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International Journal of Mathematics in Operational Research

International Journal of Mathematics in Operational Research (IJMOR)

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International Journal of Mathematics in Operational Research (60 papers in press)

Regular Issues

  • Detection Model for a Suitable Waiting List with Maximizing the Discount Effort Reward Search Under the Quality Control Process   Order a copy of this article
    by Mohamed El-hadidy 
    Abstract: The economic benefits of the company are increased by improving the quality of its services. At the same time, the customers aimed to get the service with minimum cost. In this paper, we provide a detection model which satisfies these purposes. The customer chooses the suitable engineering consultancy company from independent companies. Each company has a Markovian waiting list of customers with size N. The customer arrives to the waiting list with Poisson process and its service time has an exponential distribution. Under the quality control process and some concepts like balking and reneging of each waiting list, we provide the optimal decision to consider the suitable company. We consider the searching effort is bounded by a random variable with a known probability distribution. After applying the discount effort reward search function, we solve a difficult stochastic optimisation problem to get the maximum values of the service rate, discount effort reward and the minimum value of the detection cost. A case study is provided to get these optimal values and the optimum performance measures which give the optimal expected profit.
    Keywords: detection model; services quality; waiting list; performance measures; decision-making; maximum discount effort reward.
    DOI: 10.1504/IJMOR.2021.10039787
  • A Hybrid Fuzzy Stochastic Model for Fractional Multi-commodity Network Flow Problems   Order a copy of this article
    by Salim Bavandi, Seyed Hadi Nasseri 
    Abstract: In this paper, we aim to introduce a class of multi-commodity network flow problems. Here, we deal with a multi-commodity flow problem with a fractional objective function that is investigated in a fuzzy random hybrid environment. This paper aims to provide a model that manages unknown coefficients in fractional multi-commodity networks. In this problem, the coefficients of the objective function in the numerator of the fraction and the arc capacity are assumed to be fuzzy random variables and the coefficients of the objective function in the denominator of the fraction are assumed to be fuzzy variables. Since this problem is investigated simultaneously in both random and fuzzy environments, we use a probability-possibility approach to convert the problem to a deterministic form. Next, we get the problem out of the fractional mode using the variable transformation method and finally, examine the efficiency of the proposed method by providing some numerical examples.
    Keywords: fractional programming; fuzzy random variable; multi-commodity flow problem; probability-possibility approach; decision making under uncertainty.
    DOI: 10.1504/IJMOR.2021.10039999
  • Optimizing fully interval integer two-stage transportation problems   Order a copy of this article
    by A. Akilbasha, Natarajan G 
    Abstract: The study proposes a novel technique namely, divided-united method which is framed based on the zero point method in order to optimise the fully interval integer two-stage transportation problem (FIITSTP). The proposed method offers more than one optimal solution to fully interval integer two-stage transportation problems. The optimal values of decision variables and the objective function of the fully interval integer two-stage transportation problems provided by the proposed method are interval integers. A numerical example is illustrated for a better understanding of the solution procedure of the proposed method. Since the proposed method offers more than one optimal solution therefore it is highly helpful for the decision makers when they are handling logistic models of real life situations involving interval integer parameters. Further, this method is likely to determine the perfect and effective optimal solution for fully interval integer transportation problems in a simple manner.
    Keywords: two-stage transportation problem; optimal solution; interval integers; divided-united method.
    DOI: 10.1504/IJMOR.2021.10040215
  • The New Family of Ristic-Balakhrishnan Marshall Olkin-G Distributions with Properties and Applications   Order a copy of this article
    by Peter O. Peter, Broderick Oluyede, Nkumbuludzi Ndwapi, Onkabetse Mabikwa, Huybrechts F. Bindele 
    Abstract: In this paper, we develop and study in detail a new family of distributions called Risti ´ c — Balakhrishnan Marshall Olkin-G (RBMO-G) distribution. We obtain some mathematical and statistical properties of this distribution such as hazard and reverse hazard functions, quantile function, moments and incomplete moments, moment generating functions, R´ enyi entropy and order statistics. The model parameters are obtained through method of maximum likelihood. We finally illustrate the usefulness of this family of distributions via simulation experiments. Furthermore, we apply a special case of this family of distributions to some real data to assess and compare its performance with other non-nested models.
    Keywords: Ristic-Balakhrishnan; Marshall-Olkin; distributions; moments; maximum likelihood; simulations.
    DOI: 10.1504/IJMOR.2021.10040443
  • An Optional Arrival Process of the Oscillatory Demands in the Inventory System with Queue Dependent Service Rate   Order a copy of this article
    by Jeganathan Kathirvel, Selvakumar Subramanian 
    Abstract: In this paper, we study a classical retrial queueing-inventory system (CRQIS) with an optional arrival process of an oscillatory customer (OC) who may enter into the waiting hall or an infinite orbit directly under Bernoulli trials. The orbital customer emulates their requirements through the waiting hall only over the classical retrial policy (ClRP) whenever it is less than its capacity and the service rate of customer depends on the queue length at an epoch. This system contains a perishing item, too, and replenishment can be done following the (s, Q) ordering policy. The server can do an orbital search which follows Bernoulli process. Neuts approach is applied for the matrix-geometric approximation (MGA) to find a stationary probability vector and the Laplace-Stieltjes transform method (LSTM) is used to derive waiting time of both arrivals. Also, sufficient numerical problems are to be explored for the assumed model.
