scholarly journals Mathematical models and heuristic algorithms for pallet building problems with practical constraints

2021 ◽  
Author(s):  
Gabriele Calzavara ◽  
Manuel Iori ◽  
Marco Locatelli ◽  
Mayron C. O. Moreira ◽  
Tiago Silveira
Keyword(s):  
Mathematical Models ◽  
Real World ◽  
Mathematical Description ◽  
Heuristic Algorithms ◽  
Practical Case ◽  
Operational Constraints ◽  
Practical Constraints ◽  
Horizontal Layers

AbstractIn the pallet building problem, we aim at loading a given set of items into one or more pallets, by satisfying specific constraints and minimizing the number of pallets used. In this paper, we address a practical case of this problem that originates from a real-world robotized application, subject to some non-trivial operational constraints. In practice, items are grouped into families and must be packed into horizontal layers. To facilitate loading/unloading operations, items of the same type packed into the same layer should be contiguous and at least one of them should be visible from the outside. We present a formal mathematical description for layer and pallet creation subproblems and then we propose heuristic, metaheuristic, matheuristic algorithms to solve the overall problem. The performance of the algorithms is assessed through extensive computational tests on real-world instances.

scholarly journals New Challenges Arising in Engineering Problems with Fractional and Integer Order

2021 ◽  
Vol 5 (2) ◽  
pp. 35
Author(s):  
Haci Mehmet Baskonus ◽  
Luis Manuel Sánchez Ruiz ◽  
Armando Ciancio
Keyword(s):  
Mathematical Models ◽  
Real World ◽  
Integer Order ◽  
Engineering Problems ◽  
New Challenges ◽  
Real World Problems

Mathematical models have been frequently studied in recent decades in order to obtain the deeper properties of real-world problems [...]

An algebraic approach to N-soft sets with application in decision-making using TOPSIS

2021 ◽  
pp. 1-21
Author(s):  
Muhammad Shabir ◽  
Rimsha Mushtaq ◽  
Munazza Naz
Keyword(s):  
Decision Making ◽  
Mathematical Models ◽  
Real World ◽  
Algebraic Approach ◽  
Multi Criteria Decision Making ◽  
Commutative Monoids ◽  
Soft Sets ◽  
Algebraic Properties ◽  
Different Types ◽  
Selection Of

In this paper, we focus on two main objectives. Firstly, we define some binary and unary operations on N-soft sets and study their algebraic properties. In unary operations, three different types of complements are studied. We prove De Morgan’s laws concerning top complements and for bottom complements for N-soft sets where N is fixed and provide a counterexample to show that De Morgan’s laws do not hold if we take different N. Then, we study different collections of N-soft sets which become idempotent commutative monoids and consequently show, that, these monoids give rise to hemirings of N-soft sets. Some of these hemirings are turned out as lattices. Finally, we show that the collection of all N-soft sets with full parameter set E and collection of all N-soft sets with parameter subset A are Stone Algebras. The second objective is to integrate the well-known technique of TOPSIS and N-soft set-based mathematical models from the real world. We discuss a hybrid model of multi-criteria decision-making combining the TOPSIS and N-soft sets and present an algorithm with implementation on the selection of the best model of laptop.

Call for Manuscripts for the 2015 Focus Issue: Mathematical Modeling

2013 ◽  
Vol 18 (9) ◽  
pp. 571
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Models ◽  
Real World ◽  
The Real

This call for manuscripts is requesting articles that address how to use mathematical models to analyze, predict, and resolve issues arising in the real world.

scholarly journals Finding A Small Vertex Cover in Massive Sparse Graphs: Construct, Local Search, and Preprocess

2017 ◽  
Vol 59 ◽  
pp. 463-494 ◽  
Author(s):  
Shaowei Cai ◽  
Jinkun Lin ◽  
Chuan Luo
Keyword(s):  
Local Search ◽  
Real World ◽  
Large Scale ◽  
Heuristic Algorithms ◽  
Search Algorithm ◽  
Vertex Cover ◽  
Search Algorithms ◽  
Theory And Practice ◽  
Sparse Graphs ◽  
Massive Graphs

The problem of finding a minimum vertex cover (MinVC) in a graph is a well known NP-hard combinatorial optimization problem of great importance in theory and practice. Due to its NP-hardness, there has been much interest in developing heuristic algorithms for finding a small vertex cover in reasonable time. Previously, heuristic algorithms for MinVC have focused on solving graphs of relatively small size, and they are not suitable for solving massive graphs as they usually have high-complexity heuristics. This paper explores techniques for solving MinVC in very large scale real-world graphs, including a construction algorithm, a local search algorithm and a preprocessing algorithm. Both the construction and search algorithms are based on low-complexity heuristics, and we combine them to develop a heuristic algorithm for MinVC called FastVC. Experimental results on a broad range of real-world massive graphs show that, our algorithms are very fast and have better performance than previous heuristic algorithms for MinVC. We also develop a preprocessing algorithm to simplify graphs for MinVC algorithms. By applying the preprocessing algorithm to local search algorithms, we obtain two efficient MinVC solvers called NuMVC2+p and FastVC2+p, which show further improvement on the massive graphs.

scholarly journals Ground station scheduling optimization for a model of a real-world problem instance

