Forthcoming and Online First Articles
International Journal of Mathematics in Operational Research
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International Journal of Mathematics in Operational Research (67 papers in press)
Abstract: Delivering parcels using a combination of drones and trucks represents a promising new package delivery method. In previous studies, several truck/drone delivery planning problems and their solutions have been proposed. However, little research has been done to determine which delivery method is most appropriate. The reason for this is that it is difficult to obtain an exact solution for such problems, and thus the accuracy of the solutions is an issue. In this study, we propose an accurate solution procedure for the flying sidekick travelling salesman problem (FSTSP) and the parallel drone scheduling travelling salesman problem (PDSTSP), and establish which delivery method is most suitable based on the solutions obtained.
Keywords: drone; vehicle routing problem; travelling salesman problem; parcel delivery; heuristics.
Bi-criteria two-machine flow shop scheduling problem involving sequence-dependent setup times and pieces multiplicity
by Djedjiga Ouiddir, Mourad Boudhar, Karima Bouibede-Hocine
Abstract: This work addresses a just-in-time (JiT) scheduling problem on two-machine flow shop. We consider the case where each order (job) is composed of several pieces with sequence-dependent setup times. This scheduling problem involves the reducing waste, inventory costs and making goods available as and when needed. Here, the jobs incur either penalties or storage costs if they are not completed within their specific due dates. The aim is to obtain a sequence which minimises two criteria: the total weighted earliness and the total weighted tardiness. For the resolution of this problem, we propose a linear mathematical model, three heuristics and two meta-heuristics, the fast and elitist multi-objective genetic algorithm (NSGA-II) and the multi-objective tabu search algorithm (MOTS). The computational experiments, presented and discussed on randomly generated instances, are showed the effectiveness of the proposed model and NSGA-II.
Keywords: flow shop; just-in-time; JiT; pieces multiplicity; multi-criteria; mixed integer linear programming; MILP; meta-heuristics.
A neutrosophic approach in the optimal solution of a neutrosophic fuzzy capital budgeting problem
by T. Nagalakshmi
Abstract: This paper is proposed to apply neutrosophic fuzzy dynamic programming to solve neutrosophic fuzzy capital budgeting problems (NFCBPs). This paper proposes an optimal solution to a NFCBP with indefinite parameters. In this proposed approach, the revenues are taken as neutrosophic triangular fuzzy numbers (NTFNs). Neutrosophic numbers are used to state indeterminate and inconsistent information. In this paper, ÃN(a1, a2, a3; b1, b2, b3; c1, c2, c3) is taken as a NTFN whose truth membership indeterminacy membership TÃN and falsity membership IÃN are defined in such a way that 0 ≤ TÃN(x) + IÃN(x) + FÃN(x) ≤ 3, x ∈ ÃN(x). Both forward and backward recursive equations are formulated with neutrosophic fuzzy approach to find the fuzzy optimal solution. The approach is illustrated by a numerical example. This proposed approach will pave the way for further researches in fuzzy dynamic programming models with neutrosophic approach.
Keywords: neutrosophic fuzzy dynamic programming; NFDP; neutrosophic triangular fuzzy numbers; NTFNs; neutrosophic optimisation; capital budgeting problem; fuzzy recursive equations; neutrosophic fuzzy capital budgeting problem; NFCBP.
Analysis and simulation of modified susceptible-infected-recovered model with vaccination for COVID-19 outbreak
by Yeong Kin Teoh, Rizauddin Saian, Suzanawati Abu Hasan
Abstract: In this paper, we develop and analyse a modified susceptible-infected-recovered (SIR) compartment model by integrating the vaccination factor as a model parameter to investigate the effect of vaccination parameter on the long-term outcomes of the COVID-19 pandemic. Mathematical analysis is used to determine the disease-free equilibrium, the endemic equilibrium, and the basic reproduction number of the developed model. The stability of the model is studied using the Routh-Hurwitz criterion, and numerical simulations are conducted to assess the impact of vaccination on the disease at different rates. The findings suggest that vaccination rate influences the transmission dynamics, and the vaccine can speed up the COVID-19 recovery and contain the outbreak.
Keywords: simulation; susceptible-infected-recovered model; vaccination; coronavirus; disease free equilibrium; endemic equilibrium; basic reproduction number; stability analysis; Routh-Hurwitz criterion.
Integration of Supplier Evaluation and Closed-loop Supply Chain Network Design from Internal and External Stakeholders Perspectives Using Gray Hybrid SWARA-COPRAS Methods
by Mehdi Seifbarghy, Mohsen Hamidi
Abstract: Today, due to environmental, social, and financial considerations as well as customer expectations, designing closed-loop supply chain (CLSC) networks has become very important form all stakeholders perspectives. In this paper, an integrated model for a CLSC network is presented in four stages. In the first stage, the hybrid SWARA-COPRAS method is applied to score suppliers. In the second stage, environmental and social scores of the refurbishment sites are computed. In the third stage, the customer priorities for substitute products are calculated. In the fourth stage, an integrated four-objective integer linear programming model is proposed from the perspectives of organisation, customers, suppliers, and community. The model selects suppliers, locates refurbishment sites, and determines the flows between supply chain entities. In addition to maximising supply from the most qualified suppliers and producing desirable products for customers, the sustainability of supply chain from environmental, social, and financial perspectives has been considered.
Keywords: closed-loop supply chain network design; CLSC; supplier evaluation; sustainability; customer satisfaction; SWARA-COPRAS.
Impact of advertisement on retailers inventory for time-varying perishable rate with preservation technology investment under customer return and trade credit policy
by Amrita Bhadoriya, Mrudul Jani, Santoshkumar Sharma, Urmila Chaudhari
Abstract: In any business worldwide, inventory management is a challenging task for every organisation. This article demonstrates an inventory model for deteriorating products from the retailers point of view in which: 1) demand is determined by price and frequency of advertisement; 2) the influence of trade credit on expanding small business and their consumers is the focus of this research; 3) product deteriorates with an expiry date; 4) retailer invests money in preservation technology to preserve the deterioration of a product; 5) customer returns the product to the company are the significant factors among the interrelation of supplier and retailer for a highly demanding product. The main objective of this article is to optimise the retailers total profit in terms of cycle length, price, frequency of advertisement, and capital in preservation technology. Also, for optimality, an algorithm is created. Finally, the results were validated by solving two numerical illustrations and conducting sensitivity analysis of the main factors resulting from the following managerial implications: 1) if the retailer receives a longer allowable delay period from the supplier, the retailer can maximise total profit; 2) an increase in the ordering cost per order the overall profit decreases.
Keywords: customer returns; frequency of advertisement; maximum fixed lifetime; price-advertisement dependent demand; preservation technology investment; trade credit.
Multi-Release Software Reliability Assessment: Testing Coverage Based Approach
by Anu G. Aggarwal, Sudeep Kumar, Ritu Gupta
Abstract: Software development companies continue to improve their products to stay up with the markets growing needs by adding new features and fixing previously identified bugs. Software reliability growth models (SRGMs) with testing effort function are the incredibly valuable and have been widely utilised by software engineers. Many researchers have built SRGMs that incorporate the concept testing coverage in the model building for the multi-release software system. The proposed model intends to give three different models of multi-release software reliability modelling with testing coverage function. Three models describe testing coverage by exponential function, delayed S-shaped function and logistic function respectively, with the testing effort function assumed to be Weibull in nature. Real-world data is used to estimate parameters in order to validate the proposed SRGM of four releases from Tandem Computers and the model goodness-of-fit is assessed. The results suggest that the proposed model matches the failure data effectively.
Keywords: SRGMs; software reliability; testing coverage; testing effort; NHPP.
The Topp-Leone Type II Exponentiated Half Logistic-G Family of Distributions with Applications
by Morongwa Gabanakgosi, Broderick Oluyede
Abstract: In this paper, we introduce a new continuous family of distributions called the Topp-Leone type II exponentiated half logistic-G (TL-TIIEHL-G). We also present some of the special cases of the new model. Some statistical properties of the new family of distributions are explored. The statistical properties studied include the expansion of the density function, hazard and quantile functions, moments, moment generating functions, probability weighted moments, stochastic ordering, distribution of order statistics and R
Keywords: Topp-Leone distribution; type 11 distribution; exponentiated half-logistic-G; maximum likelihood estimation.