    Keywords: optional arrival process; oscillatory customer; queue dependent service rate; QDSR; classical retrial policy; waiting time.
    DOI: 10.1504/IJMOR.2021.10040594
  • Neutrosophy based transportation problem and its solution approach.   Order a copy of this article
    by Tuhin Bera, N.K. Mahapatra 
    Abstract: This study designs a transportation problem (T p-problem) by taking the transportation cost, availabilities, demands and quantity of goods to be transported as single valued trapezoidal neutrosophic number (svtn-number). Then experts can include their hesitancy in decision making independently in uncertain climate. The proposed form of T p-problem is solved in four distinct methods and, optimality test of their initial outcomes are performed. The respective algorithms are developed with the help of existing crisp notions. A parameter-based linear ranking function of svtn-number is drawn here in order to that. This parameter of ranking function helps to incorporate the relevant characters involved indirectly in a T p-problem beside the provided constraints in its solution approach. The way of treatment of uncertainty and the incorporation of relevant character in a T p-problem designed here make its outcome more realistic and acceptable to the experts. The efficiencies of proposed concepts are tested in real ground. The optimal values are analyzed to opt the better method applicable for that problem.
    Keywords: single valued trapezoidal neutrosophic number; svtn-number; ranking of svtn-numbers; neutrosophy-based transportation problem; N t-problem.
    DOI: 10.1504/IJMOR.2021.10040595
  • A MAP/PH1, PH2/1 system with two types of heterogeneous service, setup, closedown, vacation, immediate feedback, breakdown and repair   Order a copy of this article
    Abstract: In this article, we examine a classical queueing model with single unreliable server who can offer two types of heterogeneous services namely, types I and II. Customers reach the system by following the Markovian arrival process (MAP). The service times of both types of services are considered to be phase-type (PH) distributed. We have considered a service clock which begins at the commencement of the service after the setup/repair process and immediate feedback for the unsatisfied customers. If the service clock expires, the server will start the closedown process and consequently goes on vacation. The assumptions of our model have greater significance on small scale industries. By utilising the matrix-analytic method, we have examined our model and investigated the active period and the waiting time distribution of our model. We have also carried out the cost analysis for our model. To the end, some numerical and graphical exemplifications are presented for clear insight into our model.
    Keywords: PH distribution; Markovian arrival process; MAP; two types of services; vacation; service clock; setup; closedown; immediate feedback.
    DOI: 10.1504/IJMOR.2021.10040826
  • Inventory Policies for Monotonic Change in the Purchase Price   Order a copy of this article
    by Suresha Kharvi, T.P.M. Pakkala 
    Abstract: This article considers an optimal inventory policy for monotonic change in the purchase price where price change depends on the number of orders made. The planning horizon is considered as finite and yearly demand is assumed to be constant and known. A closed-form solution is obtained for the optimal order lengths. These closed-form solutions will be very useful to business managers. An algorithm is given to determine the optimal number of orders during the planning horizon. Some of the interesting properties of the optimal order quantities are discussed. A numerical example and sensitivity analysis are carried out to support the theoretical results.
    Keywords: inventory; monotonic price change; optimal policy; optimal cost; optimal order lengths.
    DOI: 10.1504/IJMOR.2021.10040827
  • Develop an optimization model for relief facility location in disaster   Order a copy of this article
    by Amirmasoud Soltanzadeh, Vahid Baradaran, Faezeh Soltanzadeh 
    Abstract: This research was conducted to study the issue of relief facility location hierarchically by consideration of possible road closure during the disaster, road safety, and arrival time of relief facility under disaster circumstances. A multi-objective model was developed to minimise the pre-disaster and pro-disaster costs. The main contribution of this study is road safety and reduction in time taken to have a critical facility in affected areas. To investigate the functional accuracy of the mathematical model, a numerical example with small dimensions was solved using CPLEX solver, and required sensitivity analysis was described. As the facility location-allocation is an NP-hard issue, three metaheuristic algorithms were used to solve numerical representations in real dimensions to examine numerical analyses effectively. Results showed that the grey wolf algorithm had the highest efficiency compared to other developed algorithms. The obtained results can be used as an efficient managerial tool in management organisations involved in the disaster.
    Keywords: hierarchical location; disaster management; multi-objective optimisation model; metaheuristic algorithms.
    DOI: 10.1504/IJMOR.2021.10040858
  • A Simulation Approach to Modified Searls Estimation of Population Mean under Two-Phase Random Sampling   Order a copy of this article
    by S.K. Yadav, Dinesh K. Sharma, Madhulika Dube 
    Abstract: A new extended Searls type estimator is suggested in this paper to assess the population mean of an essential variable more efficiently. The suggested estimator utilises a known supplementary variable in a two-phase (double sampling) design for improved estimation. The bias and mean squared error (MSE) of the introduced estimator are retained to approximate degree one for studying the sampling distribution properties. The Searls constants’ optimal values that provide minimum MSE of the novel introduced estimator have also been acquired. The MSE of the introduced estimator was compared with the MSEs of other estimators in competition under double sampling, and the conditions of efficiency are obtained. The efficiency conditions obtained in theoretical comparison for the proposed estimator are verified using four natural data sets. A simulation study has also been performed using the natural populations’ parameters to see the results’ consistency.
