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Development and Optimization of Mathematical Models for Operations Research

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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (31 July 2022) | Viewed by 24962

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Dr. Humberto Rocha

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Centre for Business and Economics Research, University of Coimbra, Av. Dias da Silva, 3004-512 Coimbra, Portugal
Interests: optimization; applied mathematics; operations research; computer science
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Dr. Ana Maria Rocha

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Department of Production and Systems, School of Engineering, University of Minho, 4704-553 Braga, Portugal
Interests: global optimization; non-linear optimization; integer-mixed programming
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Special Issue Information

Dear Colleagues,

Programming theory of the optimization model, queuing theory of the queuing model, and game theory of the game model are the first three important branches of operations research. The development of mathematical models and their optimization are fundamental for the effective resolution of many problems in operational research. In recent years, increased insights into real-world problems have led to the development of new mathematical models, new optimization algorithms, or both, contributing to the development of a research area with increasing practical relevance.

This Special Issue is dedicated to works at the interface between mathematical modeling, optimization and operations research with a special focus on real-world applications. In addition to research papers, high-quality review articles on mathematical models/algorithms developed for a challenging real-world application are welcome.

Topics of interest include (but are not limited to):
* Mathematical models/Optimization: continuous and discrete optimization, linear and nonlinear optimization, derivative-free optimization, deterministic and stochastic algorithms, nature-inspired algorithms and other metaheuristic algorithms;

* Applications: all areas of sciences, engineering and industry, including economics, medicine, biology, earth sciences and social sciences.

Prof. Dr. Humberto Rocha
Prof. Dr. Ana Maria Rocha
Guest Editors

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Keywords

Optimization
Continuous and discrete optimization
Linear and nonlinear optimization
Derivative-free optimization
Mathematical modeling
Deterministic and stochastic algorithms
Operations research
Mathematical programming
Programming theory
Decision theory
Game theory
Queuing theory
Reliability theory
Real-world applications

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Published Papers (10 papers)

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Research

24 pages, 2400 KiB

Open AccessArticle

An Optimized Discrete Dragonfly Algorithm Tackling the Low Exploitation Problem for Solving TSP

by Bibi Aamirah Shafaa Emambocus, Muhammed Basheer Jasser, Angela Amphawan and Ali Wagdy Mohamed

Mathematics 2022, 10(19), 3647; https://doi.org/10.3390/math10193647 - 5 Oct 2022

Cited by 9 | Viewed by 1665

Abstract

Optimization problems are prevalent in almost all areas and hence optimization algorithms are crucial for a myriad of real-world applications. Deterministic optimization algorithms tend to be computationally costly and time-consuming. Hence, heuristic and metaheuristic algorithms are more favoured as they provide near-optimal solutions in an acceptable amount of time. Swarm intelligence algorithms are being increasingly used for optimization problems owing to their simplicity and good performance. The Dragonfly Algorithm (DA) is one which is inspired by the swarming behaviours of dragonflies, and it has been proven to have a superior performance than other algorithms in multiple applications. Hence, it is worth considering its application to the traveling salesman problem which is a predominant discrete optimization problem. The original DA is only suitable for solving continuous optimization problems and, although there is a binary version of the algorithm, it is not easily adapted for solving discrete optimization problems like TSP. We have previously proposed a discrete adapted DA algorithm suitable for TSP. However, it has low effectiveness, and it has not been used for large TSP problems. In this paper, we propose an optimized discrete adapted DA by using the steepest ascent hill climbing algorithm as a local search. The algorithm is applied to a TSP problem modelling a package delivery system in the Kuala Lumpur area and to benchmark TSP problems, and it is found to have a higher effectiveness than the discrete adapted DA and some other swarm intelligence algorithms. It also has a higher efficiency than the discrete adapted DA. Full article

(This article belongs to the Special Issue Development and Optimization of Mathematical Models for Operations Research)

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37 pages, 902 KiB

Open AccessArticle

A Family of Hybrid Stochastic Conjugate Gradient Algorithms for Local and Global Minimization Problems

by Khalid Abdulaziz Alnowibet, Salem Mahdi, Ahmad M. Alshamrani, Karam M. Sallam and Ali Wagdy Mohamed