2021 ◽  
Author(s):  
Bryce Wildish
Keyword(s):  
Real World ◽  
Heuristic Algorithms ◽  
Complex Problem ◽  
Initial Guess ◽  
Fine Tuning ◽  
Problem Instance ◽  
Ground Station ◽  
Real World Problem ◽  
Crucial Component ◽  
Orbiting Spacecraft

Effective scheduling of communication windows between orbiting spacecraft and ground stations is a crucial component of efficiently using spacecraft resources. In all but the most trivial cases, this forces the operator to choose a subset of the potentially available access windows such that they can achieve the best possible usage of their hardware and other resources. This is a complex problem not normally solvable analytically, and as a result the standard approach is to apply heuristic algorithms which take an initial guess at a solution and improve upon it in order to increase its quality. Various such algorithms exist, with some being in common practice for this particular problem. This thesis covers the application of several of the most commonly-used algorithms on a problem instance. Additionally, a real-world problem instance is used, and the resultant practical constraints are addressed when applying the heuristics and fine-tuning them for this application.

scholarly journals Analysis on Present Mathematical Model for Predicting the Crop Production

2020 ◽  
Vol 9 (12) ◽  
pp. 168-170
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Real World ◽  
Crop Production ◽  
Ghg Emissions ◽  
Data Set ◽  
Factors Affecting ◽  
The Government ◽  
The Mathematical Model ◽  
Government Website

India is a worldwide agriculture business powerhouse. Future of agriculture-based products depends on the crop production. A mathematical model might be characterized as a lot of equations that speak to the conduct of a framework. By using mathematical model in agriculture field, we can predict the production of crop in particular area. There are various factors affecting crops such as Rainfall, GHG Emissions, Temperature, Urbanization, climate, humidity etc. A mathematical model is a simplified representation of a real-world system. It forms the system using mathematical principles in the form of a condition or a set of conditions. Suppose we need to increase the crop production, at that time the mathematical model plays a major role and our work can be easier, more significant by using the mathematical model. Through the mathematical model we predict the crop production in upcoming years. .AI, ML, IOT play a major role to predict the future of agriculture, but without mathematical models it is not possible to predict crop production accurately. To solve the real-world agriculture problem, mathematical models play a major role for accurate results. Correlation Analysis, Multiple Regression analysis and fuzzy logic simulation standards have been utilized for building a grain production benefit depending model from crop production. Prediction of crop is beneficiary to the farmer to analyze the crop management. By using the present agriculture data set which is available on the government website, we can build a mathematical model.

scholarly journals Mathematical models for a batch scheduling problem to minimize earliness and tardiness

2018 ◽  
Vol 11 (3) ◽  
pp. 390 ◽  
Author(s):  
Basar Ogun ◽  
Çigdem Alabas-Uslu
Keyword(s):  
Mathematical Models ◽  
Real World ◽  
Lean Manufacturing ◽  
Programming Model ◽  
Computational Study ◽  
Batch Scheduling ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Earliness And Tardiness ◽  
Customer Orders

Purpose: Today’s manufacturing facilities are challenged by highly customized products and just in time manufacturing and delivery of these products. In this study, a batch scheduling problem is addressed to provide on-time completion of customer orders in the environment of lean manufacturing. The problem is to optimize partitioning of product components into batches and scheduling of the resulting batches where each customer order is received as a set of products made of various components.Design/methodology/approach: Three different mathematical models for minimization of total earliness and tardiness of customer orders are developed to provide on-time completion of customer orders and also, to avoid from inventory of final products. The first model is a non-linear integer programming model while the second is a linearized version of the first. Finally, to solve larger sized instances of the problem, an alternative linear integer model is presented.Findings: Computational study using a suit set of test instances showed that the alternative linear integer model is able to solve all test instances in varying sizes within quite shorter computer times comparing to the other two models. It was also showed that the alternative model can solve moderate sized real-world problems.Originality/value: The problem under study differentiates from existing batch scheduling problems in the literature since it includes new circumstances which may arise in real-world applications. This research, also, contributes the literature of batch scheduling problem by presenting new optimization models.

Mathematical models of optimal management of material support of educational and scientific activities of industrial universities

2020 ◽  
pp. 79-90
Author(s):  
N. V. Kalganova ◽  
Keyword(s):  
Higher Education ◽  
Mathematical Models ◽  
Numerical Solution ◽  
Mathematical Description ◽  
Financial Support ◽  
Software Package ◽  
Optimal Management ◽  
Material Support ◽  
Support Strategy ◽  
The University

The paper considers mathematical differential models for managing the achievement of planned values of material support for educational and scientific activities of the university based on the analysis of this area of activity of transport universities. Models contain a mathematical description of the material and financial processes under study, which analytically show their dynamics for a certain period. The models are quite simple and can be used for planning and forecasting the financial support strategy of higher education institutions. In her research, the author relied on the work of Russian scientists, in particular, on [1-5]. This paper presents a mathematical description of the set of possible options for the system, predicting the consequences of the implemented options, and justifying the rational choice of management to achieve optimal educational and material support of the university. In this paper, we used methods for solving and investigating differential equations, as well as the MathCAD 15 software package for their numerical solution [6-8].

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