Questions tagged [optimization]

For questions involving mathematical problems that aim to minimize or maximize some objective function, possibly subject to one or more constraints.

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24
votes
15answers
1k views

Recommended books/materials for practical applications of Operations Research in industry

I have a Masters' degree in Mathematics. I've very fair understanding of methods and techniques of Operations Research. I am looking for a good book/material where I can see a lot of examples on Math ...
6
votes
1answer
1k views

How to linearize min function as a constraint?

I'm trying to solve an optimization problem including following constraint, and I need to linearize it in a maximization nonlinear programming model. Please help me to reformulate it with mixed ...
12
votes
2answers
454 views

Expressing a chain of boolean ORs using ILP

How to express a chain of OR operations in an ILP in which each expression is a less than or equal constraint and the left hand side variable in all inequalities is always the same? All the variables ...
35
votes
8answers
856 views

Why is the programming code of many algorithms not public in the OR community?

In recent years, a huge number of scholars in AI and ML community are using Python to develop their algorithms and then publishing their papers and codes in GitHub. This provides an opportunity for ...
24
votes
9answers
3k views

What are Operations Research applications for 'good causes'?

I am looking for applications of OR for good causes, possibly with some literature. I intend a good cause loosely defined in the sense that the scope is that of improving the well-being of others, e.g....
11
votes
1answer
241 views

Expressing a chain of boolean ORs using ILP involving different variables

How can I express a chain of OR operations in an ILP, given that each operand is an inequality between two binary variables? I have asked a similar question here: Chain of Boolean ORs. In that ...
10
votes
2answers
630 views

How to use warm start to solve MIPs efficiently?

I'm working on the scheduling model which takes a long time to solve to optimality (even for a small instance), therefore I would like to use a warm start (MIP start) to solve the problem. I'm using ...
6
votes
5answers
2k views

Algorithms vs LP or MIP

Is there a way of writing an algorithm with if-, while-statements to find an optimal solution without using linear-programming (LP)/MIP? If so, what would the benefits be against the LP/MIP? Is it ...
-3
votes
2answers
193 views

Some theories and laws of Operations Research? [closed]

Can I know some theories and laws of Operation Research which has being widely used nowadays?
17
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3answers
768 views

What is the connection of Operations Research and Reinforcement Learning?

I know that Markov Chains and Markov Decision Processes have been studied in the OR community too. But, I was wondering what is the relationship of Operations Research (OR) and Reinforcement Learning (...
27
votes
4answers
311 views

How to avoid having your optimization models rusting?

When designing optimization models for external organizations, I have witnessed the following: We design an optimization model for a given problem. We fine-tune it based on a portfolio of ...
21
votes
5answers
2k views

Validation and verification of mathematical models

Within the subject of simulation I have found some literature on validation and verification (e.g. Sargent's paper). My question is, what techniques do you use to validate and verify your mathematical ...
19
votes
3answers
240 views

Variable bounds in column generation

Consider the set covering problem \[ \begin{align} \min&\ \sum_{j=1}^nc_jx_j\\ s.t.:&\ \sum_{j=1}^na_{ij}x_j\geq 1,\quad \forall i=1,\dots,m\\ &\ 0\leq x_j \leq 1 \end{align} \] ...
17
votes
6answers
1k views

Infeasibility in mathematical optimization models

Sometimes, when solving mathematical optimization models (especially MIPs), they may be infeasible. Is there any comprehensive method to deal with the infeasibility conditions? (especially in complex ...
19
votes
5answers
2k views

Ordered list of OR journals

Is there any compact resource that includes a list of all academic journals in the OR/MS space, ranked by journal importance? Although there are some helpful features offered by publisher websites ...
12
votes
2answers
403 views

How to handle an IP sub-problem with an objective function in Benders Decomposition

I have a question on Benders Decomposition (BD). Suppose I have an MILP model which can be decomposed into a master problem (MP) including integer and continuous variables and a subproblem (SP) ...
15
votes
4answers
658 views

Optimization models for portfolio optimization

What are the mainstream models for portfolio optimization? We have Markowitz mean-variance model and CVaR-based models (e.g., max return subject to a CVaR constraint). What else is out there in terms ...
14
votes
1answer
330 views

Are there any real-world problems where quadratization helps to solve something that couldn't have been solved without quadratization?

