Editorial

4 pages, 165 KiB

Open AccessEditorial

Special Issue “Mathematical Methods for Operations Research Problems”

by Frank Werner

Mathematics 2021, 9(21), 2762; https://doi.org/10.3390/math9212762 - 30 Oct 2021

Cited by 1 | Viewed by 1390

This Special Issue of Mathematics is dedicated to the application of Operations Research methods to a wide range of problems [...] Full article

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Research

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19 pages, 349 KiB

Open AccessArticle

Solving a University Course Timetabling Problem Based on AACSB Policies

by Nancy M. Arratia-Martinez, Paulina A. Avila-Torres and Juana C. Trujillo-Reyes

Mathematics 2021, 9(19), 2500; https://doi.org/10.3390/math9192500 - 06 Oct 2021

Cited by 3 | Viewed by 2601

Abstract

The purpose of this research is to solve the university course timetabling problem (UCTP) that consists of designing a schedule of the courses to be offered in one academic period based on students’ demand, faculty composition and institutional constraints considering the policies established [...] Read more.

The purpose of this research is to solve the university course timetabling problem (UCTP) that consists of designing a schedule of the courses to be offered in one academic period based on students’ demand, faculty composition and institutional constraints considering the policies established in the standards of the Association to Advance Collegiate Schools of Business (AACSB) accreditation. These standards involve faculty assignment with high level credentials that have to be fulfilled for business schools on the road to seek recognition and differentiation while providing exceptional learning. A new mathematical model for UCTP is proposed. The model allows the course-section-professor-time slot to be assigned for an academic department strategically using the faculty workload, course overload, and the fulfillment of the AACSB criteria. Further, the courses that will require new hires are classified according to the faculty qualifications stablished by AACSB. A real-world case is described and solved to show the efficiency of the proposed model. An analysis of different strategies derived from institutional policies that impacts the resulting timetabling is also presented. The results show the course overload could be a valuable strategy for helping mitigate the total of new hires needed. The proposed model allows to create the course at the same time the AACSB standards are met. Full article

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15 pages, 837 KiB

Open AccessArticle

On Little’s Formula in Multiphase Queues

by Saulius Minkevičius, Igor Katin, Joana Katina and Irina Vinogradova-Zinkevič

Mathematics 2021, 9(18), 2282; https://doi.org/10.3390/math9182282 - 16 Sep 2021

Cited by 2 | Viewed by 2140

Abstract

The structure of this work in the field of queuing theory consists of two stages. The first stage presents Little’s Law in Multiphase Systems (MSs). To obtain this result, the Strong Law of Large Numbers (SLLN)-type theorems for the most important MS probability [...] Read more.

The structure of this work in the field of queuing theory consists of two stages. The first stage presents Little’s Law in Multiphase Systems (MSs). To obtain this result, the Strong Law of Large Numbers (SLLN)-type theorems for the most important MS probability characteristics (i.e., queue length of jobs and virtual waiting time of a job) are proven. The next stage of the work is to verify the result obtained in the first stage. Full article

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23 pages, 3383 KiB

Open AccessArticle

A Learning-Based Hybrid Framework for Dynamic Balancing of Exploration-Exploitation: Combining Regression Analysis and Metaheuristics

by Emanuel Vega, Ricardo Soto, Broderick Crawford, Javier Peña and Carlos Castro

Mathematics 2021, 9(16), 1976; https://doi.org/10.3390/math9161976 - 18 Aug 2021

Cited by 4 | Viewed by 1502

Abstract

The idea of hybrid approaches have become a powerful strategy for tackling several complex optimisation problems. In this regard, the present work is concerned with contributing with a novel optimisation framework, named learning-based linear balancer (

L B^{2}

). A regression model [...] Read more.