The hybrid DHP method for evaluation, ranking and selection of green supplier in the supply chain
by Elham Shadkam, Reza Yazdani, Mirpouya Mirmozaffari, Fatemeh Adinehkalat
Abstract: This paper presents a hybrid method called the DHP method, which is a combination of data envelopment analysis and hierarchical analysis process methods. Evaluation, ranking, and selection of green suppliers in the supply chain are important to reduce costs and increase profits, the efficiency, and performance of the supply chain. The purpose of this paper is to evaluate and select the best green suppliers of wind turbine equipment using the proposed DHP approach. In fact, it deals with the process of hierarchical analysis of supplier performance and uses a cross-performance matrix instead of a weight matrix. Finally, in order to validate the proposed DHP method, a similar method is used to solve the problem of green supplier selection, and the results show the superiority of the proposed method in supplier selection. The most important advantage of the proposed approach is the simultaneous consideration of suppliers' performance and their evaluation according to the existing criteria.
Keywords: supply chain; green suppliers; analytical hierarchy process; data envelopment analysis; DEA; wind power plant.
The COHP hybrid Method to solve multi-objective optimization problems: Machine Scheme Selection
by Elham Shadkam
Abstract: Multi-objectives problem optimisation is always one of the most challenging problems in the field of optimisation and it is difficult to find the optimal solution due to conflicting objectives. In this paper, by combining the method of the analytical hierarchy process (AHP) and cuckoo optimisation algorithm (COA), a new hybrid method for solving multi-objective problems is presented. The hybrid method is called COHP, which is inspired by the names of its combinatorial methods. The proposed COHP method uses the analytical hierarchy process to obtain weights through a matrix of pairwise comparisons and then interactively enter these weights into the cuckoo optimisation algorithm. In order to evaluate the performance of the multi-objective problem algorithm, the machine scheme selection in digital manufacturing with three objectives of quality, time and cost has been considered. After implementing the COHP method on the mentioned problem, the results show the superiority of the COHP method compared to the similar method created from the genetic algorithm.
Keywords: cuckoo optimisation algorithm; COA; analytical hierarchy process; AHP; multi-objective optimisation; machine scheme.
Strategic Behaviour for M/M/1 Double Orbit Retrial Queue with Imperfect Service and Vacation
by Sibasish Dhibar, Madhu Jain
Abstract: In this paper, optimal strategy for double orbit retrial queue with imperfect service and vacation interruption has been studied. Sometimes, when the waiting space appears to be congested, the incoming customers may decide not to join the system. If the server is busy, the arriving customers are compelled to enter the ordinary or premium class orbit as per willingness of the customers not to pay or pay for waiting in the queue. If some customers are unsatisfied with their service during the normal busy period, they may demand additional service. Chapman-Kolmogorov governing equations are structured and solved analytically by using the probability generating functions. Several performance indices and optimal social profit with joining strategy are derived explicitly. The numerical results are obtained to analyse the effects of system descriptors on the performance indices, joining probabilities, etc. Moreover, particle swarm optimisation technique has been used to establish the optimal service policy.
Keywords: retrial queue; imperfect service; vacation; equilibrium strategy; social profit; particle swarm optimisation.
The Harris-Topp-Leone-G Family of Distributions: Properties and Applications
by Thatayaoner Moakofi, Broderick Oluyede
Abstract: In this paper, we propose a new family of continuous distributions called the Harris-Topp-Leone-G (Harris-TL-G) family of distributions that extends the Topp-Leone-G family introduced by Al-Shomrani et al. (2016). Explicit expressions for certain statistical properties of the new family of distributions including quantile function, ordinary and incomplete moments, generating functions, R
Keywords: Harris distribution; Topp-Leone distribution; maximum likelihood estimation.
Study of Green Manufacturing Practices through Survey-Ordinal Regression Analysis and Development of Theoretical Framework for Ethiopian Manufacturing Industries
by Mukesh Kumar, Atul Kumar, Vikrant Sharma
Abstract: Green manufacturing (GM) research has grown in recent years due to the perceived performance implications. However, the literature on the implications of GM practices in manufacturing firms, particularly in developing countries, is scant. This research addressed this challenge by examining the effects of GM practices on the green achievement (GA) of manufacturing firms in Ethiopia. This article conducted a mail-questionnaire survey and then used ordinal regression analysis to analyse the survey results obtained from 90 valid responses. Additionally, the authors developed a framework for theoretical implications. Three dimensions of green practices were evaluated: green products, green processes, and green supply and distribution. Except for green products, the findings indicate that all green practices dimensions are positive and significant predictors of GA. This is the first study to examine how Ethiopian manufacturing industries implement GM practices, which can serve as a model for other businesses implementing environmental programs.
Keywords: green manufacturing practices; green achievement; Ethiopian manufacturing industry; ordinal regression analysis; theoretical framework.
Elucidating two-stage flow shop multiprocessor scheduling problems using a hybrid genetic algorithm
by Shun-Chi Yu
Abstract: In the recent decades, genetic algorithms (GAs) have often been applied as heuristic techniques at various settings entailing production scheduling. However, early convergence is one of the problems associated with this approach. This study develops an efficient local search rule for the target-oriented rule in traditional GAs. It also addresses the problem of two-stage multiprocessor flowshop scheduling (FSP) by viewing the due window and sequence-dependent setup times as constraints faced by common flowshops with multiprocessor scheduling suites in the actual production scenario. Using the simulated data, this study verifies the effectiveness and robustness of the proposed algorithm. The results of data testing demonstrate that the proposed method may outperform other algorithms, including a significant hybrid algorithm, in addressing the problems considered.
Keywords: target-oriented; genetic algorithm; two-stage MFSS; due window; setup time.
A vendor-buyer supply chain model with price, warranty and green sensitive demand under greening cost, warranty cost and revenue sharing contract
by BISWARUP SAMANTA, Arpita Giri, Bibhas Giri
Abstract: This article considers a vendor-buyer supply chain model where the customer demand depends on selling price, green level and warranty period of the product. The production rate of the vendor is known and greater than the market demand. The production process is imperfect and it may yield some non-conforming items due to machine shift from an in-control state to an out-of-control state during a production run. Successive deliveries from the vendor are scheduled at a fixed time interval wherein the subsequent shipment appears when the buyers inventory from former delivery has just been cleared out. A hybrid greening cost, warranty cost and revenue sharing (HGWRS) contract is introduced, which provides more profit to individual members than their decentralised profits. The numerical study reveals that, under HGWRS contract, customers are influenced to buy a more reliable product at a lower price with higher green level. A sensitivity analysis is also carried out to examine the impact of key model-parameters on the optimal results.
Keywords: supply chain; pricing; greening; warranty; revenue sharing contract.
A new approach for non convex optimization problems applied to Hump and Benchmark functions
by Fadila Leslous, Mouloud Goubi, Mohand Ouanes
Abstract: A new approach for solving multivariate global optimisation problems with a single objective function or multi objective functions. Our method consists in reducing the multivariate case to the univariate case and then we solve an univariate global optimisation problem over an interval of R. To do this, a change of variables combined with algebraic tools and Newton method are used. An algorithm is derived to find a global optimal solution of the original problem.
Keywords: multi-objective optimisation; global optimisation; Hump functions; non-convex optimisation; Newton algorithm.
