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International Journal of Mathematics in Operational Research
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International Journal of Mathematics in Operational Research (77 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.
Fuzzy Information Inequalities and Application in Pattern Recognition
by Sapna Gahlot, Ram Naresh Saraswat
Abstract: In mathematics, an inequality is a relation that compares two numbers or other mathematical expressions in a non-equal way. Inequalities play an important role in finding relationships and solving real-life problems. Although there are many fuzzy inequalities exist in the literature, which are unable to provide solutions for specific cases. The prime objective of this paper is to establish new fuzzy information inequalities under Jensens inequality and Csiszars f-fuzzy divergence measure. Proposed a new fuzzy relative information of type k and its cases. Using proposed fuzzy inequalities, obtained some new bounds of well-known fuzzy information divergence measures in terms of fuzzy chi-square measure, fuzzy Kullback-Leibler measure and fuzzy Hellinger measure. The direct applications of proposed fuzzy inequalities in pattern recognition discussed in this paper. Fuzzy information inequalities also play a important role in medical diagnosis, decision making, etc. and can be extended to Chebyshevs inequality, holders inequality, and so on, and by this we can solve any other real-life related issues. It is a more convenient and reliable method than others.
Keywords: fuzzy set; fuzzy f-measures; inequalities; pattern recognition.
A Simple and Efficient Method to Solve Fully Interval and Fuzzy Transportation Problems
by B.S.S. PRABHAVATI, V. RAVINDRANATH
Abstract: One of the prime goals of an organisation is to establish good transportation and supply chain network to optimise the delivery costs. In practice network parameters are often expressed in either intervals or fuzzy numbers which are difficult to deal with the classical methods. In this paper, we have proposed modified minimum supply demand method to solve interval transportation problem and extended it to fully fuzzy transportation problems (FTP), where the supply, demand and the transportation cost parameters are either triangle or trapezoidal fuzzy numbers. The interval solution for the FTP has been proved to lie within the interval range of the corresponding optimum fuzzy solution. If the parameters are either triangle or trapezoidal fuzzy numbers, our solution coincides with the optimal solution and the method is demonstrated with a numerical example of logistics problem in the field of pharmaceutics.
Keywords: interval transportation problem; ITP; fuzzy transportation problem; FTP; optimum interval solution; minimum supply demand; trapezoidal fuzzy number; triangular fuzzy number.
Optimization on a constrained integrated supply chain for multiple steel products with investment and freight cost discount
by Tharani S, R. Uthayakumar
Abstract: This paper intends to help the reader to understand a new inventory control model for steel products. This model introduces a steel marketing supply chain between a manufacturer and a merchant with multiple steel products. The purpose of this work is to influence a price discount on backorder for the merchant, ordering cost reduction and setup cost reduction, proceeding with the cogitation of discount on freight cost. We hold the freight cost to be a function of the orders quantity, and it is to be in the format of all-unit-discount costs. We thus assimilate freight costs into the system comprehensively and straightforwardly and have worked out the optimal solution procedures for working with the posed inventory model. A numerical example and sensitivity analyses are also carried out to demonstrate the studys implementations and performances.
Keywords: multiple steel products; investment; price discount; freight cost.
An EOQ Model for Deteriorating Item with Continuous Linear Time Dependent Demand with Trade of Credit and Replenishment Time being Demand Dependent
by Asim K. Das, Prokash Mondal, Tapan Kumar Roy
Abstract: This study is about an inventory model with continuous linear time dependent demand rate with constant rate of deterioration in the consideration of partial backorder including delay in payment and time period is demand dependent. Demand is the fundamental attribute for consideration of inventory related problem. In reality, there is some inter connection of demand function among various time interval for which the demand cannot change drastically at some critical point during the appearance of another state of system. Thus, it is quite natural that the demand function should be continuous in nature in inventory management problem. So, here the most prominent part of our present study is the consideration of time dependent continuous demand in the proposed model. A supportive numerical example of the proposed model is illustrated for insightful investigation. The solution method and sensitivity analysis has also been presented.
Keywords: inventory; deterioration; delay in payment; trade credit period; backlog dependent.