The idea of hybrid approaches have become a powerful strategy for tackling several complex optimisation problems. In this regard, the present work is concerned with contributing with a novel optimisation framework, named learning-based linear balancer (

L B^{2}

). A regression model is designed, with the objective to predict better movements for the approach and improve the performance. The main idea is to balance the intensification and diversification performed by the hybrid model in an online-fashion. In this paper, we employ movement operators of a spotted hyena optimiser, a modern algorithm which has proved to yield good results in the literature. In order to test the performance of our hybrid approach, we solve 15 benchmark functions, composed of unimodal, multimodal, and mutimodal functions with fixed dimension. Additionally, regarding the competitiveness, we carry out a comparison against state-of-the-art algorithms, and the sequential parameter optimisation procedure, which is part of multiple successful tuning methods proposed in the literature. Finally, we compare against the traditional implementation of a spotted hyena optimiser and a neural network approach, the respective statistical analysis is carried out. We illustrate experimental results, where we obtain interesting performance and robustness, which allows us to conclude that our hybrid approach is a competitive alternative in the optimisation field. Full article

(This article belongs to the Special Issue Mathematical Methods for Operations Research Problems)

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28 pages, 1074 KiB

Open AccessArticle

A Self-Adaptive Cuckoo Search Algorithm Using a Machine Learning Technique

by Nicolás Caselli, Ricardo Soto, Broderick Crawford, Sergio Valdivia and Rodrigo Olivares

Mathematics 2021, 9(16), 1840; https://doi.org/10.3390/math9161840 - 04 Aug 2021

Cited by 8 | Viewed by 2321

Abstract

Metaheuristics are intelligent problem-solvers that have been very efficient in solving huge optimization problems for more than two decades. However, the main drawback of these solvers is the need for problem-dependent and complex parameter setting in order to reach good results. This paper [...] Read more.

Metaheuristics are intelligent problem-solvers that have been very efficient in solving huge optimization problems for more than two decades. However, the main drawback of these solvers is the need for problem-dependent and complex parameter setting in order to reach good results. This paper presents a new cuckoo search algorithm able to self-adapt its configuration, particularly its population and the abandon probability. The self-tuning process is governed by using machine learning, where cluster analysis is employed to autonomously and properly compute the number of agents needed at each step of the solving process. The goal is to efficiently explore the space of possible solutions while alleviating human effort in parameter configuration. We illustrate interesting experimental results on the well-known set covering problem, where the proposed approach is able to compete against various state-of-the-art algorithms, achieving better results in one single run versus 20 different configurations. In addition, the result obtained is compared with similar hybrid bio-inspired algorithms illustrating interesting results for this proposal. Full article

(This article belongs to the Special Issue Mathematical Methods for Operations Research Problems)

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26 pages, 15006 KiB

Open AccessArticle

Carbon Trading Mechanism, Low-Carbon E-Commerce Supply Chain and Sustainable Development

by Liang Shen, Xiaodi Wang, Qinqin Liu, Yuyan Wang, Lingxue Lv and Rongyun Tang

Mathematics 2021, 9(15), 1717; https://doi.org/10.3390/math9151717 - 21 Jul 2021

Cited by 14 | Viewed by 3263

Abstract

Considering the carbon trading mechanism and consumers’ preference for low-carbon products, a game decision-making model for the low-carbon e-commerce supply chain (LCE-SC) is constructed. The influences of commission and carbon trading on the optimal decisions of LCE-SC are discussed and then verified through [...] Read more.

Considering the carbon trading mechanism and consumers’ preference for low-carbon products, a game decision-making model for the low-carbon e-commerce supply chain (LCE-SC) is constructed. The influences of commission and carbon trading on the optimal decisions of LCE-SC are discussed and then verified through numerical analysis. On this basis, the influence of carbon trading on regional sustainable development is empirically analyzed. The results show that the establishment of carbon trading pilots alleviates the negative impact of unfair profit distribution. Increasing the commission rate in a reasonable range improves the profitability of LCE-SC. Nevertheless, with the enhancement of consumers’ low-carbon preference, a lower commission rate is more beneficial to carbon emission reduction. The total carbon emission is positively related to the commission rate. However, the unit carbon emission decreases first and then increases with the commission rate. The influence of the carbon price sensitivity coefficient on the service level is first positive and then negative, while the influence on the manufacturer’s profit goes the opposite. The empirical analysis confirms that the implementation of carbon trading is conducive to regional sustainable development and controlling environmental governance intensity promotes carbon productivity. Full article

(This article belongs to the Special Issue Mathematical Methods for Operations Research Problems)