Determinants of Red Meat Consumption in Qatar: Implications for Red Meat Supply Chains
by Abdelfadil Babiker I., Lamay Sabir, Mohd. Nishat Faisal
Abstract: The rising income and population in Qatar have led to an increase in the consumption of red meat. However, the supply side of a red meat supply chain is located outside the country with little control over supply chain (SC) transparency. Extant literature suggests that colour, safety, and nutritional value are essential attributes of red meat. However, studies related to their impact on consumer choices and SC is limited. This research explores the parameters that determine household consumption of red meat and uses the analytic hierarchy process (AHP) approach to prioritise the most-important parameters that influence red meat consumption for Qatari and non-Qatari customers indicating significant differences. Qatari nationals consider nutrition as an important attribute, while non-Qatari consumers consider price as an important attribute in their purchase decision. The results would be helpful for managers of red meat SCs to improve transparency and revisit their strategies for the supply of red meat to Qatar.
Keywords: red meat; transparency; Qatar; supply chain; analytic hierarchy process; AHP.
Algorithms of algebraic order nine for numerically solving second-order boundary and initial value problems in ordinary differential equations
by Ezekiel Omole, F.O. Obarhua, Adefunke Bosede FAMILUA, Ali Shokri
Abstract: A new numerical algorithm comprising of two-step with six off-step points is presented in this paper. The new method adopted interpolation of the approximate solution and collocation of the differential system in the development of the methods. The main method and its supplementary methods are combined to form the required integrators which are self-starting in nature. The implementation strategy is discussed and the new method has an algebraic order nine with significant properties that vindicate its effectiveness when applied to solve some standard second-order initial and boundary problems of ordinary differential equations such as nonlinear problem, variable coefficient problem, stiff problem, two body problem, Classical nonlinear Bratus BVP in one-dimensional planar coordinates, Troeschs problem, Michaelis-Menten oxygen diffusion problem with uptake kinetic and the van der Pol oscillatory problem. The comparison of the new methods with some already existing methods confirmed that the method gives better accuracy. The effectiveness and efficiency are also demonstrated in the curves.
Keywords: two-step algorithms; ninth order algebraic methods; second order initial and boundary value problem; Michaelis-Menten oxygen diffusion problem.
Impact of inflation and discount on optimum ordering and preservation technology expenses scheme of perishable inventory model
by Chanda Nautiyal
Abstract: This study coins an inventory model for deteriorating articles. The work devises an optimal approach of expenditure on preservation technology to attenuate the degradation process. The demand in the inventory model is both price and stock level sensitive. Demand in the form of price dependence is again a convex combination of linear and nonlinear prices. The investigation proliferates state-of-the-art strategy by presenting the concept of discount if payment is done in advance. The suggested model scrutinises the impact of inflation on optimality plan as well. The object of this exercise is to find optimal cycle length and preservation technology expenses to minimise the total cost per unit time. Stock is backlogged partially. Solution methodology of nonlinear minimisation problem embodies derivation of theorems and propositions. The final results are validated with the help of three examples, convexity of graphical schemes and sensitivity analysis. The paper also outlines the managerial point of view.
Keywords: advance payment; price and stock dependent demand; discount; preservation technology; partial backlogging; inflation; mathematical modelling.
Comparing different types of robust possibilistic programming approaches in designing closed-loop networks
by Mona Bahrami, Mehdi Seifbarghy, Mohsen Hamidi, Farshad Faghihzade
Abstract: This paper introduces a multi-objective, multi-product, and multi-period closed-loop supply chain network model with uncertainty. The network includes suppliers, plants, distribution centres, hybrid processing centres, and customers in its forward chain while in the backward chain; it is composed of customers, collection centres, disposal centres, hybrid processing centres, and plants. The problem has three objectives for optimising profit, delivery time, and quality. With these three objectives, the model creates a balance between customer satisfaction and business profitability. The model also considers the impact of average useful life of products on their return. We use several types of robust possibilistic approaches and multi-choice goal programming to tackle uncertainty and the multi-objective nature of the problem. The model is applicable in a variety of businesses such as automobile, electrical, and electronic industries.
Keywords: supply chain planning; robust possibilistic programming; RPP; multi-choice goal programming; uncertainty; closed-loop networks.
The Exponentiated Half Logistic-Kumaraswamy-G Family of Distributions with Properties and Applications
by Bakang Tlhaloganyang, Whatmore Sengweni, Broderick Oluyede
Abstract: In this paper, a new generalised family of lifetime models called the exponentiated half logistic-Kumaraswamy-G (EHL-KUM-G) distribution is introduced and studied. We derive explicit expressions for the structural properties which includes quantile function, linear representation, ordinary and incomplete moments, moment generating functions, R
Keywords: exponentiated half logistic distribution; Kumaraswamy-G distribution; exponentiated half logistic-Kumaraswamy-Weibull distribution.
An M^[X]/G^(1,K)/1 Queue with Unreliable Server and Bernoulli Vacation
by P. Nagarajan, Kalyanaraman R
Abstract: A Poisson arrival queue with batch arrival, service in a batch of variable size with a minimum of
Keywords: Poisson process; batch arrival; batch service; Bernoulli vacation; unreliable server; supplementary variable technique; operating characteristics.
Classification and Feature Selection for Micro array Cancer Dataset using an improved African Vulture Optimization Algorithm
by Balakrishnan K, R. Dhanalakshmi
Abstract: The African vulture optimisation algorithm (AVOA) is a recently developed metaheuristic algorithm that imitates the eating and movement patterns of authentic African vultures. AVOAs convergence accuracy and stability, like that of various state-of-the-art metaheuristics, will degrade as optimisation problems get more complicated and variable. Furthermore, the traditional AVOA only searches in one direction, limiting its convergence capacity and causing stagnation at local minima. To address these shortcomings, this work offers LOBL-AVOA, a better version of AVOA hybridised with the lens opposition-based learning (LOBL) technique for classification. The LOBL enhances global exploratory capacity while preventing premature convergence. The suggested LOBL-AVOA findings are compared to traditional AVOA results. The efficacy of LOBL-AVOA is assessed employing six high-dimensional microarray datasets and three distinct classifiers such as support vector machine (SVM), K-nearest-neighbour (KNN) and random forest (RF). As an outcome, the proposed method surpasses traditional AVOA in terms of convergence capability, statistical analysis and classification accuracy.
Keywords: African vulture optimisation algorithm; AVOA; classification; feature selection; microarray dataset.
Application of Regenerative Processes Approach for the Approximation of the Ruin Probability in a Bivariate Classical Risk Model with Large Claims
by Safia HOCINE, Djamil AÏSSANI, Aicha BARECHE, Zina BENOUARET
Abstract: In order to reflect more accurately the insurance companys activity, risk models that have been recently studied in the literature are becoming increasingly complex. Moreover, the ruin probability associated with these models cannot be found explicitly. Using the theory of regenerative processes, the present paper focusses on the stability analysis of a two-dimensional classical risk model with large and independent claims. The obtained stability bound is explicitly written and applied to estimate the deviation of the ruin probability under the clarified perturbation domain of the parameters governing the considered model. This proposed approach based on the theory of regenerative processes is more suitable for the stability analysis of ruin probabilities of a risk model since it takes into account large claims, unlike the strong stability method based on Markov chains. A numerical comparison between the stability bounds obtained with both approaches (regenerative process approach and Markov chains approach) is performed, based on simulation results.
Keywords: regenerative process; strong stability; Markov chain; approximation; two-dimensional risk model; ruin probability.
Scheduling preemptive jobs on parallel machines with a conflict graph : A graph multi-coloring approach
by Adlane Baaziz, HACENE AITHADDADENE, AMMAR OULAMARA, AHMED KOUIDER
Abstract: This paper addresses the problem of scheduling n preemptive jobs, which must be carried before a predefined overall deadline, on a set of m parallel machines. This deadline corresponds to the end of the planning horizon. Each job has its own processing time and a predetermined gain assigned to it when it is completely executed. Resources are distinguished into two types: shared and critical resources. Jobs requiring the same critical resource are subjected to conflicting constraints modelled by an undirected graph. The goal is to optimise three objectives: the main one is maximising the total gain of the performed jobs. The two others objectives consider the manner of the jobs accomplishment, where the number of interruptions and the total completion time have to be minimised. To solve this NP-hard problem, an improved simulated annealing based on: 1) a minimum lost gain strategy for vertices colouring procedure; 2) a new technique for the selection of a new solution is proposed. Extensive computational experiments show the capability of the proposed algorithm to obtain optimal solutions in a reasonable amount of CPU time for small instances, and significantly better results than in the rest methods of the literature for large instances.