Mathematics 2022, 10(19), 3595; https://doi.org/10.3390/math10193595 - 1 Oct 2022

Cited by 3 | Viewed by 1808

Abstract

This paper contains two main parts, Part I and Part II, which discuss the local and global minimization problems, respectively. In Part I, a fresh conjugate gradient (CG) technique is suggested and then combined with a line-search technique to obtain a globally convergent algorithm. The finite difference approximations approach is used to compute the approximate values of the first derivative of the function f. The convergence analysis of the suggested method is established. The comparisons between the performance of the new CG method and the performance of four other CG methods demonstrate that the proposed CG method is promising and competitive for finding a local optimum point. In Part II, three formulas are designed by which a group of solutions are generated. This set of random formulas is hybridized with the globally convergent CG algorithm to obtain a hybrid stochastic conjugate gradient algorithm denoted by HSSZH. The HSSZH algorithm finds the approximate value of the global solution of a global optimization problem. Five combined stochastic conjugate gradient algorithms are constructed. The performance profiles are used to assess and compare the rendition of the family of hybrid stochastic conjugate gradient algorithms. The comparison results between our proposed HSSZH algorithm and four other hybrid stochastic conjugate gradient techniques demonstrate that the suggested HSSZH method is competitive with, and in all cases superior to, the four algorithms in terms of the efficiency, reliability and effectiveness to find the approximate solution of the global optimization problem that contains a non-convex function. Full article

(This article belongs to the Special Issue Development and Optimization of Mathematical Models for Operations Research)

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19 pages, 1909 KiB

Open AccessArticle

A Statistical Comparison of Metaheuristics for Unrelated Parallel Machine Scheduling Problems with Setup Times

by Ana Rita Antunes, Marina A. Matos, Ana Maria A. C. Rocha, Lino A. Costa and Leonilde R. Varela

Mathematics 2022, 10(14), 2431; https://doi.org/10.3390/math10142431 - 12 Jul 2022

Cited by 5 | Viewed by 1957

Abstract

Manufacturing scheduling aims to optimize one or more performance measures by allocating a set of resources to a set of jobs or tasks over a given period of time. It is an area that considers a very important decision-making process for manufacturing and production systems. In this paper, the unrelated parallel machine scheduling problem with machine-dependent and job-sequence-dependent setup times is addressed. This problem involves the scheduling of tasks on unrelated machines with setup times in order to minimize the makespan. The genetic algorithm is used to solve small and large instances of this problem when processing and setup times are balanced (Balanced problems), when processing times are dominant (Dominant P problems), and when setup times are dominant (Dominant S problems). For small instances, most of the values achieved the optimal makespan value, and, when compared to the metaheuristic ant colony optimization (ACOII) algorithm referred to in the literature, it was found that there were no significant differences between the two methods. However, in terms of large instances, there were significant differences between the optimal makespan obtained by the two methods, revealing overall better performance by the genetic algorithm for Dominant S and Dominant P problems. Full article

(This article belongs to the Special Issue Development and Optimization of Mathematical Models for Operations Research)

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23 pages, 3343 KiB

Open AccessArticle

Roadmap Optimization: Multi-Annual Project Portfolio Selection Method

by Ran Etgar and Yuval Cohen

Mathematics 2022, 10(9), 1601; https://doi.org/10.3390/math10091601 - 8 May 2022

Cited by 4 | Viewed by 2142

Abstract

The process of project portfolio selection is crucial in many organizations, especially R&D organizations. There is a need to make informed decisions on the investment in various projects or lack thereof. As the projects may continue over more than 1 year, and as there are connections between various projects, there is a need to not only decide which project to invest in but also when to invest. Since future benefits from projects are to be depreciated in comparison with near-future ones, and due to the interdependency among projects, the question of allocating the limited resources becomes quite complex. This research provides a novel heuristic method for allocating the limited resources over multi-annual planning horizons and examines its results in comparison with an exact branch and bound solution and various heuristic ones. This paper culminates with an efficient tool that can provide both practical and academic benefits. Full article