    Keywords: main variable; Searls type estimator; auxiliary variable; bias; mean squared error; MSE; percentage relative efficiency; PRE.
    DOI: 10.1504/IJMOR.2021.10040901
  • A Sustainable Inventory Model for Setup and Ordering Cost Reduction under a Controllable Lead Time   Order a copy of this article
    by Malleeswaran Balasubramani, R. Uthayakumar 
    Abstract: In this study, we consider an integrated vendor-buyer supply chain (SC) model. This paper investigates the impact of setup and ordering cost reduction in a continuous review inventory policy with controllable lead time. The probability distribution is the most aspect of this model, within free distribution, including as mean and standard deviation. We obtain the annual minimum cost by considering setup and ordering cost reductions. The solution procedure is used to determine the optimal solutions of order quantity, setup cost, ordering cost, lead time, and the number of shipments from the single vendor (SV)-single buyer (SB) in one production run. This model has vital perspectives to present a venture by considering with and without distribution under a controllable lead time.
    Keywords: supply chain management; SCM; logarithmic investment; integrated approach; probability distribution; controllable lead time.
    DOI: 10.1504/IJMOR.2021.10041084
  • A Robust Global Optimization Framework for Stochastic Integrated Refinery Planning with Demand and Price Uncertainties   Order a copy of this article
    by Mahmud Siamizade, Theodore Trafalis 
    Abstract: This study presents a global optimisation framework for the strategic planning of an integrated oil refinery while accounting for the uncertainties in the crude oil and final product demand and market prices. To model the uncertainties, three modelling schemes have been utilised: 1) a robust optimisation framework; 2) a fuzzy possibilistic programming approach; 3) a risk aversion two-stage stochastic model with financial risk management. These methodologies are applied to an industrial case study, comprising an integrated oil refinery with tasks spanning from unloading crude oil at the refinery’s front to distributing refined products to distribution centres by pipelines. The notable feature of this study is developing an optimisation approach with a multi-period mixed-integer nonlinear programming (MINLP) model and solving it through an aggregation/disaggregation linearisation algorithm and obtaining ?-global optimal solutions. The results indicate significant economical and operational advantage of the robust optimisation scheme depending on the decision maker’s risk attitude.
    Keywords: integrated refinery planning; global optimisation algorithms; uncertainty appraisal; robust programming; fuzzy possibilistic programming; stochastic programming; financial risk management.
    DOI: 10.1504/IJMOR.2021.10041135
    by André G. Medeiros, Leandro Resendo 
    Abstract: In this work, mathematical models were developed to maximise oil production in offshore petroleum fields. Wells considered can be equipped with continuous gas-lift, electrical submersible pumps and naturally flowing, and connected by manifold or satellite. Platforms’ fluid processing capacity and operational condition were considered as well. Two nonlinear models were developed: one model that considered the pipeline network as a fixed parameter, analysing the system configuration; and another that allows the assignment of wells to manifolds, analysing production improvement with network changes. Using piecewise linearisation for multidimensional functions, four mixed-integer linear formulations were proposed. Two-variable functions were linearised using the diagonal method and triangle method and three-variable functions were linearised using plane method. Using a real scenario, there were investigated the piecewise refinement, computational complexity, and solutions error. Results shown the models applicability for daily adjustments and indicates the necessity of new investments in pipeline connections.
    Keywords: mixed integer linear programming; MILP; offshore oilfield; linearisation; diagonal method; triangle method; plane method; production optimisation.
    DOI: 10.1504/IJMOR.2021.10041209
  • Modeling time-series process of an agricultural crop production process by EWMA quality control chart   Order a copy of this article
    by Zeina Mohammed  
    Abstract: Control charts are considered to be one of the main tools for analysing and controlling the steps of a product chain process. This research emphasises the control charts’ versatility not only in manufacturing but in taking enough actions for maintaining the quality of the crops with more flexibility. The time-series quality proceedings for crops that utilised the statistical process control (SPC) method serve as a case study in the EWMA control chart. One week of 168 hours of observation data is analysed with a sampling time of one hour. These measurements have been investigated over three models; AR, MA, and ARMA. The results of plotting EWMA for autoregressive (AR), moving average (MA), and ARMA models included eight points at which the process is out of control. It is found that a higher order of AR or MA model shows a lower out-of-control process. This satisfies the concluded point that higher order of the ARMA model means lower out-of-control process points.
    Keywords: statistical process control; SPC; control chart; EWMA; AR; MA; ARMA.