Keywords: parallel machines scheduling; graph multi-colouring; meta-heuristic approach.
Solving aggregate production planning problem with uncertainty using fuzzy goal programming
by Alaa Alden Al Mohamed, Sobhi Al Mohamed, Marwa Ahmad
Abstract: This study proposes a fuzzy goal programming (FGP) model to address planning problem in the work environment, especially in the field of production and the factors affecting production planning, had a great role in increasing the interest in the function of aggregate production planning and everything related to activities and processes that contribute to products manufacturing through the optimal use of all available resources in organisations. This paper aimed to solve the problem of aggregate production planning in general corporation for the sugar industry, in a way that helps decision-makers to take appropriate decisions, especially under the fuzzy environment in which all sugar production companies operate, by identifying decision variables, levels of aspiration and tolerance. Using the fuzzy goal programming, to reduce the cost of production and storage and the change in the level of the workforce, to help the company meets the market need for the products it produces.
Keywords: aggregate production planning; APP; fuzzy goal programming; FGP; fuzzy logic; goal programming; plastic industry.
A MODEL ON AN EOQ OPTIMAL ORDERING POLICY VARYING WITH TIME-DEPENDENT CUBIC DEMAND AND VARIABLE DETERIORATION UNDER DELAY IN PAYMENT CONDITIONS
by Sephali Mohanty, Trailokyanath Singh
Abstract: The main objective of the proposed paper is to extend Khanra et al.s (2011) model with the following characteristics: 1) delay in payment is acceptable; 2) demand is a generalised demand pattern and is a cubic function of time; 3) deteriorating items follow a variable deterioration rate, which is a linear function of time; 4) neither partial backlogging nor complete backlogging has been taken into consideration. For settling the account, the formulation of the model is derived under two main approaches: case 1
Keywords: delay in payment; deteriorating items; EOQ; time-dependent cubic demand; variable deterioration.
On the Existence of the Tracking Model for N-dimensional Brownian Particle in the Fluid
by Mohamed El-hadidy, Alaa Alzulaibani
Abstract: In this work, an existential study of the tracking technique of N-dimensional Brownian particle in the fluid has been discussed. A set of nano-robot sensors start the tracking process from the origin of N-dimensional space. Besides giving the conditions which present the finiteness of the expected value of the first meeting time between one of the nano-robot sensors and the particle, we provide the computational expected value of this time.
Keywords: probabilistic methods; statistical physics; mathematical analysis; N-dimensional Brownian motion; purify impurities.
A Pricing and Inventory Control for Perishable items with the Inflation Rate and Retailers Returns
by Fateme Kharidar, Mostafa Kazemi, Alireza Pooya, Amirmohammad Fakoor Saghih
Abstract: The impact of inflation and retail returns on perishable item joint pricing and inventory control is explored in this research, and a new model is given. The model is tested using a price and time-dependent demand function, as well as retailers returns as a function of the selling price and order volume. The major aims to determine the optimal selling price, replenishment cycles, and order quantity all simultaneously, to maximise the present value of the total profit over a given time horizon. Furthermore, it is displayed that the optimal replenishment cycle is unique at any price. Then illustrated that the present value of the total profit is a concave function of price with an optimal value. Also, a simple algorithm was described for determining the optimal solution and model variables. Finally, a numerical example is used to indicate the solution algorithm, and the models effectiveness is demonstrated by sensitivity analysis.
Keywords: pricing; inventory control; simultaneous pricing and inventory control; perishable; retailer; inflation; retailers returns; time value of money; TVM; Iran.
Solving Bi-Level Linear Fractional Programming Problems with Fuzzy Interval Coefficients Using Game Matrix
by Nejmaddin Sulaiman, Gulnar Wasim, Basiya Kakawla
Abstract: In this paper, a bi-level linear fractional programming problems (BILLFPP) with fuzzy interval coefficients (FIC) considered where all of it is coefficients in the goal function and constraints are fuzzy intervals (FIs). Firstly, to resolve this issue, we construct two LFPP with fuzzy coefficients one of these problems is a LFPP where all of it is coefficients are upper approximations of (FIs) and the other is a LFPP, where all of it is coefficients are lower approximations of (FIs) secondly, the BILLFPP are converted in to a single objective LFPP and QFPP. At the end, and we use game matrix technique which yields an efficient resolution of the original BILLFPP with fuzzy interval, the single objective LFPP or QFPP is resolved by modified simplex technique. Finally, numerical examples are given to demonstrate the results.
Keywords: LFPP; BILLFPP; FBILLFPP; BILLFPP with fuzzy interval; FBILLFPP with fuzzy interval; modified simplex technique.
A distinct management of Linear Programming in uncertain atmosphere
by Tuhin Bera, N.K. Mahapatra
Abstract: For a linear programming problem (Lp-problem), a fluctuation of the optimal objective value may occur when some relevant parameters are additionally acted upon the system. An Lp-problem is here structured in the parlance of a number of such parameters to have a fair end. Each parameter corresponds one objective function and thus the problem is multi-objective. The coefficient of objective function is set upon the experts past experience and its degree of functionality so that a particular problem can also support the different atmosphere. The experimental data is described by three kinds of single valued triangular neutrosophic number (Svtrn-number) to deal with uncertainty. To manipulate huge number of data in uncertain climate, graded mean integration concept is practiced to find the score of an Svtrn-number. An user friendly algorithm is developed to solve an Lp-problem. The model is applied on a fishery planning to justify its efficiency. The obtained result is analysed, and is compared in existing frames to claim the superiority of this work.
Keywords: neutrosophic set; single valued triangular neutrosophic number; score function; linear programming in neutrosophic arena.
Mixed Integer Linear Programming formulations for the permutation flow shop scheduling problem with preventive maintenance activities
by Wahiba Jomaa, Mansour Eddaly, Bassem Jarboui
Abstract: This paper investigates the flow shop scheduling problem in the non-resumable case using an arbitrary number of preventive maintenance activities on each machine, with the optimized criterion being the makespan. Three mixed integer linear programming (MILP) models are proposed for three different problem types with respect to the considered maintenance policies within fixed-time windows, after a fixed number of finished jobs, and within an optimal preventive maintenance period. The computational results based on the randomly generated test problems demonstrate the high performance of the proposed MILP models in solving a wide range of instances, particularly, in small- and medium-scale problems.
Keywords: Scheduling; Permutation Flow shop; Preventive Maintenance ;mixed integer linear programming.
Throughput optimization in reentrant circular regular robot cells
by Ali Khebouche, Mourad Boudhar, El-sedik Lamini
Abstract: We consider robot cells of type reentrant circular flow shop served by a single-gripper central robot having the ability to swap. The objective is to find a cyclic sequence of robot moves that minimises the cycle time of one-unit required to produce a part or, equivalently, that maximises the throughput. We analysed three-machine robot cells in-depth showing that four of the feasible one-unit cycles dominate the remaining 17 cycles. We determined the parameter regions in which each of the four cycles is optimal. In the case of m machines, we gave two new lower bounds with an emphasis on four cycles that are specific among all one-unit cycles. Initially, cycle time formulas are created for the four cycles of one-unit. In addition, we established the parameter regions where each of the cycles is best. Finally, we showed that a specific cycle provides a 3/2-approximation for the remaining unique region.
Keywords: circular robot cells; chain-reentrant; throughput maximisation; cyclic production; flow-shop scheduling.