Hesitant Fuzzy sets with non-uniform Linguistic Terms: An application in Multi-Attribute Decision Making
by Eshika Aggarwal, Bhaba Krishna Mohanty
Abstract: The paper introduces a novel methodology for solving multi-attribute decision-making problems under hesitant fuzzy linguistic environment. It includes non-uniform, non-regular, or arbitrarily defined linguistic terms in hesitant fuzzy linguistic term set. The proposed methodology takes both normal and non-normal fuzzy numbers to represent linguistic terms in HFLTS. The combined approach of the concept of existence in ranking of fuzzy sets, ?-cuts of fuzzy numbers, and ordering relations for hesitant fuzzy sets is used to value each alternative numerically. Binary integer programming is used to verify the consistency level of pairwise comparison matrix conforming to specified linguistic preferences as per the decision makers expressions. The pairwise comparison matrices are aggregated over attributes to obtain the aggregated pairwise comparison matrix. The derived aggregated matrix calculates dominance/non-dominance levels of alternatives and selects best alternative. The proposed method is demonstrated with a numerical example, compared with similar methods and the advantages are highlighted.
Keywords: non-uniform linguistic term set; hesitant fuzzy linguistic term set; fuzzy number comparison; binary integer programming; aggregated pairwise comparison matrix; dominance degree.
New efficient class of estimators of population mean using two-phase sampling
by Shashi Bhushan, Anoop Kumar
Abstract: This manuscript proffers a new efficient class of estimators for population mean in two-phase sampling using the known population proportion. The usual mean estimator, classical ratio estimator, Singh (2011) estimator and log type estimator are identified as the members of the proposed class of estimators for suitably chosen values of characterising scalars. The expression of mean square error of the proffered estimators is obtained to the first order of approximation. A comparative study is accomplished concerning the relevant contemporary estimators existing till date. Further, an empirical study is carried out using different real datasets. The empirical results are turned out to be rewarding showing better amelioration over all the existing prominent estimators.
Keywords: bias; efficiency; mean square error; two-phase sampling.
Simulation of Batch Service Lateness Queues with Multiple Vacations and Two Bernoulli Catastrophes using the developed "goLHS" generator
by Anfal REZGUI, Hafida SAGGOU, Megdouda Ourbih-Tari, Meriem BOUBALOU
Abstract: This paper considers a new model of a single server queue subject to two different Bernoulli catastrophes with service lateness which represents the control duration and the service duration where both are in batches of fixed size K. We assume that catastrophes can occur when the server is in service or when it is on vacation. This proposed model is then solved using the appropriate generating functions, which gives steady state probabilities and some performance measures. Numerical results are sketched out to illustrate the effect of the system parameters on the main performance measures. To manage the proposed model with large batches, a Monte Carlo simulation is performed. For this purpose, a Latin hypercube sampling (LHS) generator called
Keywords: batch service; Bernoulli catastrophe; multiple vacations; service lateness; Monte Carlo simulation; Latin hypercube sampling; LHS.
A Production Inventory Model for Non-Instantaneous Deteriorating Items with Two-Phase Production Period, Stock-Dependent Demand and Shortages
by Mustapha Lawal Malumfashi, Majid Khan Majahar Ali
Abstract: In this paper, a production inventory model for non-instantaneous deteriorating items with two-phase production periods are developed. The production rates of the two different production periods differ while the demand within such periods are the same and constant. Also, the demand within the demanding period before deterioration starts is assumed to be stock-dependent while that of within deterioration and shortage periods are constant. Shortages are allowed and completely backlogged. A theorem and lemmas were framed to characterise the optimality of the model developed and a numerical experiment is conducted to show the applicability of the model. Finally, sensitivity analysis is carried out to demonstrate the effects of change of some system parameters on the optimal solutions obtained during the numerical experiment and some suggestions and recommendations are presented based on the results obtained.
Keywords: economic production quantity; EPQ; cycle length; stock-dependent demand; holding cost; delayed deterioration; shortages; backlogged.