    DOI: 10.1504/IJMOR.2021.10041381
  • The problem of resource leveling in multi-project mode by Cuckoo Optimization Algorithm   Order a copy of this article
    by Elham Shadkam 
    Abstract: Project resource levelling is very important and project managers need a schedule based on the optimal use of resources needed to complete their projects. Most resource levelling research has been done in a single project, while in many organisations several projects are done simultaneously. For this purpose, a mathematical model with the aim of minimising the level of change in various resources of consumption by all projects is presented in this paper. The cuckoo optimisation algorithm has been used for this model, which is one of the newest and most efficient evolutionary optimisation algorithms. The obtained results by solving the problem with the cuckoo optimisation algorithm and comparing it with the exact approach indicate that the exact approach is more appropriate in low dimensions and as the dimensions of the problem increase, the cuckoo optimisation algorithm solves the problem faster and in less elapsed time with the same accuracy. Therefore, this algorithm is more suitable for large-scale problems that are close to the real world problem.
    Keywords: resource levelling problem; cuckoo optimisation algorithm; COA; multi-project control; meta-heuristic algorithms; multi-resources.
    DOI: 10.1504/IJMOR.2021.10041537
  • A Revisit of the Proposed Model for Solving Fuzzy Linear Fractional Programming Problem   Order a copy of this article
    by Nemat Taghi-Nezhad 
    Abstract: Linear fractional programming (LFP) problem is used worldwide in solving real world problems. In real life situations the parameters of the problem are imprecise instead of fixed real numbers. So, a procedure for modelling these impreciseness in mathematical form is required. Fuzzy set theory is a best tool to deal with such situations. In this paper LFP problem with fuzzy parameters are studied. A fuzzy linear fractional programming (FLFP) problem is considered by Das et al. (2018) where a simple ranking approach between two triangular fuzzy numbers is provided. Then, in their study a tri-objective LFP problem is formulated to calculate the upper, middle and the lower bounds of the fuzzy optimal value. There are some errors and shortcomings in Das et al. method. Hence, in this study errors and shortcomings of Das et al. method are pointed out. Also, to overcome these errors, a simple method is presented to obtain optimal solution and fuzzy optimal value of the objective function. Moreover, by solving some numerical examples these errors are demonstrated and using the new proposed algorithm the correct optimal solution and the fuzzy optimal value of objective function are obtained.
    Keywords: linear fractional programing problem; fuzzy number; fuzzy linear fractional programing problem; fuzzy optimal value.
    DOI: 10.1504/IJMOR.2021.10041791
  • Modeling and Performance Evaluation in the (R, s,lnQ) Inventory System   Order a copy of this article
    by Nedjma Aiane, Fazia RAHMOUNE, Djamil Aissani 
    Abstract: In this work, we propose to analyse a periodic review inventory model with an (R, s, lnQ) policy and an instant replenishment via a discrete Markov chain approach. Then, we adopt the strong stability method to evaluate the characteristics of the considered model in the case of the perturbation of some of its parameters (demand rate and demand law). Thus, we find the approximation bounds of the stationary distribution, with an exact computation of the constants, to evaluate the error generated by this approximation. Finally, we study numerically the effect of the perturbation of the arrival rate and the demand law respectively on the average stock and the total cost of the considered inventory model. Several numerical examples have been performed to illustrate the performance of this approach
    Keywords: inventory control; (R; s; lnQ) policy; Markov chains; transition Kernel; strong stability; stability inequalities; stationary distributions; relative error; the error on the average stock; total cost.
    DOI: 10.1504/IJMOR.2021.10042002
  • Multi-queue system with finite shared buffer under Batch Poisson and/or Interrupted Batch Poisson arrivals: a computational analysis   Order a copy of this article
    by Miron Vinarskiy 
    Abstract: This paper studies a model of a multi-queue system with a finite common buffer shared by queues with batch arrivals. The study is performed for a few buffer sharing policies. For batch Poisson arrivals with an arbitrary batch size distribution, the analysis benefits from the fact that the stationary state distribution has a product form. For the special case of geometrically distributed batches, closed form solutions for normalisation constant are obtained. They lead to efficient computational procedures. For bursty interrupted batch Poisson arrivals, it is shown that an exact numerical analytic analysis is only possible for very small models. For real-life sized systems, an approximation method has been developed.
    Keywords: queuing; multi-queue; batch arrivals; finite buffer; losses.
    DOI: 10.1504/IJMOR.2021.10042132
  • Neuro-fuzzy Computing and Optimization Results for Batch Discrete time Retrial Queue   Order a copy of this article
    by Shweta Upadhyaya, Geetika Malik, Richa Sharma 
    Abstract: The present investigation involves the application of discrete time bulk entrance recurrent queuing model on asynchronous transfer mode (ATM) technology. This analysis includes the concept of Bernoulli feedback along with priority and impatient customers wherein server may undergo starting failure. Once a service is accomplished, the service provider/server either waits for succeeding customer or leave for a vacation of random time span. The service period, vacation period and retrial period all are presumed to follow general distribution. Firstly, we calculate necessary performance indices using generating function method. Thereafter, we approximate all calculated results with the help of adaptive neuro-fuzzy interface system (ANFIS). Furthermore, we discuss how this model can solve issues related to traffic management and control in ATM networks. Lastly, to make the system more economical, we have computationally analysed the model via particle swarm optimisation (PSO) and genetic algorithm (GA) techniques.
    Keywords: batch arrival; Bernoulli vacation; starting failure; ATM network; adaptive neuro-fuzzy interface system; ANFIS; cost optimisation.