An algorithm for solving a min-max problem by adaptive method
by Aghiles AZIZEN, Louadj Kahina, Aidene Mohamed
Abstract: Min-max problems occupies an important place linear programming (LP), as it addresses in a large number of optimisation problems, in various fields of science. In this study, an algorithm using adaptive method is proposed for solving the min-max problem in linear programming. It consists on finding the maximum of the minimum of a function (where the essential constraints are in equality and the direct constraints are bounded) in a minimum execution time. A solving algorithm is built using the principle of the adaptive method and it is based on the concept of the support matrix of the problem. Necessary and sufficient conditions for the optimality of a support feasible solution are established and suboptimality criterion is derived. This algorithm allows to solve directly the considered problem, without modifying it and avoids the drawbacks of the increase in the number of the variables and the constraints, thus, improve the convergence speed of the method. Its performance is tested on a numerical example.
Keywords: min-max problem; linear programming; adaptive method; suboptimality estimate; change of support; optimisation; feasible solution; optimality criterion.
FIXED POINT RESULTS USING MULTIVALUED AND ORBITAL CONTINUOUS MAPPING IN QUASI PARTIAL METRIC SPACE
by Lekha Dey, Sanjay Sharma
Abstract: The aim of the work is to generalise some fixed-point results for mapping that is multivalued in quasi-partial-metric space. It is an extension of fixed points for dominated mappings in partial metric space. The work modifies and extends all results of partial metric space Ahmad et al. (2013) into quasi-partial metric space. The work also proves some fixed-point theorem for orbitally continuous operators defined in quasi-partial metric space. This paper reveals that both theorems can be given better results in quasi-partial metric space as well as obtained results are associated with the other operators. Finally, we provide an example to support the last theorem.
Keywords: fixed point theory; partial metric space; quasi partial metric space; multi valued mappings; Cauchy sequence; distance function; orbitally complete QPMS.
Equitable coloring and scheduling on identical machines
by Sarah Nouri, Mourad Boudhar
Abstract: This paper deals in the first place with the problems of two-equitable colouring of a union of complete bipartite graphs and three-equitable colouring of connected bipartite graphs, where their N P-completeness is proved. In the second place, it studies the scheduling problem of conflicting jobs on identical machines, while distributing the load evenly between them. Jobs with conflicting constraints cannot be executed on the same machine, these constraints are modelled by a conflict graph. Such problem with identical processing times can be seen as an m-equitable colouring. If the conflict graph is a star graph or a union of chains, this paper demonstrates that the addressed scheduling problem remains N P-hard. Furthermore, the paper describes mixed integer linear programming formulations, followed by some heuristics. The computational experiments show that one of the MILPs can optimally solve some instances with 100 jobs, and the proposed heuristics perform well.
Keywords: equitable colouring; scheduling; conflict graphs; heuristics; mixed integer linear programming; MILP.
Study of two heterogeneous servers with service feedback, vacation and particular service interruption.
by Nitin Mahla, Alka Choudhary, Dinesh Chandra Sharma
Abstract: Due to the huge impact on real-life application, queueing models with different types of servers have been studied widely. This paper-based on M/M/2 queues presents the study of two heterogeneous servers with particular service interruption, vacation and maintenance. Feedback facility is provided to the customers which are served by a particular server and this server will be interrupted by reactive maintenance after getting a threshold number of negative feedback. Another server will work simultaneously and no feedback will be recorded for this server. To derive the steady-state probabilities, a detailed computational procedure is followed using the matrix geometric method, and then performance measures are calculated. The economic analysis of the model is done. This model is compared with the M/M/1 model in which the server is interrupted by reactive maintenance after getting threshold number of negative feedback.
Keywords: M/M/2 queueing model; Feedback; Service interruption; Maintenance.
A Greedy Heuristic and a Lower Bound on a Nonlinear Stochastic TSP with Partially Satisfied Node Demand Coverage Constraint
by Murat Cal, Senol Altan
Abstract: The combinatorial travelling salesman problem (TSP) has driven researchers to find faster ways to solve the problem in reasonable times. As a result, researchers modified and created new TSP combinations such as multi-objective TSP or TSP with stochastic constraints. One of these constraints is the node demand coverage constraint. It makes sure that the demand of each node is satisfied in a route. In this study, we re-modify the node demand coverage constraint to be satisfied by some percentage of the time. This approach is more realistic because a node can be visited without covering its demand, allowing the missing of some nodes during the demand covering process while making our model nonlinear. We then provide a greedy heuristic in MATLAB and a lower bound determination procedure for this model and experiment with some predefined datasets.
Keywords: travelling salesman problem; TSP; chance constraints; nonlinear optimisation.
Availability modeling and analysis of a two-component parallel system under stochastic dependence
by Ziyad Bahou, Krimi Issam, Abdessamad AitElCadi, Nizar Elhachemi
Abstract: In real-world settings, machines are not available all the time. They can undergo different collapses and malfunctions. This may increase costs and sometimes gravely threaten safety. To face this challenge, it is important to assess the availability based on the different dependencies between their components. The purpose of this paper is to compute exactly the availability of a two-component parallel system considering stochastic dependence. We propose an efficient and user-friendly model, based on Cox proportional hazards model using the generalised Weibull distribution. A calculation framework is presented to compute more realistic system availability even for real systems provided with a history of failures. A numerical example is given to assess the stochastic dependence effect on the availability of the system and to illustrate the model. A managerial insight is provided to allow the practitioners to better estimate this latter in order to develop adequate maintenance strategies.
Keywords: availability modelling; multi-components systems; stochastic dependence; Cox proportional-hazards model.
Analysis of S-shaped, U-shaped and V-shaped Transfer Functions in IoMT datasets using Binary Aquila Optimization Techniques
by Surendra Babu Nallagorla, R. Dhanalakshmi
Abstract: The Aquila optimisation (AO), a metaheuristic approach, is motivated by the Aquilas natural behaviour when collecting prey. However, while the method shines at several benchmark functions, it fails to solve the binary optimisation problem. We suggested a binary version of AO (BAO) for feature selection (FS) concerns in classification tasks in this research using internet of medical things (IoMT) datasets. We used 12 (S, U, and V-shaped) transfer functions (TF) to transform continuous data into binary values. The proposed TFs demonstrate that BAO techniques, particularly S2-BAO, outperform alternative transfer functions. According to the results, the suggested approach, as compared to traditional transfer functions, converges to the global minimum in multiple rounds based on the selection of optimal attributes, fitness values, and improved classification accuracy.
Keywords: Aquila optimisation; classification; feature selection; metaheuristic optimisation.
Unreliable single server retrial queueing model with repeated vacation
by Ebenesar Anna Bagyam J, SUGANTHI POOMALAI, Visali P
Abstract: The steady-state behaviour of a single server retrial queueing model with server breakdown and repeated vacation is analysed. If the server is accessible, the customer gets service immediately; otherwise, the customer waits for his turn. After each service, the server may take a vacation with a certain probability. However, if the system is empty, the server takes repeated vacations until the server finds at least one customer in the system. If the server is prone to breakdown, the repair of the server starts immediately. After the repair, the server continues the service to the same customer. The retrial, service, repair, and vacation times are assumed as arbitrary distributed. The steady-state solutions for various performance measures are determined using the supplementary variable method.
Keywords: retrial queue; repeated vacation; server breakdown; repair; unreliable server; performance measures; numerical analysis; call centre; multiple vacation; supplementary variable technique.
Transient Solution of fractional M/M/c queue
by NANDURI SUJATHA, GVSR Deekshitulu
Abstract: In queuing models, sometimes the server may not work with full efficiency or may stop working also. Such problems are modelled with the help of fractional differential equations. Differential-difference equations involving fractional derivatives in the sense of Mittag-Leffler function have been employed to model the problems with partial activity of the server. In this paper, transient analysis of fractional M/M/c queue has been carried out analytically and results are obtained using MATLAB. The validity and efficiency of the above model is demonstrated with a numerical example. The results obtained by this new approach are justified by comparing them with solutions of classical queue which are available in the literature.
Keywords: transient analysis; fractional derivatives; Mittag-Leffler function.