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21 pages, 367 KiB

Open AccessArticle

Cryptocurrency Portfolio Selection—A Multicriteria Approach

by Zdravka Aljinović, Branka Marasović and Tea Šestanović

Mathematics 2021, 9(14), 1677; https://doi.org/10.3390/math9141677 - 16 Jul 2021

Cited by 15 | Viewed by 5463

Abstract

This paper proposes the PROMETHEE II based multicriteria approach for cryptocurrency portfolio selection. Such an approach allows considering a number of variables important for cryptocurrencies rather than limiting them to the commonly employed return and risk. The proposed multiobjective decision making model gives [...] Read more.

This paper proposes the PROMETHEE II based multicriteria approach for cryptocurrency portfolio selection. Such an approach allows considering a number of variables important for cryptocurrencies rather than limiting them to the commonly employed return and risk. The proposed multiobjective decision making model gives the best cryptocurrency portfolio considering the daily return, standard deviation, value-at-risk, conditional value-at-risk, volume, market capitalization and attractiveness of nine cryptocurrencies from January 2017 to February 2020. The optimal portfolios are calculated at the first of each month by taking the previous 6 months of daily data for the calculations yielding with 32 optimal portfolios in 32 successive months. The out-of-sample performances of the proposed model are compared with five commonly used optimal portfolio models, i.e., naïve portfolio, two mean-variance models (in the middle and at the end of the efficient frontier), maximum Sharpe ratio and the middle of the mean-CVaR (conditional value-at-risk) efficient frontier, based on the average return, standard deviation and VaR (value-at-risk) of the returns in the next 30 days and the return in the next trading day for all portfolios on 32 dates. The proposed model wins against all other models according to all observed indicators, with the winnings spanning from 50% up to 94%, proving the benefits of employing more criteria and the appropriate multicriteria approach in the cryptocurrency portfolio selection process. Full article

(This article belongs to the Special Issue Mathematical Methods for Operations Research Problems)

15 pages, 916 KiB

Open AccessArticle

Perishable Inventory System with N-Policy, MAP Arrivals, and Impatient Customers

by R. Suganya, Lewis Nkenyereye, N. Anbazhagan, S. Amutha, M. Kameswari, Srijana Acharya and Gyanendra Prasad Joshi

Mathematics 2021, 9(13), 1514; https://doi.org/10.3390/math9131514 - 28 Jun 2021

Cited by 7 | Viewed by 1705

Abstract

In this study, we consider a perishable inventory system that has an (s, Q) ordering policy, along with a finite waiting hall. The single server, which provides an item to the customer after completing the required service performance for that [...] Read more.

In this study, we consider a perishable inventory system that has an (s, Q) ordering policy, along with a finite waiting hall. The single server, which provides an item to the customer after completing the required service performance for that item, only begins serving after N customers have arrived. Impatient demand is assumed in that the customers waiting to be served lose patience and leave the system if the server’s idle time overextends or if the arriving customers find the system to be full and will not enter the system. This article analyzes the impatient demands caused by the N-policy server to an inventory system. In the steadystate, we obtain the joint probability distribution of the level of inventory and the number of customers in the system. We analyze some measures of system performance and get the total expected cost rate in the steadystate. We present a beneficial cost function and confer the numerical illustration that describes the impact of impatient customers caused by N-policy on the inventory system’s total expected cost rate. Full article

(This article belongs to the Special Issue Mathematical Methods for Operations Research Problems)

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21 pages, 855 KiB

Open AccessArticle

A Knowledge-Based Hybrid Approach on Particle Swarm Optimization Using Hidden Markov Models

by Mauricio Castillo, Ricardo Soto, Broderick Crawford, Carlos Castro and Rodrigo Olivares

Mathematics 2021, 9(12), 1417; https://doi.org/10.3390/math9121417 - 18 Jun 2021

Cited by 4 | Viewed by 1824

Abstract

Bio-inspired computing is an engaging area of artificial intelligence which studies how natural phenomena provide a rich source of inspiration in the design of smart procedures able to become powerful algorithms. Many of these procedures have been successfully used in classification, prediction, and [...] Read more.