    DOI: 10.1504/IJMOR.2021.10042136
  • New Hybrid Method for Direct Numerical Solution of Nonlinear Second, Third and Fourth Orders Ordinary Differential Equations   Order a copy of this article
    by Olusola E. 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.
    DOI: 10.1504/IJMOR.2021.10042183
  • ANFIS computing and analysis of cost optimization by upgrading service rate with N-policy, server vacation in M/M/1 model   Order a copy of this article
    by Anamika Jain, Komal Shekhawat, Bhoopendra Pachauri 
    Abstract: This study investigates an M/M/1/? model that emphasises the effect of various system parameters on the cost factor, with respect to upgraded service rates when the system follows N-policy and server vacation. Most often, the reason for customer dissatisfaction is the annoyingly protracted wait for the service. Therefore, given the customer’s total satisfaction with the service, an upgradation in service rates is required. As a result, this study investigates the effect of different parameters on cost factors by considering the upgraded service rates, which help in better decision making. The well-known QBD process of the Markov chain is analysed using a matrix-geometric approach, and the steady-state probabilities are also observed. The system will continue in a working vacation state until the N threshold value is applied, as it follows N-policy. The adaptive neuro-fuzzy inference system (ANFIS) is utilised to approximate the nonlinear function.
    Keywords: optimisation; balking; working vacation; matrix-geometric method; N-policy.
    DOI: 10.1504/IJMOR.2021.10042236
    by Rallabandi L. N. Pradeep Kumar, V. RAVINDRANATH 
    Abstract: In analytic hierarchy process (AHP), pairwise comparison matrix (PCM) is used to rank the alternatives in the decision-making problem. The priority vector, derived from the PCM, is accepted only when the PCM is consistent. However, in many practical situations the PCM obtained by the judgments of expert may be inconsistent. Several indices have been proposed to measure the consistency level of PCM over the years and one among them is cosine consistency index (CCI). In this paper, an algorithm is proposed to improve the consistency of PCM in terms of CCI. For examining the consistency of the given PCM, the new threshold values for CCI are proposed. Correlation and regression analysis is used to derive the relation between CCI and consistency ratio (CR) from which the threshold values of CCI for PCMs of order 3 to 15 are determined. The derived regression models have been validated by using statistical techniques.
    Keywords: cosine consistency index; CCI; pairwise comparison matrix; PCM; consistency ratio; analytic hierarchy process; AHP.
    DOI: 10.1504/IJMOR.2021.10042367
  • A Multi-Item Sustainable Production Inventory Constrained Model to Study and Analyze the Effective Green Investment and Replenishment Quantity   Order a copy of this article
    by Nabajyoti Bhattacharjee, Nabendu Sen 
    Abstract: In the study of supply chain management (SCM) of bioethanol, it is a challenging problem for the manager to regulate the flow of raw material in the production unit and the finished products in the market. Apart from that the several other decision-making processes like the implementation of preservation technologies, green investment, ordering optimum replenishment quantities, etc. are some relevant issues which demand a profound industrial framework to lead the decision-making process, especially when we are dealing with multi-items. In our present research we propose multi-item supply chain production inventory model to study the effect of green investment and optimum replenishment quantity on production cost. Preservation cost is a linear function of time. Energy cost and labour cost is considered together with finite energy supply and definite production capacity. In order to solve the model, we apply weighted PSO with statistical verification. We perform sensitivity analysis and provide managerial implication of the proposed model.
    Keywords: multi-item; production inventory; preservation technology cost; carbon emission; green investment; optimisation; supply chain management; SCM.

  • Optimal Control of an Epidemic by Vaccination using Dynamic Programming Approach   Order a copy of this article
    by Bouremani Touffik, Benterki Djamel, Yacine SLIMANI 
    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 Tr
    Keywords: optimal control; differential inclusion; Pontryagin’s maximum principle; dynamic programming; Hamiltonian flow; value function; verification theorem.
    DOI: 10.1504/IJMOR.2021.10042624
  • Effect of Disaster and Balking on M/M/1 driven Fluid Queue with Working Vacation   Order a copy of this article
    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.
    DOI: 10.1504/IJMOR.2021.10042818
  • Numerical Optimization Technique to Solve Imprecisely Defined Nonlinear System of Equations with Bounded Parameters   Order a copy of this article
    by Sukanta Nayak, Pooja J. 
    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.
    DOI: 10.1504/IJMOR.2021.10042970
  • Analysis of MAP/PH_{1}^{E}, PH_{2}^{O} /1 Queue with Standby Server, Second Optional service, Variant arrival rate, Bernoulli Schedule Vacation, Impatient Behavior of Customers, Breakdown, Essential and Optional Repair   Order a copy of this article
    by AYYAPPAN Govindan, Thilagavathy Karthikeyan 
    Abstract: In this article, we consider a single-server queueing model in which customers arrive under three types of arriving rates depends on the situation in the system according to a Markovian arrival process. After receiving essential service from the server, the customers have a choice to pursue the second optional service. The service time follows a phase-type distribution. If the main server completes essential repair who may go for an optional repair option or else return to the service station. Using the Matrix-Analytic Method (MAM), we investigated the total number of customers are present in the system under the steady-state probability vector. The characteristics of the system performance measures are evaluated. We examined the stability condition, the analysis of the busy period and also discussed waiting time distribution. Some Numerical results and graphical representation are provided for a clear view of our proposed model.