Proposing a Novel Integrated OPA-MARCOS Multi-criteria Decision Making Model to Choose the Best Plastic Recycling Method (case study)
by Alireza Keshtpour, Elham Shadkam, Hooman Khorsand
Abstract: Due to the rapid reduction of natural resources and adverse global environmental changes, it is necessary to preserve natural resources and protect the environment. There are various ways to recycle plastic. Choosing the best plastic recycling method is a multi-criteria decision-making problem. This research investigated the output of reference research and then re-solved it using 17 multi-criteria decision-making methods (such as MAIRCA, ELECTRE I, II, etc.). Then, it examined and compared the answers obtained from these methods. Finally, this study evaluated and ranked plastic recycling methods using the combined OPA-MARCOS method, a combination of the OPA for weighting, and the MARCOS method for ranking the alternatives. The innovation of this research is that it combined the OPA and MARCOS methods for the first time and presented a new model. Finally, after solving the OPA-MARCOS model, the second alternative, i.e., mechanical recycling, is selected as the priority alternative. The results suggested that the multi-criteria decision-making methods and weighting methods used in this study can be used for multi-criteria decision-making in other cases.
Keywords: ordinal priority approach; OPA; MARCOS; multi-criteria decision making; MCDM; OPA-MARCOS; plastic recycling.
Steady state analysis of M/G/1 retrial queue with vacation and server timeout using a Petri net formalism
by Lyes Ikhlef, Djamil AÏSSANI, Ouiza Lekadir
Abstract: In this paper, we analyse an M/G/1 retrial queue with vacation and server timeout. When the system is empty, the server waits for a random time. At the expiration of this time, if there is no arrival to the system, the server takes a vacation. If there is at least one customer in the system, the server commences service. So, we propose an unbounded Markov regenerative stochastic Petri net (MRSP N) to model this queueing system. For the qualitative analysis of this model, we combine the Markov regenerative approach and the generating function technique. Finally, numerical illustrations are performed.
Keywords: retrial systems; Markov regenerative stochastic Petri nets; MRSPN; M/G/1; renewal theory; steady state; vacation policy; server timeout.
A Markovian risk model with possible by-claims and dividend barrier
by Sreeshamim P. P., M.J. Jacob, A.S. Dibu
Abstract: A MAP/PH risk model with possible by-claims and a dividend barrier is considered. Along with the main claim, a by-claim also can occur with a certain probability but by-claims are settled only after an inquiry and hence delayed. The model is analysed considering associated Markovian fluid models under the original timeline and an auxiliary timeline. Systems of integro differential equations (IDE) are developed for the Gerber-Shiu function (GSF) and the total dividends paid until ruin. Explicit expressions are obtained for the GSF of the models without and then with the barrier. Expressions are also provided for the moments of the total dividends paid until ruin. A dividends-penalty identity is given. The method is numerically illustrated with a two-phase model and sensitivity analysis of the model is done by varying some of the parameters involved.
Keywords: MAP claim arrivals; phase type claims; by-claims; risk reserve process; dividend barrier; Lundberg equation; Gerber-Shiu function; GSF.
Queuing Models with Customers Impatience: A Survey
by Sapana Sharma, Rakesh Kumar, Bhavneet Singh Soodan, Pradeep Singh
Abstract: Queuing systems with customers impatience are highly applicable in many real life situations, for instance, in grocery stores, banks, hospitals, barber shops, call centres, online shopping, computer-communication networks, etc. The aim of this paper is to give a review of recent results on queuing systems with customers impatience. In this paper, we present a survey and develop a classification scheme of queuing models with customers impatience that includes vacation, feedback, priority service and retention of reneging customers. First, we introduce various queuing models with customers impatience in chronological order. Second, we classify various queuing models with customers impatience. We also provide some tables to illustrate some special features of these systems.
Keywords: queuing models; customers impatience; classification; research; survey.
Cost optimization of a heterogeneous server queueing system with working breakdown using PSO
by Radhika Agarwal, Divya Agarwal, Shweta Upadhyaya
Abstract: Persuaded by the applicability of queueing models the reliability analysis and cost optimisation of MX/M/2 system consisting of heterogeneous servers (Server1 and Server2) is discussed in this article. The Server1 is steady and reliable which leaves for vacation as soon as there is no client available in the system while Server2 is unreliable and may breakdown while giving service to the client. No sooner the server fails, immediately the repair process starts and the server works at a lower speed instead of halting. The schematic diagram of the model gives the overview of the model. The sensitivity analysis is done for validation of the model by taking a numerical illustration and the results are visualised and validated with the help of graphs. Finally, the optimal service rates are obtained using particle swarm optimisation (PSO) technique for matrix method.
Keywords: heterogeneous (two) servers; matrix-geometric method; working breakdown; multiple vacations; cost optimisation; particle swarm optimisation; PSO.
A New Heavy-Tailed Exponentiated Generalized-G Family of Distributions: Properties and Applications
by Gomolemo J. Lekono, Broderick Oluyede, Lesego Gabaitiri
Abstract: In this paper, we introduce a new family of heavy-tailed distributions called the type-I heavy-tailed exponentiated generalised-G (TIHTEG-G) family of distributions. A special model of the proposed family, namely the type-I heavy-tailed exponentiated generalised-log-logistic (TIHTEG-LLoG) model is studied in detail. Statistical properties of the new family of distributions are presented. These include, among others, the hazard rate function, quantile function, moments, distribution of order statistics and R
Keywords: heavy-tailed; exponentiated generalised-G; family of distributions;properties; applications; simulation; actuarial measures.
Uncertain Bottleneck Assignment Problem Using Credibility Theory
by Debapriya Dey Sarkar, Shyamal Kumar Mondal, KAJLA BASU
Abstract: In this paper, two types of generalised bottleneck assignment problem (BGAP) namely task-BGAP and agent-BGAP have been considered with fuzzy costs, capacities and resources. In reality, most of the data are uncertain or vague in nature. The objective of this paper is to formulate and solve a more realistic model under uncertainty. A robust counterpart of these two BGAP models have been constructed using credibility measure theory to solve these optimal mini-max regret problems. Credibility theory helps the actuaries to understand the risk associated with historical data and try to reduce the losses for any organisation. So, by this approach, chance constrained programming (CCP) models have been developed. Finally, the CCP models are solved to get the optimal solution using LINGO software. The method has been illustrated using a real life application of a production factory in Section 5.
Keywords: trapezoidal fuzzy number; bottleneck assignment problem; confidence interval; credibility measure theory; robust optimisation.
Local cone approximations in nonsmooth K-univex multiobjective programming problems
by Tadeusz Antczak, Kalpana Shukla
Abstract: In this paper, we have established some results for a new class of non-smooth multi-objective problems with both inequality and equality constraints are considered. Several definitions of non-smooth (generalised) K-univex functions are gathered in a general scheme by means of the concepts of K-directional derivative and the K-subdifferential. Then, local cone approximations are used to obtain optimality and Mond-Weir duality results for aforesaid non-smooth multi-objective problems with (generalised) K-univex functions. The results established in this paper extend similar results existing in the literature to new classes of non-convex non-differentiable multi-objective programming problems. Some examples are also given for our findings.
Keywords: non-smooth multi-objective programming; K-subdifferential; local cone approximations; K-directional derivative; K-univex function.
APPROXIMATELY OPTIMUM STRATA BOUNDARIES UNDER SUPER POPULATION MODEL
by Faizan Danish, S.E.H. Rizvi
Abstract: In the present investigation, a methodology has been developed under super population model for obtaining approximately optimum strata boundaries (AOSB) on highly related variable with the variable under consideration which is applicable for the situation having more than one study variables with product estimator. Minimal equations have been obtained under certain assumptions by minimizing the generalized Variance expressions. Under this complex nature we developed Cum?(R_5 (x)) Rule or obtaining the AOSB. Empirical studies have also been made on certain density functions, which showed remarkable gain in precision.
Keywords: Product estimator; Super population; Optimum strata boundaries; Optimum stratification.
