Forthcoming and Online First Articles

International Journal of Mathematical Modelling and Numerical Optimisation

International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO)

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International Journal of Mathematical Modelling and Numerical Optimisation (9 papers in press)

Regular Issues

    by Kheira MOSTEFA HANCHOUR, Boubakeur BENAHMED 
    Abstract: We are interested in solving numerically an optimal control problem governed by advection-diffusion equation with state inequality constraints. This problem can be implemented to modelise the minimisation of air pollution. First the infinite dimensional problem is discretised by application of the upwind symmetric interior penalty galerkin (SIPG) method. Then, we write the optimality conditions for the discretised problem. We reformulate these conditions into an equivalent system of nonlinear and non-smooth equations by the use of the Fischer-Burmeister function. Then, two effective algorithms that combine the non-smooth Newton’s method and an active (index) set technique or pseudo inverse method are applied to solve this system. At the end, numerical examples are presented to illustrate the performance of our methods.
    Keywords: PDE-constrained optimisation; advection-diffusion equation; Fisher-Burmeister function; non-smooth Newton’s method; active index set method; Pseudo inverse of a matrix; saddle point system.
    DOI: 10.1504/IJMMNO.2023.10050794
  • An Investigation on MX/G/1 Queuing Model of Interrupted Services in the Manufacturing of Edible Cutlery Process   Order a copy of this article
    by Vignesh Perumal, S. Srinivasan, S. Maragathasundari, S. Kishore Eswar 
    Abstract: We are investigating queuing issues that happen during the cutlery production process’ hour in this study. Plastic is widely used all around the world as it is simple to manufacture and inexpensive to purchase. Banana leaves are commonly used to wrap food in hotels. Plastic is widely used to replace banana leaves since it is affordable and lightweight. Research on Biodegradability of Plastics did not success. Hence, researchers set out to design alternative hardwood cups and spoons for food and beverage applications. A lengthy step-by-step process is required to create this edible millet cutlery. This process is converted into a scientific queuing model and solved with supplementary variable queuing technology. For the defined queue study, the probability generating function for queue size and all other performance measures are determined. In order to validate the model at the conclusion, the conceptual study of queue theory in the creation of edible cutlery is depicted through a numerical and complex visual analysis.
    Keywords: stochastic model; manufacturing of edible cutleries; millets usage; supplementary variable technique; service interruption; delay; phases of service and queue performance measures.
    DOI: 10.1504/IJMMNO.2023.10050913
  • Tribological Behaviour of Al6061/Gr/WC Hybrid MMC’s using Multi-Response Optimization   Order a copy of this article
    by A. Ganagadhar Rao, Ravi Kumar Mandava, Pandu Ranga Vundavilli 
    Abstract: The current investigation is motivated to examine the improvement in mechanical properties and tribological behavior of Al6061/Gr/WC. Initially, the mechanical and tribological properties were evaluated after adding the reinforcement that is, graphite (Gr) at 3, 6, 9 and 12 wt% compositions. Therefore, 9wt.% of Gr generated superior properties than others. Consequently, the hybrid composites were fabricated by reinforcing tungsten carbide (WC) at 1, 2, 3wt.% and Gr at 9wt.%. The variables such as the % of WC, applying load, sliding velocity and sliding distance are treated as inputs, and the WL and COF are considered as responses. Later on, a nature inspired optimization algorithm that is, Invasive Weed Optimization (IWO) was implemented to determine the optimal wear properties and the results were compared with the Particle Swarm Optimization (PSO) and Gray Relational Analysis (GRA) approaches and with that of the experimental results.
    Keywords: Wear loss; coefficient of friction; IW; PSO; GRA.
    DOI: 10.1504/IJMMNO.2023.10051643
  • Analysis and simulation of SIR model for COVID-19 spreading with the effect of offline learning and vaccination: a case study of Indonesia   Order a copy of this article
    by Syafruddin Side, Nasiah Badwi, Nurlina Sjahrir, Muhammad Isbar Pratama, Muhammad Rifandi, Suwardi Annas 
    Abstract: This research discusses the analysis and simulation of SIR model for COVID-19 spreading with regards to the effect of offline learning and vaccination. The results of the analysis shows that the COVID-19 case in Indonesia is at a stable stage. The SIR model was chosen because it is one of the basic methods in the epidemiological model like COVID-19. The simulation results shows that if offline learning is not enforced but 99% of the students are vaccinated, the rate of spread of COVID-19 slows down and the rate of recovery has increased in just five months. The results also shown that if 50% offline learning is carried out, the basic reproduction number is R0 = 3.3715, which means that a student infected with COVID-19 can infect 11 other people and if 99% offline learning is carried out, the basic reproduction number is obtained R0 = 6.6757, which means that a student infected with COVID-19 can infect 22 other people in Indonesia.
    Keywords: COVID-19 mathematical model; SIR model; offline learning effect; vaccination effect; Indonesia.
    DOI: 10.1504/IJMMNO.2023.10048684
  • Mathematical modelling of breakdowns with soft failures and explicit analytical expressions of an M/M/1 queue's transient state probabilities   Order a copy of this article
    by B. Janani 