    Keywords: Variant Arrival Rate; Phase Type Distributions; Markovian Arrival Process; Standby Server; Impatient Behavior; Second Optional Service and Repair.
    DOI: 10.1504/IJMOR.2021.10043003
  • Third derivative method for solving stiff system of ordinary differential equations   Order a copy of this article
    by Lawrence Osa Adoghe, Ezekiel 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.
    DOI: 10.1504/IJMOR.2021.10043086
  • Optimal replenishment and preservation investment policy for hybrid demand with trade credit schemes   Order a copy of this article
    by Manisha Pant, Seema Sharma, Anand Chauhan 
    Abstract: A safe and sustainable environment has become a top priority for all kind of businesses. This research is to develop a sustainable model of frozen products for hybrid price-stock-dependent demand with preservation technology. Generally, the consumption rate is often affected by the price and stock levels for some types of consumer products. In this study, the demand of the product depends on the price and stock of the product as well, and the retailer invests in preservation technology to decrease the occurrence of deterioration of seasonal goods. This results in high demand of products, which encourage both the retailer and the consumer. A massive pile of items in the supermarket is typically found to lead the consumer to buy more and then create high demand. The objective is to optimise the replenishment cycle and preservation technology investment cost with hybrid price-stock dependent demand, time-varying carrying cost, and trade-credit policy under shortages for the dairy and frozen products. These factors will improve and encourages the purchaser judgment to buy more products with the appropriate amount. The model is illustrated numerically and validated by sensitivity analysis.
    Keywords: inventory management; hybrid price-stock dependent demand; deterioration; trade credit scheme; preservation technology; inflation.
    DOI: 10.1504/IJMOR.2021.10043152
  • Fuzzy Information Inequalities and Application in Pattern Recognition   Order a copy of this article
    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 Jensen’s inequality and Csiszar’s 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 Chebyshev’s inequality, holder’s 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.
    DOI: 10.1504/IJMOR.2021.10043348
  • Column generation approach for solving uncapacitated dynamic lot-sizing problems with time-varying cost   Order a copy of this article
    by Warut Boonphakdee, Peerayuth Charnsethikul 
    Abstract: This study proposes the column generation approach for generating the solution of the capacitated dynamic lot-sizing problems under time-varying cost. The dynamic programming approach is also applied to calculate the cost function value. However, this column generation approach generates only an optimal lot size at period one. Therefore, using the consistent arc method, search the connecting arc from period one to period N. These lot size values are an optimal solution comparing with the lot size values generated by a dynamic programming approach are the same value. Using GUROBI’s simplex method can enhance to reduce the running time on dense matrices to be less than the original simplex method, about 25.4% and 26.1% for 12 and 24 periods. The lowest raw material fluctuation price period is selected obviously to order so that the total inventory cost will still minimal. Therefore, the raw material price significantly influences procurement decision-making.
    Keywords: dynamic programming; network inventory; column generation; maximum problem size.
    DOI: 10.1504/IJMOR.2021.10043656
  • Primal-dual method for a linear program with hybrid direction   Order a copy of this article
    by Rima Guerbane, MOHAND OUAMMER 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 epsilon greater than or equal to zero, chosen in advance.
    Keywords: linear programming; duality; hybrid direction; optimality criteria; primal-dual algorithm; numerical results.
    DOI: 10.1504/IJMOR.2021.10044248
  • Effect of producer’s innovation and vendor’s sales promotion activities for perishable items under quadratic demand: A centralized Vs decentralized approach   Order a copy of this article
    by Urmila Chaudhari, Mrudul Y. Jani, Heta Patel, Manish Betheja, Bhargav Pandya 
    Abstract: This research focuses on a single producer-vendor supply chain. To increase the revenue and demand of the product, the producer employs innovation and the vendor employs sales promotion. In this article demand for the product is predetermined to be quadratic. This paper examines a supply chain for innovation activity, sales promotion activity, and replenishment time, using both centralised and decentralised approaches, with products deteriorating at a constant rate. As the centralised approach reduces the vendor’s total profit, the producer tries to convince the vendor by offering a credit facility, discount and profit-sharing. The key ambition is to calculate the optimum replenishment time, producer’s innovation activity, and vendor’s sales promotion activity by using the classical optimisation algorithm that helps to maximise the total profit of a supply chain. The numerical example is solved for both centralised and decentralised approach, and the sensitivity analysis of major parameters are eventually analysed.
    Keywords: centralised and decentralised decisions; credit period; deterioration; innovation activity; sales promotion activity.
    DOI: 10.1504/IJMOR.2021.10044276
  • A Simple and Efficient Method to Solve Fully Interval and Fuzzy Transportation Problems   Order a copy of this article
    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.
    DOI: 10.1504/IJMOR.2021.10044330
  • Optimization on a constrained integrated supply chain for multiple steel products with investment and freight cost discount   Order a copy of this article
    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 order’s 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 study’s implementations and performances.
    Keywords: multiple steel products; investment; price discount; freight cost.