(This article belongs to the Special Issue Development and Optimization of Mathematical Models for Operations Research)

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22 pages, 3316 KiB

Open AccessArticle

Impact of COVID-19 on Supply Chains: A Hybrid Trade Credit Policy

by Ping Ruan, Yung-Fu Huang and Ming-Wei Weng

Mathematics 2022, 10(8), 1209; https://doi.org/10.3390/math10081209 - 7 Apr 2022

Cited by 5 | Viewed by 2175

Abstract

The COVID-19 pandemic has affected all sectors of the world’s economy and society. Firms need to have disaster recovery and business sustainability plans and to be able to generate profits in order to develop. Trade credit may be a good way for firms to free up cash flow and finance short-term growth. Extensions of payment will provide firms with low-cost loans under the COVID-19 credit guarantee scheme. Implementation of hybrid trade credit activities has been shown to improve the financial crisis of many firms, and the effects are particularly evident within two-echelon supply chains. An economic order quantity (EOQ) model is derived under conditions of deteriorating items, an upstream full trade credit or cash discount, and downstream partial trade credit in a supply chain. A computer program is developed to provide a numerical solution and a numerical example is used to show the solution’s form and verify that the solution gives the minimum total cost per unit time. Full article

(This article belongs to the Special Issue Development and Optimization of Mathematical Models for Operations Research)

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25 pages, 339 KiB

Open AccessArticle

Using Pairwise Comparisons to Determine Consumer Preferences in Hotel Selection

by Nikolai Krivulin, Alexey Prinkov and Igor Gladkikh

Mathematics 2022, 10(5), 730; https://doi.org/10.3390/math10050730 - 25 Feb 2022

Cited by 4 | Viewed by 3107

Abstract

We consider the problem of evaluating preferences for criteria used by university students when selecting a hotel for accommodation during a professional development program in a foreign country. Input data for analysis come from a survey of 202 respondents, who indicated their age, sex and whether they have previously visited the country. The criteria under evaluation are location, accommodation cost, typical guests, free breakfast, room amenities and courtesy of staff. The respondents assess the criteria both directly by providing estimates of absolute ratings and ranks, and indirectly by relative estimates using ratios of pairwise comparisons. To improve the accuracy of ratings derived from pairwise comparisons, we concurrently apply the principal eigenvector method, the geometric mean method and the method of log-Chebyshev approximation. Then, the results from the direct and indirect evaluation of ratings and ranks are examined together to analyze how the results from pairwise comparisons may differ from each other and from the results of direct assessment by respondents. We apply statistical techniques, such as estimation of means, standard deviations and correlations, to the vectors of ratings and ranks provided directly or indirectly by respondents, and then use the estimates to make accurate assessment of the criteria under study. Full article

(This article belongs to the Special Issue Development and Optimization of Mathematical Models for Operations Research)

15 pages, 352 KiB

Open AccessArticle

New Algorithm to Solve Mixed Integer Quadratically Constrained Quadratic Programming Problems Using Piecewise Linear Approximation

by Loay Alkhalifa and Hans Mittelmann

Mathematics 2022, 10(2), 198; https://doi.org/10.3390/math10020198 - 9 Jan 2022

Cited by 6 | Viewed by 2302

Abstract

Techniques and methods of linear optimization underwent a significant improvement in the 20th century which led to the development of reliable mixed integer linear programming (MILP) solvers. It would be useful if these solvers could handle mixed integer nonlinear programming (MINLP) problems. Piecewise linear approximation (PLA) is one of most popular methods used to transform nonlinear problems into linear ones. This paper will introduce PLA with brief a background and literature review, followed by describing our contribution before presenting the results of computational experiments and our findings. The goals of this paper are (a) improving PLA models by using nonuniform domain partitioning, and (b) proposing an idea of applying PLA partially on MINLP problems, making them easier to handle. The computational experiments were done using quadratically constrained quadratic programming (QCQP) and MIQCQP and they showed that problems under PLA with nonuniform partition resulted in more accurate solutions and required less time compared to PLA with uniform partition. Full article

(This article belongs to the Special Issue Development and Optimization of Mathematical Models for Operations Research)