Bio-inspired computing is an engaging area of artificial intelligence which studies how natural phenomena provide a rich source of inspiration in the design of smart procedures able to become powerful algorithms. Many of these procedures have been successfully used in classification, prediction, and optimization problems. Swarm intelligence methods are a kind of bio-inspired algorithm that have been shown to be impressive optimization solvers for a long time. However, for these algorithms to reach their maximum performance, the proper setting of the initial parameters by an expert user is required. This task is extremely comprehensive and it must be done in a previous phase of the search process. Different online methods have been developed to support swarm intelligence techniques, however, this issue remains an open challenge. In this paper, we propose a hybrid approach that allows adjusting the parameters based on a state deducted by the swarm intelligence algorithm. The state deduction is determined by the classification of a chain of observations using the hidden Markov model. The results show that our proposal exhibits good performance compared to the original version. Full article

(This article belongs to the Special Issue Mathematical Methods for Operations Research Problems)

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25 pages, 5188 KiB

Open AccessArticle

Mixed-Integer Linear Programming Model and Heuristic for Short-Term Scheduling of Pressing Process in Multi-Layer Printed Circuit Board Manufacturing

by Teeradech Laisupannawong, Boonyarit Intiyot and Chawalit Jeenanunta

Mathematics 2021, 9(6), 653; https://doi.org/10.3390/math9060653 - 18 Mar 2021

Cited by 7 | Viewed by 2414

Abstract

The main stages of printed circuit board (PCB) manufacturing are the design, fabrication, assembly, and testing. This paper focuses on the scheduling of the pressing process, which is a part of the fabrication process of a multi-layer PCB and is a new application [...] Read more.

The main stages of printed circuit board (PCB) manufacturing are the design, fabrication, assembly, and testing. This paper focuses on the scheduling of the pressing process, which is a part of the fabrication process of a multi-layer PCB and is a new application since it has never been investigated in the literature. A novel mixed-integer linear programming (MILP) formulation for short-term scheduling of the pressing process is presented. The objective function is to minimize the makespan of the overall process. Moreover, a three-phase-PCB-pressing heuristic (3P-PCB-PH) for short-term scheduling of the pressing process is also presented. To illustrate the proposed MILP model and 3P-PCB-PH, the test problems generated from the real data acquired from a PCB company are solved. The results show that the proposed MILP model can find an optimal schedule for all small- and medium-sized problems but can do so only for some large-sized problems using the CPLEX solver within a time limit of 2 h. However, the proposed 3P-PCB-PH could find an optimal schedule for all problems that the MILP could find using much less computational time. Furthermore, it can also quickly find a near-optimal schedule for other large-sized problems that the MILP could not solved optimally. Full article

(This article belongs to the Special Issue Mathematical Methods for Operations Research Problems)

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18 pages, 422 KiB

Open AccessArticle

Branch Less, Cut More and Schedule Jobs with Release and Delivery Times on Uniform Machines

by Nodari Vakhania and Frank Werner

Mathematics 2021, 9(6), 633; https://doi.org/10.3390/math9060633 - 16 Mar 2021

Cited by 2 | Viewed by 1679

Abstract

We consider the problem of scheduling n jobs with identical processing times and given release as well as delivery times on m uniform machines. The goal is to minimize the makespan, i.e., the maximum full completion time of any job. This problem is [...] Read more.

We consider the problem of scheduling n jobs with identical processing times and given release as well as delivery times on m uniform machines. The goal is to minimize the makespan, i.e., the maximum full completion time of any job. This problem is well-known to have an open complexity status even if the number of jobs is fixed. We present a polynomial-time algorithm for the problem which is based on the earlier introduced algorithmic framework blesscmore (“branch less and cut more”). We extend the analysis of the so-called behavior alternatives developed earlier for the version of the problem with identical parallel machines and show how the earlier used technique for identical machines can be extended to the uniform machine environment if a special condition on the job parameters is imposed. The time complexity of the proposed algorithm is

O (γ m^{2} n log n)

, where

γ

can be either n or the maximum job delivery time

q_{max}

. This complexity can even be reduced further by using a smaller number

κ < n

in the estimation describing the number of jobs of particular types. However, this number