Component Sourcing Under Disruption Risk
by Ping Su, Xiangling Hu, Jaideep Motwani
Abstract: This paper considers the components sourcing problem for a manufacturer that makes a product consisting of two key components under supply disruption risks. Most of operations management papers focus on the sourcing decision of one component. However, many products are made of multiple components and the shortage of one component affects the production of the final product. In our model, the manufacturer has the option to source each component from one of the two suppliers at different costs. Both suppliers face supply disruption risks. One of the components is also available on the spot market at a higher cost. We provide the complete characterisation of conditions under which one sourcing strategy outperforms another strategy. We summarise the conditions for each of the four sourcing strategies to be optimal. We also study the impact of the key parameters such as selling price, sourcing costs, spot market price, disruption risks and supplier setup cost on the optimal sourcing strategy.
Keywords: multiple-component sourcing; supply disruption risks; dual sourcing; spot market.
A Continuous Five-step Implicit Block Unification Method for Numerical Solution of Second-Order Elliptic Partial Differential Equations (PDEs)
by Emmanuel O. Adeyefa, Ezekiel Omole
Abstract: A continuous implicit block unification method (CIBUM) is developed through the interpolation and collocation approach using Hermite polynomial as the basis function. The method is chosen within the interval of step-number of five. The basis function was interpolated at the first two consecutive points while the collocation was done at all the points within the interval of integration. The discrete scheme and their corresponding first derivative were combined to form the five-step implicit block unification method (FIBUM) of order six. The FIBUM is applied to solve second-order elliptic partial differential equations via the method of lines by transforming the PDEs into ODEs. The basic properties of FIBUM were investigated and found to be convergence and p-stable. The method was implemented on five test problems varying from linear, nonlinear, and nonlinear Klein-Gordon differential equations, and the results were presented. The results established the accuracy of the FIBUM over the existing ones.
Keywords: implicit block unification method; method of lines; second-order elliptic PDEs; convergence; hermite polynomial; initial and boundary value problems; nonlinear Klein-Gordon differential equations.
System reliability analysis based on Pythagorean fuzzy set
by Mintu Kumar, S.B. Singh, Deepak Kumar
Abstract: Generally, fuzzy sets and intuitionistic fuzzy sets are utilised to examine the system reliability, however, in this work the concept of intuitionistic fuzzy set (IFS) is extended in the form of Pythagorean fuzzy set (PFS). The current research is focused on the study of the reliability indices of some systems under the fuzzy environment using a Pythagorean fuzzy exponential distribution. Expressions for fuzzy hazard function, fuzzy reliability, fuzzy mean time to failure and their ?-cut set along with the sensitivity have been determined when the considered systems follow the aforesaid distribution. At the end, numerical illustrations have been discussed to appraise the reliability characteristics of the systems using the proposed environment. This approach is very useful in various application areas like information measures, decision making, and aggregation operators.
Keywords: Pythagorean fuzzy set; mean time to failure; hazard function; exponential distribution; fuzzy reliability.
An Optimization Model of Drug Order Quantity and Distribution Using Continuous Review Approach by Considering Secondary Suppliers
by Benedicta Amadea Karina Dewi, Cucuk Nur Rosyidi, Azizah Aisyati
Abstract: Drug shortages and inefficiencies in drug supply delivery are caused by poor drug purchase and distribution management in the hospital supply chain. A shortage occurs when a product is not available in sufficient numbers to satisfy demand. This research presents a mixed-integer linear programming model with the objective function to minimise the total costs comprising purchase costs, storage costs, distribution costs, and penalty costs due to shortages. The existence of secondary suppliers is considered in this research to overcome drug shortages. Purchases through a secondary supplier will occur if the primary supplier is unable to meet the hospitals demand. The model focuses on the decision-making of determining the number and drugs in each purchase and their distribution to each care unit. The hospital uses a continuous review inventory policy. Moreover, a numerical example is provided to show the applicability of the model using a real case study in a teaching hospital. The optimal solution was found using Lingo 18.0 software. Finally, sensitivity analysis is conducted by changing several parameters values to determine their effects on the objective function and the decision variables.
Keywords: optimisation model; MILP; ordering and distribution models; continuous review; primary suppliers; secondary suppliers.