A SINGLE SERVER MARKOVIAN DIFFERENTIATED WORKING VACATION QUEUE WITH SERVER BREAKDOWN
by V. Suvitha, Kalyanaraman R, V. Karthick
Abstract: A single server Markovian queue with server breakdown has been considered here. In addition, the server goes on two types vacation namely type-I and type-II. Type-I vacation is taken after busy period of non-zero duration and type-II vacation is happen, at the completion of type-I vacation when there is no customers in the system, where both type-I and type-II vacations are working vacations. Also in type-I vacation the server may breakdown and immediately the repair takes place. We analysed as a quasi-birth-and-death (QBD) process, using the matrix geometric method, the steady state probability vector of the number of people in the queue and the stability conditions are produced. There are some system performance measures found. The effects of various parameters on the system performance measures are illustrated numerically.
Keywords: single server; differentiated vacation; breakdown; repair; QBD process.
Risk analysis on Product quality improvement and supply chain performance for return contract with warranty
by Shirsendu Nandi
Abstract: Products which require after sales services and associated with a warranty clause often pass through a series of quality checks and quality control measures. Improvement of quality of the product is an ongoing exercise and the manufacturer and the channel coordinator are expected to explore the impact of any initiative for quality improvement on the profitability and performance of the supply chain. It is important to carry out a risk benefit analysis before undertaking such quality improvement initiatives since it requires major financial investment. It is necessary to redesign the contract parameters after successful implementation of any quality improvement programme. The paper analyses the impact of the quality improvement initiative upon the profitability of the supply chain and describes how to redesign the contract parameters when return contracts are practised. It also does a risk analysis of the parties and the entire supply chain when return contract is practised along with warranty. It examines how change in order quantity and warranty length impacts supply chain risk as measured by variance of profit.
Keywords: warranty; quality; risk analysis; supply chain contract; return contracts; supply chain performance; redesign; supply chain risk.
Optimal order quantity and credit period for a time-dependent deteriorated green item under two-level trade credit with reminder cost: A new approach
by Gautam Kumar, Sukhendu Bera, GURUPRASAD SAMANTA, Manoranjan Maiti
Abstract: Nowadays, people prefer to buy green products. In the present competitive market, the wholesalers and retailers offer trade credit to their downstream customers. Against retailers offers, some customers become defaulters. In rural India, money landers engage some people to remind the defaulters for payment. Following this idea, we introduce reminder costs in trade-credited systems to reduce default risk, though this system negatively affects the demand. Along with the conventional, a new approach for a two-level trade-credited EOQ model with a time-dependent deteriorated green item is presented, allowing default risk and reminder cost and solved by using the generalised reduced gradient method through LINGO 19.0. The new approach gives better results than the conventional ones, and in both approaches, the introduction of reminder cost gives more profit. The nature of profit and its dissection concerning decision variables are presented. Some managerial decisions are derived.
Keywords: inventory; two-level trade credit; deterioration; default risk; reminder cost; new approach.
AN EOQ INVENTORY POLICY VARYING WITH EXPONENTIAL- CONSTANT-EXPONETIAL DEMAND AND SHORTAGES
by Itishree Rout, Trailokyanath Singh, A.K. Nayak
Abstract: In real market situations, it is often seen that the demands of the most of the seasonal commodities run through three different phases, e.g., growth, steady and decline. The demand and the deterioration are taken as exponential-constant-exponential functions of time and constant, respectively. The model is divided into three policies according to the occurrence of the shortages period. The main purpose of the present paper is to investigate the effect of exponential-constant-exponential demand with seasonal commodities within the economic order quantity (EOQ) framework. Shortages as well as complete backlogged demand have been taken into consideration. A simple analytical procedure is presented to compute the optimal solutions of each policy. The model is well-explained with the help of three numerical examples. Finally, sensitivity analyses of all examples have also been performed to study the effectiveness of several system parameters on optimal solutions.
Keywords: backlogging; deterioration; economic order quantity; EOQ; exponential-constant-exponential type; replenishment.
New Population-Based Simple Algorithms for Solving Global Optimization Problems
by BASKAR AMALADOSAN, M. Arunachalam Sai Balaji, Jitendra Kumar Katiyar, Bharti Nagpal, J. Rajesh Babu
Abstract: Heuristic algorithms have effectively been used for solving global optimization problems in a continuous space. It can be applied to both constrained and unconstrained problems. Presently, several population-based algorithms were proposed by researchers and available in the literature but those are not enough to solve the issues. Therefore, this study has proposed five new populations base simple algorithms that do not require any tuning parameter. A different strategy was used for updating the solution set. Unlike other algorithms, the solution set is constructed using three or four expressions to ensure effective search and move towards the optimal/ near-optimal solution. Each expression is used to build the population partially and the best one is selected for the next iteration. Further, it is compared with the recent popular Arithmetic Optimization Algorithm (AOA) using different benchmark functions. The dimensions are varied from 2 to 1000. Five real-world problems with constraints are also analyzed.
Keywords: Population-Based; Benchmark Function; Arithmetic Optimization Algorithm; Trigonometric Algorithm; Constrained Optimization; Unconstrained Optimization.
The Topp-Leone Harris-G Family of Distributions with Applications
by Broderick Oluyede, Neo Dingalo, Fastel Chipepa
Abstract: In this paper, we present the Topp-Leone Harris-G (TL-Harris-G) family of distributions. Some special cases, such as Topp-Leone Harris-Log-Logistic (TL-Harris-LLog), Topp-Leone Harris-Uniform (TL-Harris-U) and Topp-Leone Harris-Weibull (TL-Harris-W) distributions are given. We examine some structural properties, such as moments, generating function, distribution of order statistics, entropy, and probability weighted moments (PWMs) of the new family of distributions. The maximum likelihood estimation method is used to estimate model parameters. To illustrate the consistency and efficiency of parameter estimations, simulations are run, and real-world data sets are used to demonstrate the applicability of the proposed model. The proposed model proves to be a better alternative to some well known models.
Keywords: Harris Distribution; Topp-Leone Distribution; Maximum Likelihood Estimation; Simulation Study; Goodness-of-fit Statistics.
A BACKORDER INVENTORY MODEL CONSIDERING PRICE-SENSITIVE AND STOCK-DEPENDENT DEMAND
by Dharma Lesmono, Taufik Limansyah, Ignatius A. Sandy
Abstract: In the inventory management system, time and quantity are crucial factors to be considered in relation to inventory costs. Demand is another external factor that influences the availability of goods for customers. In fact, demand varies from time to time, being dependent on price, time, stock or other relevant factors. The dynamics of this condition can be described by developing a mathematical model. In this paper, we develop a backorder inventory model considering price-sensitive and stock-dependent demand. From the model, we determine the cycle length and the time when the inventory drops to zero as decision variables in order to minimize the total inventory cost. Based on the sensitivity analysis, we found that generally speaking, changes in certain parameter values will substantial affect the decision variables of the model. Having this information at their disposal, retailers can determine which specific parameters should be managed in order to minimize the total inventory cost.
Keywords: inventory; price- and stock-dependent demand; backorder.
Optimal Server Analysis of M/M/c Queueing Model to Reduce the Waiting Time of Patients in Healthcare Service
by Preethi Sowndharya Kumar, Ebenesar Anna Bagyam J
Abstract: Queueing system is a mathematical design known to be theory of overcrowding. Healthcare organization is one of the applications for queueing theory. This paper provides about the healthcare setting at the Arathana ortho local hospital at Pollachi. The proposed queuing model has used the multi-server system with a first come, first server queue discipline. The arrival rate follows Poisson distribution and service rate follows an exponential distribution. The actual data were collected in the ortho hospital and examined using the windows based TORA optimization technique. Performance measures and optimal number of server were found. The result shows that the optimal server to serve the patients and also to reduce the waiting time of patients. The technique is manageable to utilize in the hospital.
Keywords: service cost; Patients waiting time cost; optimal server level,Service time.