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21 pages, 2360 KiB

Open AccessArticle

Impact of Trapezoidal Demand and Deteriorating Preventing Technology in an Inventory Model in Interval Uncertainty under Backlogging Situation

by Rajan Mondal, Ali Akbar Shaikh, Asoke Kumar Bhunia, Ibrahim M. Hezam and Ripon K. Chakrabortty

Mathematics 2022, 10(1), 78; https://doi.org/10.3390/math10010078 - 27 Dec 2021

Cited by 8 | Viewed by 2966

Abstract

The demand for a product is one of the important components of inventory management. In most cases, it is not constant; it may vary from time to time depending upon several factors which cannot be ignored. For any seasonal product, it is observed that at the beginning of the season, demand escalates over time, then it is stable and after that, it decreases. This type of demand is known as the trapezoidal type. Also, due to the uncertainty of customers’ behavior, inventory parameters are not always fixed. Combining these two concepts together, an inventory model is formulated for decaying items in an interval environment. Preservative technology is incorporated to preserve the product from deterioration. The corresponding mathematical formulation is derived in such a way that the profit of the inventory system is maximized. Consequently, the corresponding optimization problem is converted into an interval optimization problem. To solve the same, different variants of quantum-behaved particle swarm optimization (QPSO) techniques are employed to determine the duration of stock-in time and preservation technology cost. To illustrate and also to validate the model, three numerical examples are considered and solved. Then the computational results are compared. Thereafter, to study the impact of different parameters of the proposed model on the best found (optimal or very close to optimal) solution, sensitivity analysis are performed graphically. Full article

(This article belongs to the Special Issue Development and Optimization of Mathematical Models for Operations Research)

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29 pages, 3269 KiB

Open AccessArticle

A Scheduling Approach for the Combination Scheme and Train Timetable of a Heavy-Haul Railway

by Hanxiao Zhou, Leishan Zhou, Bin Guo, Zixi Bai, Zeyu Wang and Lu Yang

Mathematics 2021, 9(23), 3068; https://doi.org/10.3390/math9233068 - 29 Nov 2021

Cited by 5 | Viewed by 2552

Abstract

Heavy-haul railway transport is a critical mode of regional bulk cargo transport. It dramatically improves the freight transport capacity of railway lines by combining several unit trains into one combined train. In order to improve the efficiency of the heavy-haul transport system and reduce the transportation cost, a critical problem involves arranging the combination scheme in the combination station (CBS) and scheduling the train timetable along the trains’ journey. With this consideration, this paper establishes two integer programming models in stages involving the train service plan problem (TSPP) model and train timetabling problem (TTP) model. The TSPP model aims to obtain a train service plan according to the freight demands by minimizing the operation cost. Based on the train service plan, the TTP model is to simultaneously schedule the combination scheme and train timetable, considering the utilization optimal for the CBS. Then, an effective hybrid genetic algorithm (HGA) is designed to solve the model and obtain the combination scheme and train timetable. Finally, some experiments are implemented to illustrate the feasibility of the proposed approaches and demonstrate the effectiveness of the HGA. Full article

(This article belongs to the Special Issue Development and Optimization of Mathematical Models for Operations Research)

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23 pages, 811 KiB

Open AccessArticle

Multi-Time Generalized Nash Equilibria with Dynamic Flow Applications

by Shipra Singh, Aviv Gibali and Simeon Reich

Mathematics 2021, 9(14), 1658; https://doi.org/10.3390/math9141658 - 14 Jul 2021

Cited by 1 | Viewed by 1932

Abstract

We propose a multi-time generalized Nash equilibrium problem and prove its equivalence with a multi-time quasi-variational inequality problem. Then, we establish the existence of equilibria. Furthermore, we demonstrate that our multi-time generalized Nash equilibrium problem can be applied to solving traffic network problems, the aim of which is to minimize the traffic cost of each route and to solving a river basin pollution problem. Moreover, we also study the proposed multi-time generalized Nash equilibrium problem as a projected dynamical system and numerically illustrate our theoretical results. Full article

(This article belongs to the Special Issue Development and Optimization of Mathematical Models for Operations Research)

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