WEBSITE SELECTION FOR ONLINE SHOPPING BY MULTI-CRITERIA DECISION ANALYSIS USING SYMMETRIC HENDECAGONAL FUZZY NUMBER
by Revathi Muthu, Valliathal M
Abstract: Fuzzy decision-making offers comprehensive resources that can tackle with uncertainty in different categories of decision-making problems that can be developed for best website selection. The main intention of this research is to propose a website evaluation model using fuzzy multi-criteria group decision-making (FMCGDM) method. The opinions of the experts are recorded by linguistic terms that can be conveyed in a new generalised structure of the fuzzy number named symmetric hendecagonal fuzzy number (SymmHDFN). On this basis, the evaluation model is suggested and implemented for four major online shopping websites with alternatives, and the influential criteria that control online shopping are taken into account. Simple additive weighting (SAW) procedure is applied to evaluate the websites in this study. A ranking system based on the centroid procedure is extended to SymmHDFN and implemented on the websites being considered.
Keywords: symmetric hendecagonal fuzzy number; SymmHDFN; fuzzy decision-making; centroid method; simple additive weighting; SAW; ranking fuzzy numbers.
Weight Computation of Criteria in a Decision Making Problem by Entropy Measure Under Interval-Valued Fuzzy Environment
by Satyajit Das, Amrita De
Abstract: In general, weights of criteria play an important role in decision-making scenarios where criteria are conflicting in nature and how to measure the weights of these criteria is an interesting research issue. This work proposes an objective weight generation method for determining importance of criteria in a real-life multi-criteria decision-making problem where information are expressed as interval-valued fuzzy sets. We use entropy measure as a tool to determine criteria weights because entropy measure is a significant measure in information science. We develop a weight computation method on the basis of entropy measure to determine the criteria weights. Here we consider the information related to criteria weights which are completely unknown and partly known. For illustrating the proposed weight determination method a real-life example is presented. Finally, a comparative study is carried out to validate the result.
Keywords: interval-valued fuzzy set; intuitionistic fuzzy set; multi-criteria decision-making problem; positive ideal solution; negative ideal solution; entropy.
Study on Fuzzy Inventory Model for Deteriorating Items with Recurring Seasonal Demand Pattern
by Sanju Kumar, Ravish Kumar Yadav, Aashish Singh
Abstract: In this study, a fuzzy inventory model has been developed for deteriorating items with recurring seasonal demand pattern and ramp type growth in demand season-by-season which varies with time. It is well known, there is a lot of complexity in the market and hence cost components cannot be calculated precisely. Therefore, to handle this impreciseness, a triangular fuzzy number is assigned for different cost components and defuzzified by using signed distance method. We optimised the total cost function which depends on the time length of the planning period. Proposed model has been illustrated by numerical examples. Sensitivity analysis has also been carried out on variation of different parameters.
Keywords: fuzzy inventory; recurring seasonal demand pattern; deterioration; triangular fuzzy number; signed distance method.
Analysis on a non-Markovian batch arrival queuing model with Phases of service and multi vacations in Cloud computing services
by Radha S, S. Maragathasundari, C. Swedheetha
Abstract: We investigate a new variant of the MX / G / 1 queue model with three levels of service and a single server in this study. Arrival and service follows Poisson and general distribution correspondingly. The initial phase of service includes two types of service. Following that, the server provides the second level of service. During the service period, service interruption is unavoidable. This system also assumes that an interruption will occur during the second phase of service. As a result, it enters the repair process without delay. In addition, a vacation concept is introduced in this queuing system to carry out server maintenance work. A pre-processing work is performed in the setup time stage prior to the vacation stages .This model includes additional parameters such as Reneging, Setup time. Performance measures are derived and the model is justified by application of cloud computing services.
Keywords: Supplementary variable technique; ; Multi Vacations ; Stages of service; Standby server and Reneging.
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.
Analysis of MAP_1^I,PH_2^O/PH_1^I,PH_2^O/1 Retrial Queue with Two Way Communication, Optional Service, Single Vacation, Closedown, Setup and Balking.
by AYYAPPAN Govindan, Archana Gurulakshmi, SOMASUNDARAM B
Abstract: A single server constant retrial queueing model with close down, vacation, setup, optional service and balking are studied in this article. There are two kinds of arrivals, namely incoming and outgoing calls. If the server is idle, arriving incoming calls will be served instantly. After completion of the service, the server becomes idle. The server goes on vacation, while the system is void. Before taking the vacation server will closedown the system and after completion of the vacation, the server will set up the system to give the service. The server will give optional service for incoming calls if the customer needs. The incoming calls follow the Markovian arrival process (MAP) and outgoing calls and service times follow PH-type distribution. We derived the busy period analysis and cost analysis. Also, some important performance measures are obtained which are illustrated graphically/numerically.