    DOI: 10.1504/IJMOR.2021.10044420
  • An EOQ Model for Deteriorating Item with Continuous Linear Time Dependent Demand with Trade of Credit and Replenishment Time being Demand Dependent   Order a copy of this article
    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.
    DOI: 10.1504/IJMOR.2021.10044421
  • Hesitant Fuzzy sets with non-uniform Linguistic Terms: An application in Multi-Attribute Decision Making   Order a copy of this article
    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 maker’s 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.
    DOI: 10.1504/IJMOR.2021.10044478
  • New efficient class of estimators of population mean using two-phase sampling   Order a copy of this article
    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.
    DOI: 10.1504/IJMOR.2021.10044653
  • Simulation of Batch Service Lateness Queues with Multiple Vacations and Two Bernoulli Catastrophes using the developed "goLHS" generator   Order a copy of this article
    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.
    DOI: 10.1504/IJMOR.2021.10044728
  • Searls Estimation Strategy for Population Mean of a Sensitive Study Variable Harnessing Non-Sensitive Auxiliary Information   Order a copy of this article
    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 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.
    DOI: 10.1504/IJMOR.2021.10045248
  • A Production Inventory Model for Non-Instantaneous Deteriorating Items with Two-Phase Production Period, Stock-Dependent Demand and Shortages   Order a copy of this article
    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.
    DOI: 10.1504/IJMOR.2021.10045307
  • Component Sourcing Under Disruption Risk   Order a copy of this article
    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.
    DOI: 10.1504/IJMOR.2022.10045952
  • A Continuous Five-step Implicit Block Unification Method for Numerical Solution of Second-Order Elliptic Partial Differential Equations (PDEs)   Order a copy of this article
    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.
    DOI: 10.1504/IJMOR.2022.10046014
  • System reliability analysis based on Pythagorean fuzzy set   Order a copy of this article
    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.
    DOI: 10.1504/IJMOR.2022.10046592
  • An Optimization Model of Drug Order Quantity and Distribution Using Continuous Review Approach by Considering Secondary Suppliers   Order a copy of this article
    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 hospital’s 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.
    DOI: 10.1504/IJMOR.2022.10046617
    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.
    DOI: 10.1504/IJMOR.2022.10046636
  • Weight Computation of Criteria in a Decision Making Problem by Entropy Measure Under Interval-Valued Fuzzy Environment   Order a copy of this article
    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.
    DOI: 10.1504/IJMOR.2021.10046639
  • Study on Fuzzy Inventory Model for Deteriorating Items with Recurring Seasonal Demand Pattern   Order a copy of this article
    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.
    DOI: 10.1504/IJMOR.2022.10046711
  • Determining the Optimal Parcel Delivery Method Using One Drone and One Truck   Order a copy of this article
    by Kazuki Satoh, Hiroshi Morita 
    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.
    DOI: 10.1504/IJMOR.2022.10047093
  • Analysis on a non-Markovian batch arrival queuing model with Phases of service and multi vacations in Cloud computing services   Order a copy of this article
    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.
    DOI: 10.1504/IJMOR.2022.10047103
  • Bi-criteria two-machine flow shop scheduling problem involving sequence-dependent setup times and pieces multiplicity   Order a copy of this article
    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.
    DOI: 10.1504/IJMOR.2022.10047530
  • A neutrosophic approach in the optimal solution of a neutrosophic fuzzy capital budgeting problem   Order a copy of this article
    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, xÃN(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.
    DOI: 10.1504/IJMOR.2022.10047558
  • Analysis and simulation of modified susceptible-infected-recovered model with vaccination for COVID-19 outbreak   Order a copy of this article
    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.
    DOI: 10.1504/IJMOR.2022.10047684
  • Integration of Supplier Evaluation and Closed-loop Supply Chain Network Design from Internal and External Stakeholders’ Perspectives Using Gray Hybrid SWARA-COPRAS Methods   Order a copy of this article
    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.
    DOI: 10.1504/IJMOR.2022.10047685
  • An optimal inventory model for a deteriorating item with multivariate demand function   Order a copy of this article
    by Mahsa Ghandehari, Mohsen Karimi-Lenji 
    Abstract: Managing the inventory of perishable items is a vital task in the supply chain. The demand for some deteriorating items is influenced by many factors that make their management a complicated task. Therefore, it is important to take multiple key factors into account to develop a more realistic model. In this paper, an inventory model for non-instantaneous deteriorating items is proposed, for the case where the quality and quantity of the item decrease over time. The demand is an additive, continuous, and differentiable function of price, stock level, and also age of the product. The deterioration starts after a fixed period with a constant rate and the shortage is not allowed. Permissible delay in payment and time value of money are also considered in the model. First, we formulate the problem in a piecewise mixed-integer nonlinear programming model. We then propose an algorithm to solve a number of examples.
    Keywords: replenishment policy; deteriorating items; multivariate demand function; delay in payment.