κ

becomes only known when the algorithm has terminated. Full article

(This article belongs to the Special Issue Mathematical Methods for Operations Research Problems)

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13 pages, 384 KiB

Open AccessArticle

A Numerical Comparison of the Sensitivity of the Geometric Mean Method, Eigenvalue Method, and Best–Worst Method

by Jiří Mazurek, Radomír Perzina, Jaroslav Ramík and David Bartl

Mathematics 2021, 9(5), 554; https://doi.org/10.3390/math9050554 - 05 Mar 2021

Cited by 12 | Viewed by 1824

Abstract

In this paper, we compare three methods for deriving a priority vector in the theoretical framework of pairwise comparisons—the Geometric Mean Method (GMM), Eigenvalue Method (EVM) and Best–Worst Method (BWM)—with respect to two features: sensitivity and order violation. As the research method, we [...] Read more.

In this paper, we compare three methods for deriving a priority vector in the theoretical framework of pairwise comparisons—the Geometric Mean Method (GMM), Eigenvalue Method (EVM) and Best–Worst Method (BWM)—with respect to two features: sensitivity and order violation. As the research method, we apply One-Factor-At-a-Time (OFAT) sensitivity analysis via Monte Carlo simulations; the number of compared objects ranges from 3 to 8, and the comparison scale coincides with Saaty’s fundamental scale from 1 to 9 with reciprocals. Our findings suggest that the BWM is, on average, significantly more sensitive statistically (and thus less robust) and more susceptible to order violation than the GMM and EVM for every examined matrix (vector) size, even after adjustment for the different numbers of pairwise comparisons required by each method. On the other hand, differences in sensitivity and order violation between the GMM and EMM were found to be mostly statistically insignificant. Full article

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13 pages, 295 KiB

Open AccessArticle

Properties of the Global Total k-Domination Number

by Frank A. Hernández Mira, Ernesto Parra Inza, José M. Sigarreta Almira and Nodari Vakhania

Mathematics 2021, 9(5), 480; https://doi.org/10.3390/math9050480 - 26 Feb 2021

Cited by 2 | Viewed by 1442

Abstract

A nonempty subset

D \subset V

of vertices of a graph

G = (V, E)

is a dominating set if every vertex of this graph is adjacent to at least one vertex from this set except the vertices which belong [...] Read more.

A nonempty subset

D \subset V

of vertices of a graph

G = (V, E)

is a dominating set if every vertex of this graph is adjacent to at least one vertex from this set except the vertices which belong to this set itself.

D \subseteq V

is a total k-dominating set if there are at least k vertices in set D adjacent to every vertex

v \in V

, and it is a global total k-dominating set if D is a total k-dominating set of both G and

\bar{G}

. The global total k-domination number of G, denoted by

γ_{k t}^{g} (G)

, is the minimum cardinality of a global total k-dominating set of G, GTkD-set. Here we derive upper and lower bounds of

γ_{k t}^{g} (G)

, and develop a method that generates a GTkD-set from a GT

(k - 1)

D-set for the successively increasing values of k. Based on this method, we establish a relationship between

γ_{(k - 1) t}^{g} (G)

and

γ_{k t}^{g} (G)

, which, in turn, provides another upper bound on

γ_{k t}^{g} (G)

. Full article

(This article belongs to the Special Issue Mathematical Methods for Operations Research Problems)

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30 pages, 459 KiB

Open AccessArticle

Unified Polynomial Dynamic Programming Algorithms for P-Center Variants in a 2D Pareto Front

by Nicolas Dupin, Frank Nielsen and El-Ghazali Talbi

Mathematics 2021, 9(4), 453; https://doi.org/10.3390/math9040453 - 23 Feb 2021

Cited by 10 | Viewed by 2557

Abstract

With many efficient solutions for a multi-objective optimization problem, this paper aims to cluster the Pareto Front in a given number of clusters K and to detect isolated points. K-center problems and variants are investigated with a unified formulation considering the discrete [...] Read more.