    Abstract: In the last decade, the increasing usage of digital electronics and software has given rise to a new form of failure occurrence known as soft failure. Soft failure is not the same as catastrophic failure. Catastrophic failure removes all waiting customers, including those receiving service, and the system enters the repair state, whereas soft failure does not require the removal of customers and instead requires the customer to wait for the server reactivation because repair can be accomplished by simply rebooting the system. A new approach for categorising and analysing these events is necessary to characterise and distinguish soft failures from hardware catastrophic failures. As a result, this paper considers a single server queueing model with soft failure. The system is prone to random breakdowns while providing service to the customer. When a system malfunctions, repair work begins right away. During the repair period, new customers are not permitted to join the system. For the first time, the transient state probabilities of an M/M/1 queue with soft failures are computed explicitly. Some performance metrics, such as availability and reliability, are derived. Numerical examples are also provided to demonstrate the effect of parameters.
    Keywords: random breakdown; soft failure; hard failure; time dependent probabilities; Laplace transform; generating function.
    DOI: 10.1504/IJMMNO.2023.10048480
  • Enhanced estimation of population mean under two-phase sampling   Order a copy of this article
    by Shashi Bhushan, Anoop Kumar 
    Abstract: This study investigates an enhanced estimation procedure for the estimation of the population mean of the study variable by using the information on an auxiliary attribute under two-phase sampling. The suggested class of estimator incorporates several well-established estimators for suitably chosen values of characterising scalars. The properties such as bias and mean square error of suggested estimator are studied to the first order of approximation. The efficiency conditions are derived by comparing the MSE of the suggested class of estimator with the MSE of the existing estimators. The efficiency conditions are enhanced by an empirical study using some real datasets. The empirical findings are clearly demonstrating the ascendancy of the suggested class of estimator over all of the works discussed.
    Keywords: auxiliary attribute; bias; mean square error; MSE; efficiency; two-phase sampling.
    DOI: 10.1504/IJMMNO.2023.10048394
  • An application of spectral linearisation method on the steady two-dimensional radial flow of Au-water and Ag-water nanofluids between two inclined plane walls   Order a copy of this article
    by Upendar Mendu 
    Abstract: The present work purveys the steady two-dimensional viscous incompressible radial flow of Au-water and Ag-water nanofluids between plane walls which either converge or diverge in the presence of MHD effect. A uniform magnetic field is applied. The governing partial differential equations of the present physics and their appropriate boundary conditions are initially cast into the dimensionless forms to reduce into the ordinary differential equation. The resulting equation thus formed is then solved by adopting the spectral linearisation method (SLM) to get the accurate numerical solution. Solution errors and residual norms were analysed to elaborate the convergence and accuracy of the numerical solution. The present results are validated with favourable comparisons to previously published results due to the current investigations' unique cases. Parametric study of the governing parameters, namely the magnetic field strength parameter M, Reynolds number Re, angle of inclination α, and the volume fraction parameter ɸ on the non-dimensional velocity is conducted. The analysis discloses that the profiles of the flow are largely impacted by the physical parameters.
    Keywords: Jeffery-Hammel flow; Au-water nanofluid; Ag-water nanofluid; MHD; spectral linearisation method; SLM.
    DOI: 10.1504/IJMMNO.2023.10050789
  • Numerical solution of Lane-Emden pantograph delay differential equation: stability and convergence analysis   Order a copy of this article
    by Nikhil Sriwastav, Amit K. Barnwal 
    Abstract: In this work, a collocation approach-based Bernstein operational matrix of differentiation method is used for obtaining the numerical solution of a class of modified Lane-Emden equation with delay in pantograph sense. The proposed numerical algorithm provides numerical solution by discretising the Lane-Emden pantograph delay differential equation into a system of algebraic equations which can be solved directly using any mathematical software. The consistency of the proposed numerical technique is verified with the convergence analysis of the proposed algorithm. The stability analysis of the model is also given using the Lyapunov function. Test examples and graphical representations of their solutions are included to illustrate the applicability and superiority of the proposed method over existing methods.
    Keywords: Lane-Emden equation; pantograph delay differential equation; PDDE; Bernstein polynomials; collocation method; convergence analysis.
    DOI: 10.1504/IJMMNO.2023.10049441
  • Multi-level multi-objective linear fractional programming problem: a solution approach   Order a copy of this article
    by Suvasis Nayak, Sujit Maharana, Rashmi Ranjan Ota 
    Abstract: In this paper, a multi-level multi-objective linear fractional programming problem (ML-MOLFPP) which arises in hierarchical organisations is solved by two proposed methods based on goal programming approach and certain linear functions. These methods deal with two different situations of cooperative and non-cooperative DMs respectively. Each level comprises several objectives as fraction of affine functions. All the numerator and denominator functions belonging to a certain level are combined to construct two new functions using their relative best and worst values. It implements the concept to maintain farthest distance from the worst values so as to be at a shortest distance from the best values or vice-versa. Goal programming approach using reduction of under deviations from the aspiration level generates the best compromise solution of the whole problem. Two illustrative numerical examples including a comparison with an existing method are presented to demonstrate the proposed methods.
    Keywords: multi-level programming; multi-objective optimisation; goal programming; linear fractional programming.
    DOI: 10.1504/IJMMNO.2023.10049623