Mean Time to Failure Modeling and Sensitivity Analysis of Mixed Standby Serial Systems
by Ibrahim Yusuf, Muhammad Sagir Aliyu, Mus'abu Musa
Abstract: Abstract: In this article, we investigate and compares the mean time to failure (MTTF) of series-parallel systems. This paper considers four different configurations with each having exponential failure and repair time. Each configuration consisting of the main, warm and cold standby units. A cold standby unit is included in Configuration 1 together with two warm standby units. Two cold standby units and one warm standby unit make up Configuration 2. In configuration number three, there are four primary units, two warm standby units, and one cold standby unit. The configuration 4 consists of six primary units, one warm standby unit, and two cold standby units. First order linear differential difference equations are used to produce a mathematical formula for mean time to failure (MTTF) for each configuration, which is then verified through analytical and numerical testing. Through the analytical and ranking experiment, Configuration 1 is found to be optimal.
Keywords: Keywords: Mean time to failure; mixed standby; redundancy; series-parallel.
Decision-Making Analysis for a new variant of the classical Secretary Problem
by Y.U. WU
Abstract: In this paper, a new variant of the classic secretary problem is studied, in which the interviewer has a look-ahead privilege to observe partial future candidates before making a decision each time. Different from the classic problem, a decision can be deferred till some subsequent candidates are interviewed in this variant. We define the degree of look-ahead privilege on one candidate as how many candidates are sequentially interviewed from when this candidate is interviewed to when its decision is made. We first propose a general optimal decision strategy framework that can maximize the probability of successfully selecting the best candidate. Then, focusing on one specially structured look-ahead privilege, we apply the proposed strategy framework and obtain the probability of success in a closed function, to which an explicit solution will give the concrete optimal strategy; and further, through computational experiments, we study relationships between related parameters.
Keywords: Secretary Problem; Look-ahead Privilege; Optimal Strategy.
Statistical-based Multi-Criteria Decision Making Approach for prediction of the grade of an Institution in NAAC.
by SUKARNA D.E.Y. MONDAL, Dipendra Nath Ghosh, Pabitra Kumar Dey
Abstract: In the modern era, innumerable colleges and universities have been established in India but sometimes quality education is not imparted by the authority of colleges/universities. It has been a major challenge for the Indian government to assess the quality education in India. Through a well-versed assessment procedure, National Assessment and Accreditation Council (NAAC) was established to assist higher education institutions in identifying their assets, strengths, and weaknesses. In this paper, an innovative mathematical model is proposed to calculate and justify the NAAC grading of a well-known Engineering College while taking into consideration the NAAC grading of nine other well-known affiliated colleges/autonomous colleges/universities. This model is making a prediction based on the data obtained from SSR (Self Study Report) of them after DVV (Data Validation and Verification) and the result of the model is found very accurate while comparing the overall NAAC grade of the college given by NAAC.
Keywords: NAAC Grade; MCDM techniques; ANOVA test; P-test; Combined MCDM techniques; and Linear Regression method.
Comparative study of purchasing EOQ model for time-sensitive holding cost under different demand with and without deterioration
by Rakesh Tripathi
Abstract: This paper investigates the effects of carrying cost, deterioration and different demand rates on the optimal control system. We proposed three EOQ models to compare over the cycle time in which carrying cost is linearly time dependent. Three models are considered. In the first model demand rate is stock -sensitive, while in the second model constant deterioration is included in addition to model one. In the third model constant deterioration and exponential demand rate is taken in to account. The total inventory cost in inventory systems is modeled. The optimal solution is derived for proposed models. The planned model is demonstrated with numerical examples and sensitivity analysis is detailed for finding decision-making insights. Based on the optimal solution some important theorems are obtained. Finally, comparisons of three proposed models are discussed. Mathematica 7.0, software is used to find the numerical outcomes.
Keywords: Inventory; stock-linked demand; exponential; deterioration; lot-size.
Multi-objective perishable multi-item green inventory models with uncertain finite time horizons and constraints by neutrosophic optimization approach
by Chaitali Kar, Manoranjan De, Manoranjan Maiti, Pritha Das
Abstract: The business period of seasonal products, such as mango, broccoli, etc. is finite over the years due to their availability, which is again uncertain for seasonal variations. According to FAO, about 40% of Indias fruits and vegetables perish before reaching consumers. Due to global warming, firms have incorporated carbon management into business decisions. The resources in business are always limited and uncertain. Considering these facts, multi-objective perishable multi-product EOQ models with stock-dependent demand are formulated under crisp, uncertain (fuzzy, random, rough and neutrosophic) time horizons and constraints. The objective is to maximise total profit while minimising wastage costs and carbon emissions. Proposed models are solved using neutrosophic optimisation approach. The multi-objective problems are transformed into single ones using the weighted-sum method and solved through GRG (LINGO 11.0) method. Models are illustrated with numerical examples, and some sensitivity analyses are presented. A trade-off between profit and carbon emission is depicted.
Keywords: inventory; seasonal products; uncertain time horizon; carbon emission; neutrosophic optimisation.
Aspiration level-based non-dominated sorting genetic algorithm- II & III for multi-objective shortest path problem in trapezoidal environment
by Aniket Todkar, Jayesh Dhodiya
Abstract: The present article provides aspiration level (AL)-based non-dominated sorting genetic algorithm (NSGA)-II and AL-based NSGA-III utilising an exponential membership function (EMF) with possibility distribution to tackle fuzzy multi-objective shortest path problem (FMOSPP). In this study, fuzzy judgement for trapezoidal fuzzy number is classified for the decision maker (DM) to optimise fuzzy objective function scenarios like optimistic, most likely lower, most likely upper, and pessimistic at the same time, utilising ?-level sets. A numerical demonstration and a dataset have been offered to portray the application of the recommended methodologies. This study suggests that AL-based NSGA-II and AL-based NSGA-III can handle FMOSPP effectively and efficiently with optimal outputs. These methods provide solutions as per DMs AL. Thus it is very effective to manage real-world multi-objective shortest path problems (MOSPPs).
Keywords: multi-objective shortest path problem; MOSPP; aspiration level; exponential membership function; EMF; ?-level set; trapezoidal fuzzy number; genetic algorithm.
Dependability Prediction of a Hybrid Multi Client Computer Networking System Using Gumbel-Hougaard Family Copula
by Abdul Kareem Lado, Abubakar Bawa Zarogi, Nura Jibrin Fagge
Abstract: This paper presents a Markov model of a computer networking system. It consists of four subsystems: z client, router, load balancer, and two distributed data based servers. They are arranged in a series-parallel configuration and integrated with a switch. The paper research objectives include evaluating the system for various dependability metrics and to see the effect of the repairs. Unit failure is presumed to be continuous and follows exponential distribution, and two repairs are available: general repair addresses partially failed states while copula repair addresses the system failure. The derived equations are studied utilising supplementary variables techniques and Laplace conversion procedures in order to obtain dependability metrics expressions such as reliability, availability, MTTF, sensitivity, and costs. The results were justified using numerical examples and presented in Tables and Figures. It was observed that copula repair produces better outcomes than general repair and therefore recommended for optimal performance of the system.
Keywords: availability; reliability; cost implication; computer networking; system.
A hybrid modified cuckoo search algorithm for the uncapacitated examination timetabling
by Cheraitia Meryem, Rewayda Razaq Abo Alsabeh
Abstract: In this study, we investigate the effectiveness of cuckoo search algorithm (CSA) for solving the uncapacitated examination timetabling problem (UETTP). CSA is a popular metaheuristic optimisation algorithm that mimics the behaviour of cuckoos. Compared with other nature-inspired algorithms, it is more generic and robust for many optimisation problems. The CSA is easy to understand and implement. Furthermore, it represents a powerful search method with few controllable parameters and can be combined with additional strategies to increase effectiveness. We proposed a modified version of CSA. Moreover, a local search strategy is utilised to reinforce the CSA and improve the exploitation phase to develop and provide high-quality solutions. Extensive experiments were conducted using Carter benchmark datasets consisting of 12 instances selected from several real-world universities. The obtained results confirm that the hybrid modified CSA outperforms the basic CSA and it has comparable performance in comparison with other algorithms proposed in the literature.
Keywords: examination timetabling; metaheuristic; cuckoo search algorithm; CSA; simulated annealing.