With many efficient solutions for a multi-objective optimization problem, this paper aims to cluster the Pareto Front in a given number of clusters K and to detect isolated points. K-center problems and variants are investigated with a unified formulation considering the discrete and continuous versions, partial K-center problems, and their min-sum-K-radii variants. In dimension three (or upper), this induces NP-hard complexities. In the planar case, common optimality property is proven: non-nested optimal solutions exist. This induces a common dynamic programming algorithm running in polynomial time. Specific improvements hold for some variants, such as K-center problems and min-sum K-radii on a line. When applied to N points and allowing to uncover

M < N

points, K-center and min-sum-K-radii variants are, respectively, solvable in

O (K (M + 1) N log N)

and

O (K (M + 1) N^{2})

time. Such complexity of results allows an efficient straightforward implementation. Parallel implementations can also be designed for a practical speed-up. Their application inside multi-objective heuristics is discussed to archive partial Pareto fronts, with a special interest in partial clustering variants. Full article

(This article belongs to the Special Issue Mathematical Methods for Operations Research Problems)

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23 pages, 821 KiB

Open AccessArticle

Adding Negative Learning to Ant Colony Optimization: A Comprehensive Study

by Teddy Nurcahyadi and Christian Blum

Mathematics 2021, 9(4), 361; https://doi.org/10.3390/math9040361 - 11 Feb 2021

Cited by 16 | Viewed by 2356

Abstract

Ant colony optimization is a metaheuristic that is mainly used for solving hard combinatorial optimization problems. The distinctive feature of ant colony optimization is a learning mechanism that is based on learning from positive examples. This is also the case in other learning-based [...] Read more.

Ant colony optimization is a metaheuristic that is mainly used for solving hard combinatorial optimization problems. The distinctive feature of ant colony optimization is a learning mechanism that is based on learning from positive examples. This is also the case in other learning-based metaheuristics such as evolutionary algorithms and particle swarm optimization. Examples from nature, however, indicate that negative learning—in addition to positive learning—can beneficially be used for certain purposes. Several research papers have explored this topic over the last decades in the context of ant colony optimization, mostly with limited success. In this work we present and study an alternative mechanism making use of mathematical programming for the incorporation of negative learning in ant colony optimization. Moreover, we compare our proposal to some well-known existing negative learning approaches from the related literature. Our study considers two classical combinatorial optimization problems: the minimum dominating set problem and the multi dimensional knapsack problem. In both cases we are able to show that our approach significantly improves over standard ant colony optimization and over the competing negative learning mechanisms from the literature. Full article

(This article belongs to the Special Issue Mathematical Methods for Operations Research Problems)

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20 pages, 422 KiB

Open AccessArticle

Discrete Optimization: The Case of Generalized BCC Lattice

by Gergely Kovács, Benedek Nagy, Gergely Stomfai, Neşet Deniz Turgay and Béla Vizvári

Mathematics 2021, 9(3), 208; https://doi.org/10.3390/math9030208 - 20 Jan 2021

Cited by 5 | Viewed by 1901

Abstract

Recently, operations research, especially linear integer-programming, is used in various grids to find optimal paths and, based on that, digital distance. The 4 and higher-dimensional body-centered-cubic grids is the nD (

n \geq 4

) equivalent of the 3D body-centered cubic grid, [...] Read more.

Recently, operations research, especially linear integer-programming, is used in various grids to find optimal paths and, based on that, digital distance. The 4 and higher-dimensional body-centered-cubic grids is the nD (

n \geq 4

) equivalent of the 3D body-centered cubic grid, a well-known grid from solid state physics. These grids consist of integer points such that the parity of all coordinates are the same: either all coordinates are odd or even. A popular type digital distance, the chamfer distance, is used which is based on chamfer paths. There are two types of neighbors (closest same parity and closest different parity point-pairs), and the two weights for the steps between the neighbors are fixed. Finding the minimal path between two points is equivalent to an integer-programming problem. First, we solve its linear programming relaxation. The optimal path is found if this solution is integer-valued. Otherwise, the Gomory-cut is applied to obtain the integer-programming optimum. Using the special properties of the optimization problem, an optimal solution is determined for all cases of positive weights. The geometry of the paths are described by the Hilbert basis of the non-negative part of the kernel space of matrix of steps. Full article

(This article belongs to the Special Issue Mathematical Methods for Operations Research Problems)

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