Keywords: retrial queues; two way communication; vacation; closedown; setup; optional service; balking.
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.
Reliability and performance analysis of a series- parallel Photovoltaic system with Human operators Using Gumbel Hougaard family copula
by Anas Maihulla, Ibrahim Yusuf, Saminu I. Bala
Abstract: This study offers a complete technique for evaluating the reliability efficiency of medium grid-connected photovoltaic (PV) power systems with two out of three PV panels, one out of two charge controller, two out of two batteries and one out of two inverters. State enumeration is used to examine real-world grid-connected PV systems. A set of reliability indices is defined to assess the dependability performance of PV systems. The systems dependability and availability were analysed and visually shown, as were the sensitivity parameters. The Gumbel-Haugaard family copula approach is used to create and solve Chapmen-Kolmogorov differential equations. There include numerical numbers for availability, reliability, mean time to failure (MTTF), cost analysis, and sensitivity analysis. The implications of failure rates on different solar photovoltaic subsystems were studied. To demonstrate the acquired results and to assess the influence of various system characteristics, numerical examples are provided. The current study may help companies and their repairers overcome some of the problems that repairers of specific manufacturing and industrial systems confront.
Keywords: sensitivity; subsystems; reliability; charge controller; availability.
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.
Integrated Centralized Routing Mechanism for optimizing total travel time
by Seyed Omid Hasanpour Jesri, Mohsen Akbarpour Shirazi
Abstract: Online vehicle routing is a fascinating and challenging topic in terms of research and functionality. Current approaches to routing generally suffer from two major problems which this paper attempts to resolve. Firstly, current approaches to routing primarily aim at user optimality, which does not lead to total system optimality. In this paper, we have presented the integrated centralised routing mechanism (ICRM), a holistic model that minimises the total travel time of all users via the central traffic control centre (CTCC), as a way to mitigate this problem. Gathering the origin and destination of all vehicles and the flow rates of all routes, the system calculates the optimum routes for all vehicles and directions thereof. The second problem has to do with the effects of the ongoing origin-destination (OD) demands on routing; current approaches show little regard for future demands while it strongly affects travel time. In our proposed model, future OD demands are considered as one of the main inputs of the system. The numerical test points to a significant improvement in total time travel in our proposed model vis-
Keywords: integrated centralised routing mechanism; ICRM; system optimality; traffic management; urban planning; optimisation.
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.
Analysis of Non-Markovian Batch Service Queue with Second Optional Service under Transient and Steady State Domain
by Vijaya Laxmi Pikkala, Andwilile Abrahamu George
Abstract: This paper analyses the transient and steady state behaviour of a non-Markovian batch service queue with second optional service. The transient state probabilities are computed using the probability generating function, Rouches theorem, and Laplace transform (L.T.) methods. The Tauberian property in the L.T. expressions is used to get steady state probabilities. Also, we obtain various performance measures along with cost optimisation and numerical results are presented by taking special cases of the service times. The results show the standard observation that the Erlang-k type distribution reduces to an exponential distribution when k = 1 and when k takes a large value, it becomes deterministic.
Keywords: non-Markovian; transient and steady state analysis; batch service queue; first essential service; second optional service.
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.
An Optimisation Model for Lecturer-Committee Assignment Problem: A Case Study
by Nurul Izzati Sydina, Aida Mauziah Benjamin, Norazura Ahmad, Ditdit Nugeraha Utama
Abstract: This study focuses on the lecturer-committee assignment problem at the School of Quantitative Sciences (SQS), Universiti Utara Malaysia (UUM). In SQS, committees are established to support the school in achieving the UUM key performance indicators (KPIs). Therefore, each committee requires several lecturers to organise activities within their job specifications. Currently, lecturers are assigned manually to the committees by the SQS management team. There is no systematic approach to assign the lecturers to the committees. This may cause a lack of interest of the lecturers in their commitments and take a longer time for the whole process to complete. This study develops an Integer Programming (IP) model to assign the lecturers to committees by considering the lecturers and management teams preferences to overcome these drawbacks. The optimal solution of the IP model provides a higher total preference weight than the current practice with an increment of 19.91%, reflecting a better solution.