The closest thing I know is the computer vision problem, in which an image is de-blurred and/or de-noised by quadratizing a quartic problem into a quadratic optimization problem (QUBO) and then the ...
12
votes
2answers
328 views

Convex Maximization with Linear Constraints

I am doing active research in convex maximization w.r.t. linear constraints. There are many cases which can be efficiently approximately solved, e.g., convex quadratic maximization, log-sum-exp ...
11
votes
3answers
276 views

Is my approach to my internship project good? Optimal allocation of product across stores, constrained optimization

Context: I am a CS student currently in a non-CS internship (logistics, supply chain). My manager wants to leverage my knowledge of programming to build a program to solve the following problem: As ...
8
votes
1answer
390 views

Finding minimum time for vehicle to reach to its destination

Given a set of Vehicles with source and destination I need to find the minimum time of travel for all the vehicles, there are also some charging stations and its necessary for vehicles to charge 1 ...
15
votes
3answers
317 views

Benchmark problems for scenario-based stochastic optimization

$\newcommand{\E}{\mathbb{E}}$I am working on numerical algorithms for solving convex large-scale multistage scenario-based problems and I am looking for some standard benchmarks problems. I have so ...
12
votes
2answers
145 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 ...
12
votes
3answers
1k views

Allocating credit card points

I’m interested in the idea behind this in general, so I thought this would be the best place to post, though I have a practical and semi-urgent need of allocating the points on my credit card towards ...
10
votes
2answers
979 views

Linear programming: objective function with “buckets”

I had a linear programming problem with the following objective function $$f(x) = \sum_{j}x_jq_jp_j - \sum_{i}\left(\sum_{j}x_jq_jC_{ij} \right) c_i$$ Where $q, p, C, c$ are known. This problem was ...
9
votes
2answers
348 views

What is the difference between job shop scheduling and resource constrained project scheduling?

I read here https://slideplayer.com/slide/3353960/ that RCPS is a generalized version of job shop scheduling. I'm new to this area and I'm trying to classify a specific variation of these types of ...
6
votes
2answers
261 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, ...
12
votes
2answers
295 views

Expressing an implication as ILP where each implication term comprises a chain of boolean ORs

Consider an implication of the form $A \implies B$ where both $A, B$ comprises a chain of Boolean OR variables. For example, $(a_1 \lor a_2 \lor a_3) \implies (b_1 \lor b_2 \lor b_3)$. How can this ...
9
votes
3answers
351 views

How could we simplify solving the large scale MIPs without using any advanced methods like decompositions?

Many practical optimization models (specially MIPs) are NP-Hard and solving them need much time even with the modern solvers like CPLEX or GUROBI. One of the best way (but not easy) is using ...
9
votes
2answers
134 views

When should I use a solver for IP and MIP and can I just use a library from Python, R, Matlab, etc…?

Are there any rules of thumb for figuring out when you need to use a solver like Gurobi or CPLEX, and when you can just solve you problems directly with a Python, R, or Matlab package? Is it just a ...
8
votes
2answers
396 views

Is there a greedy heuristic approach to the MILP problem?

I have the following optimization problem which is an MILP. I can solve it with an MILP solver. \begin{alignat}{1}\max_{x_n,t}\,&\quad t\quad\\\text{s.t.}&\quad\sum_{n=1}^{N} x_n \,&= M\\...
8
votes
2answers
2k views

How can I add this conditional constraint to my model in Python?

I am creating an optimization model with 2 sets of binary decision variables. The first, site, is regarding which of 380 cities to place manufacturing sites in, and ...
4
votes
0answers
185 views

How can I formulate this multi-objective optimization problem?

Now, for each system $X$ $(X=A,B,C,E)$, my objective is $$\max\min\frac{s_{x_u}}{d_{x_u}}$$ here, $x=a$ for system A, $x=b$ for system B and follows... and for the whole system, my objective is $$\max\...
3
votes
1answer
124 views

Resource constraint with MIP model

My question is how to model a resource constraint with MIP model (how should I modify it?) A factory is making blocks. If there is space left at that time, the block can be assembled. (If the factory ...
2
votes
1answer
111 views

Representing Date Variables in Pulp

I am working on an optimisation problem that involves minimising shipping demurrage. I am struggling to model how to represent the difference, (x-y) between dates where the ship is ready to be loaded ...
2
votes
1answer
109 views

Is my formulation correct and how to formulate this IF-THEN constraint?

I have system with $N_U$ users and $N_T$ transmitters. Multiple transmitters can transmit to a single users and one transmitter can transmit to many users, i.e., two sets of transmitters serving two ...
-6
votes
2answers
205 views

How to decide to write an objective function?

I'm working on this problem: In the Njaba river basin, the available water was allocated for the purposes of consumption, irrigation, and electric power supply among three communities. The water ...