could write their MP model in own ...
5
votes
1answer
95 views

Preemptive Goal programming by fixing nonbasic variables with non-zero reduced costs

I have been using the method of fixing nonbasic variables with non-zero reduced costs to do preemptive goal programming. It works for the most part. But I have recently noticed in a certain instance ...
4
votes
0answers
59 views

Optimal Energy Charging/discharging Scheduling Problem

I'm new to IBM CP optimizer. I want to make charging / discharging scheduling based on cost (value will change on time) and my objective function is $$\sum_{t=1}^{24}\sum_{j=1}^5x(1)^{(i,j)}x(2)^{(i,...
8
votes
3answers
602 views

Bin packing variant

I am currently struggling with a bin packing variant, where we have fuel and compartments of a tank truck. Some industry constraints apply, but the whole picture is that you must fit the total volume ...
4
votes
1answer
65 views

How exactly does OptionalIntervalVar work in OR-Tools?

I created OptionalIntervals for a number of tasks: ...
3
votes
1answer
176 views

Comparing formulation for traveling salesman

I have a graph $G$ and have a set $S$ which are the points in the graph to visit in a TSP manner. Since the length of the TSP route can't be known as it can use any number of nodes to complete the ...
5
votes
1answer
146 views

TSP with constraints in OR Tools

I am completely new to OR Tools, but what I have tried so far seems very powerful. I have, however, run into a problem that I cannot seem to figure out how to solve. I am trying to model a TSP ...
4
votes
1answer
62 views

How to model If $A \le B$ then $Y = 1$, otherwise $Y = 0$

Somehow I don't get it right. I would like to model the following: If $a\le B$ then $Y=1$ otherwise $Y=0$ where $A, B$ are reals and $Y$ is binary. I can model as follows: $Y \cdot A \le B$ and ...
5
votes
3answers
794 views

Solving continuous Minimax Optimization problem

I want to solve a linear programming minimax problem here mathematically without using software: $$\begin{align*} \text{min}\ \text{max} \quad & \{x_1,x_2,x_3\} \\ \text{s.t.} \...
7
votes
1answer
105 views

Choosing better objective function for vehicle routing problem

I have a graph $G$ and the following variables. $b_{i,j}$ is $(i,j)$ edge is taken or not. $t_{i,j}$ is time to travel $(i,j)$ $A_{i}$, $D_{i}$ are arrival and departure time at node $i$. My first ...
12
votes
1answer
126 views

Re-calculating shortest path in slightly altered graph

I was wondering if someone has come across this before and/or has a smart idea for the following: I have a directed graph $G$ with costs $c$ associated with the arcs, and I know the shortest path $P^...
11
votes
5answers
472 views

How to implement a “generic” solver for scheduling problems?

I have been accepted for an internship for 6 months. The aim of this internship is to implement a "generic" solver for scheduling/production planning problems. This solver will bill a small prototype ...
6
votes
0answers
48 views

Semi-definite Programming, non standard notation

The usual way to define a semi-definite program (SDP), e.g., as given in Boyd and Vandenberghe's convex optimization book, is: $$ \begin{array}{cl} \min & c^\top x \\ \mathrm{s.t.} & 0 \succeq ...
6
votes
0answers
25 views

Building the Scheurman's Model II constraints for a multi period linear program

Scheurman's paper discusses Model I and model II Formulation to solve harvesting and scheduling problems. It is a specific implementation to solve multi period linear programs. Both models are also ...
6
votes
0answers
30 views

MPX Queuing Software for Manufacturing with the GTHUBS Case

I'm teaching an Operations Management Class. A long time ago, there was a simple DOS-based product called MPX. It was based on queuing theory and let you model manufacturing processes. There was ...
12
votes
1answer
1k views

How do we call this problem in literature and how to model it?

I have a set of sources and a set of sinks. Each source $s$ can produce a set of different products $P_s$. The transportation inter-sources and inter-sinks are allowed. The sources do not ...
5
votes
2answers
158 views

Trade off between number of constraints and bounds of a variable

I am not familiar with the inner working of the solvers. I mostly use the python pulp or IBM CPLEX solver. For fast execution ...
5
votes
2answers
60 views

AMPL implement constraint

I'm trying to implement the following in AMPL: $$ i \in [N], j \in[N] \backslash \{i\}, t \in [T] $$ I have so far written the following: ...
3
votes
1answer
67 views

Linearizing constraint with continuous and boolean variables

I have two continuous variables $A$, $B$ and two binary variables $x$, $y$. Condition: if $A = B \wedge x = 1 \wedge y=1$ then $z = 1$ else $z = 0$ from In an integer program, how I can force a ...
5
votes
1answer
48 views

Tolerance for equality in GAMS/CPLEX

Is there an option in GAMS that sets the tolerance for declaring two real numbers to equal? For example, how can I tell GAMS or GAMS/CPLEX that $0.999100 = 0.99909$? Thank you for your help!
5
votes
1answer
82 views

assigning values to IntVar if and only if BoolVar, else zero [or-tools]

If I have an IntVar s[j] stored in a vector s, is it possible to iterate for (a period of ...
8
votes
1answer
272 views

Safety stock when there is uncertainty in order completion

Safety stocks account for uncertainty both on demand and provider lead times, but never mention how to include the effect of incomplete orders. For example, what would happen if a provider always ...
6
votes
0answers
62 views

OptionalIntervalVar enforced but not working OR-TOOLS

I'm using OptionalIntervalVar and then maximizing the starts. The optimal solution is not affecting the other variables that creates the ...
5
votes
2answers
105 views

Reducing number of suppliers for product portfolio

I have the following matrix of suppliers who are able to make a certain product, against all products in my portfolio. What is the best way of finding the solution to "the least suppliers necessary ...
6
votes
1answer
91 views

Negative reduced cost for basic variable

I am observing something unusual : after solving a linear program, some basic variables have negative reduced costs (instead of $0$) : ...
5
votes
1answer
54 views

How to formulate case distinctions in AMPLs objective function?

This is my first real optimisation problem I formulated and now trying to solve by using AMPL. The following objective function is from a linear 0-1 LP means all variables $x_i^b\in\{0,1\}$, with $i\...
7
votes
1answer
63 views

Aggregate production planning

I'm looking for an optimization model about production planning that takes the following into consideration: Single site Multi products One machine/resource Sequence-dependent Fixed batch ...

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