Keywords: assignment problem; integer programming; optimal solution; education.
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.
Parametric approach for a class of fractional variational programs involving support functions
by Navdeep Kailey, Sonali ., Vikas Sharma
Abstract: In this paper, a pair of nondifferentiable second-order multiobjective symmetrical dual fractional variational programs over arbitrary cones is constructed. We have introduced the concept of second-order $(F,alpha,rho,d)$-pseudoconvexity and an example of a function which is second-order $(F,alpha,rho,d)$-pseudoconvex but not second-order $F$-pseudoconvex has been constructed. Further, to relate the objective function value of primal and dual we proved weak, strong and converse duality theorems under second-order $(F,alpha,rho,d)$-pseudoconvexity suppositions. Moreover to validate the results of the weak duality theorem an example of multiobjective variational fractional problem and its dual model has been constructed. Several known results are also discussed as special cases.
Keywords: fractional programming; second order duality; variational problems; support functions; multiobjective programming; weak duality; strong duality; converse duality; $(F,alpha,rho,d)$ pseudoconvexity.
Pricing strategy of competing retailers in a two layer supply chain model under non-linear stochastic demand
by Totan Garai, Arpita Paul, Dipankar Chakraborty
Abstract: This paper extent a strategic issue of closed-loop supply chain (SC) in a two-echelon SC comprising of manufacturer and competing retailers under stochastic non-linear demand. The manufacturer works as the supplier. The retailers compete with each other on the basis of their retail price. The objective is to investigate a news-vendor model to govern the optimal order quantity. There is a buyback contract between the manufacturer and retailer. The scenario of shortage is also considered. The profit functions of two retailers and one manufacturer are analysed by the proposed centralized approach. To validate of the of the theoretical results, we have illustrated a numerical example. The computational results of this paper always shows that the benefit of the members of SC in integrated system.
Keywords: Pricing; News vendor; Stochastic non-linear demand; Supply chain management.
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.
New hybrid method for direct numerical solution of nonlinear second, third and fourth orders ordinary differential equations
by Olusola Ezekiel Abolarin, Bamikole Gbenga Ogunware
Abstract: A novel and efficient algorithm for the concurrent numerical solution of second, third and fourth orders of ordinary differential equations is studied in this article. Collocation and interpolation technique was employed in the derivation of the method and power series approximate solution was used as the interpolating polynomial. The fourth derivative of the power series was collocated at the entire grid and off-grid points, while the fifth and sixth derivatives of the polynomial were collocated at the endpoint only. Proper investigation of the basic properties of the method was done. The results showed that the new block method applied on a nonlinear second, third and fourth orders of ordinary differential equations were better in terms of accuracy than the existing methods. The proposed method takes away the burden of developing a separate method for the solution of second, third and fourth order initial value problem of ordinary differential equations.
Keywords: hybrid block method; collocation; higher order ODEs; interpolation; power series.
Primal-dual method for a linear program with hybrid direction
by Rima Guerbane, Mohand Ouamer Bibi
Abstract: In linear programming, the combination of primal and dual methods is of great importance in the search of efficient resolution algorithms. In the present paper, we are interested to the adaptive method with hybrid direction for the linear programs with bounded variables. After calculating the increment of the dual function with this hybrid direction, an optimality criterion for the dual problem is proved. Using this criterion and the initial speed of change for the dual function, a primal-dual algorithm with hybrid direction is suggested for solving linear programs with bounded variables. In this algorithm, the suboptimality estimate is used as a stopping criterion. A numerical example is presented and to compare the suggested method with three other methods, we have developed an implementation under the MATLAB programming language on randomly generated problems with precision ε ≥ 0, chosen in advance.
Keywords: linear programming; duality; hybrid direction; optimality criteria; primal-dual algorithm; numerical results.