    DOI: 10.1504/IJMOR.2021.10039543
  • Estimating weight of stocks using ambiguity index and its application to type-2 intuitionistic fuzzy portfolio selection   Order a copy of this article
    by Anusha Vulimiri, Sireesha Veeramachaneni 
    Abstract: In this paper a method to find the weight of stock in the portfolio is developed when the stock preferences are given in type-2 intuitionistic fuzzy numbers. Taking into the fact that ambiguity can significantly bring the outcome of weight; in this paper we compute ambiguity in the valuation of each stock and then used in weight determination process. The proposed technique allows the decision maker to assign the weights for stocks, which leads to select reliable portfolio for investment. The advantages are discussed by citing appropriate numerical examples.
    Keywords: portfolio selection; stock weights; ambiguity index; type-2 intuitionistic fuzzy set; T2IFS; Jaccard distance measure.
    DOI: 10.1504/IJMOR.2021.10040628
  • Solution of linear programming problem with trapezoidal fuzzy coefficients using score functions   Order a copy of this article
    by K. Suriyapriya, Jagadeeswari Murugan, V. Lakshmana Gomathi Nayagam 
    Abstract: Numerous real-life problems depend on incomplete and implausible information. To overcome the enigma and obscurity, Zadeh promoted fuzzy set theory in 1965. After introducing fuzzy set theory, many researchers have made numerous developments in engineering and medicine. Different ranking principles on trapezoidal fuzzy numbers are established and are applied by eminent authors in multi-criteria decision-making problems in the literature. Linear programming models are essential tools to solve optimisation problems in healthcare, production planning, financial sectors, etc. The ranking principle plays a vital role in the constraints. Recently, a complete ranking principle on the class of trapezoidal fuzzy numbers was suggested in 2018. This study proposes a method to solve the fuzzy linear programming problem whose coefficients are trapezoidal fuzzy numbers using the total ordering principle by score functions defined in 2018. Here, we formulate an equivalent multi-objective linear programming problem for the given fuzzy linear programming problem to attain the optimal solution. Furthermore, the proposed method's efficiency is illustrated through numerical examples and comparison with the existing techniques is also discussed.
    Keywords: linear programming problem; trapezoidal fuzzy coefficients; total ordering principle.
    DOI: 10.1504/IJMOR.2021.10040627
  • Efficient classes of estimators for population variance using attribute   Order a copy of this article
    by Shashi Bhushan, Anoop Kumar, Sumit Kumar 
    Abstract: This article deals with the problem of estimating population variance of study variable by using information on auxiliary attribute in simple random sampling. We have adapted the procedure of Kadilar and Cingi (2006) and established some efficient classes of estimators for population variance. The performance of the proposed estimators have been assessed by an empirical study using two real populations and the results demonstrate that the proposed estimators present an extensively greater efficiency when compared with the usual mean estimator, classical ratio, regression and exponential estimators suggested by Singh and Kumar (2011), Singh and Malik (2014) estimators, Zaman and Kadilar (2019) type estimators, Zaman (2020) type estimator and Cekim and Kadilar (2020) type estimator.
    Keywords: bias; mean square error; efficiency; auxiliary attribute.
    DOI: 10.1504/IJMOR.2021.10040442
  • On multi-objective extensions of the classical assignment model with fuzzy parameters and fuzzy goals   Order a copy of this article
    by Lanndon Ocampo, Enrico Enriquez, Carmelita Loquias, Reuella J. Bacalso, Grace Estrada 
    Abstract: This study advances the limitations of current fuzzy multi-objective assignment models by exploring some formulations with fuzzy parameters and fuzzy goals. The first formulation expresses the coefficients of the objective functions and constraints as fuzzy sets. Two crucial fuzzy transformations were adopted, along with the computational process of the epsilon-constrained multi-objective optimisation. On the other hand, the second formulation assumes the fuzzy coefficients of objective functions and constraints and extends such fuzziness by introducing fuzzy constraints. Lastly, the coefficients of the objective functions and the constraints are expressed as crisp sets while allowing permissible constraint violations. The symmetric fuzzy linear programming solution concepts in the domain literature were adopted as part of the computational process in arriving at a model solution. Actual case examples aided these formulations to gain insights into their computational complexity, efficiency, scalability, and flexibility.
    Keywords: assignment; multi-objective optimisation; fuzzy optimisation.
    DOI: 10.1504/IJMOR.2021.10039694
  • Queuing systems in the cafeterias at the University of Dodoma, Tanzania   Order a copy of this article
    by Gadde Srinivasa Rao, Evodia Andreas Mnyanga 
    Abstract: Queuing is a common practice to all public service centres where the demand surpasses the supply. The purpose of this study is the performance of queuing systems in the cafeterias at the University of Dodoma, Dodoma Tanzania. Data were recorded in a period of seven days to find the distribution pattern of the arrival and the service time through fitting them in poison and exponential distribution respectively, to determine the average waiting time in a queue by using the M/M/1 mathematical model, and to analyse the waiting time in a system by using statistical quality control chart. The results of the findings showed that the arrival time and service time for all queues in all sessions follows poison and exponential distribution respectively. Also the findings showed that the expected waiting time was high during breakfast, whereas during lunch and dinner the expected waiting time was low compared to breakfast.
    Keywords: queue; restaurant; waiting lines; M/M/1 mathematical model; arrival time and service time; Tanzania.
    DOI: 10.1504/IJMOR.2021.10040971