Searls estimation strategy for population mean of a sensitive study variable harnessing non-sensitive auxiliary information
by S.K. Yadav, Amit Kumar Misra, Tarushree Bari
Abstract: In this study, we present a Searls type regression estimator for elevated estimation of the population mean of a sensitive study variable in the presence of a known non-sensitive supplementary variable under the simple random sampling scheme. The first order of approximation is used to obtain the bias and mean square error expressions. The suggested family of estimators is compared to competing estimators both theoretically and numerically. The findings verified through the real and simulated data show that the suggested estimator is preferably chosen over many of the existing competing estimators.
Keywords: sensitive variable; scrambled variable; Searls type estimator; response bias; mean square error; MSE; simulation study.
Effect of disaster and balking on M/M/1 driven fluid queue with working vacation
by Madhu Jain, Anshul Kumar
Abstract: The fluid models are suitable for modelling traffic when individual arrival units have little effect on the system's performance. This paper aims to study the fluid model for the queueing scenario driven by the features of vacationing server, disaster, and balking. By introducing vacation strategy to the fluid model, we can provide greater flexibility for the design and control of input and output rates. By introducing the multiple working vacation strategy to the fluid model, we can provide greater flexibility to design and control the server's vacationing time and output. Continuing fraction and generating function methodologies are used to solve the fundamental framework of differential-difference equations that regulates the operation. The steady state probabilities for the different states of the fluid model have been found explicitly. The stationary distribution of the buffer content has also been derived in terms of the modified Bessel function of the first kind.
Keywords: fluid queue; working vacation; disaster; balking; generating function; continued fraction.
Optimal control of an epidemic by vaccination using dynamic programming approach
by Bouremani Touffik, Benterki Djamel, Slimani Yacine
Abstract: In this paper, we are interested in solving a SIR epidemic model which can be reformulated as a control problem. We use some recent developments of the dynamics programming method to obtain a rigorous solution of the optimal control problem formulated in Trélat (2019). We use some refinement of Cauchy's method of characteristics for stratified Hamilton-Jacobi equations to describe a large set of admissible trajectories and identify a domain on which the value function exists and is generated by some admissible controlsm, and their optimality is justified by using one of the well-known verification theorems as an argument for sufficient optimality conditions.
Keywords: optimal control; differential inclusion; Pontryagin's maximum principle; dynamic programming; Hamiltonian flow; value function; verification theorem.
Numerical optimisation technique to solve imprecisely defined nonlinear system of equations with bounded parameters
by Sukanta Nayak, J. Pooja
Abstract: This paper includes an optimisation algorithm to estimate the solution of interval nonlinear system of equations. First, the proposed optimisation algorithm converts interval nonlinear system of equations to unconstrained multivariable optimisation problem with interval uncertainties. Then the interval unconstrained multivariable optimisation problem is investigated by using inner-outer direct search approach. Finally, the obtained solutions are assembled and using the regularity principle, interval solutions are obtained. Considering these steps together, this method is named as inner outer direct search (IODS) algorithm for interval unconstrained multivariable optimisation. Example problems are investigated to demonstrate the IODS algorithm and compared the obtained results with the results by using Krawczyk, vertex and Newton's methods.
Keywords: uncertainty; interval nonlinear system of equations; unconstrained multi-variable optimisation; inner-outer direct search; uncertain width.
Third derivative method for solving stiff system of ordinary differential equations
by Lawrence Osa Adoghe, Ezekiel Olaoluwa Omole, Sunday Emmanuel Fadugba
Abstract: A continuous integration method based on the hybrid third derivative block method is constructed and used to generate solution for stiff systems of first order ordinary differential equations. The hybrid third derivative method are applied simultaneously to integrate stiff initial value problems by combining them into a single block matrix known as block hybrid third derivative method. The basic properties of block method were examined and were found to be zero-stable, consistence, convergence and A-stable. Some numerical results produced by the block method show that it is competitive with some existing ones in the literature. The results and comparison are presented in tables and curves.
Keywords: first order system of equations; ordinary differential equations; hybrid third-derivative; block method; stiff problems; A-stability; zero-stability; convergences.