International Journal of Industrial Mathematics
Volume:14 Issue: 4, Autumn 2022

In this paper, we consider Volterra integral equations of the first kind. Then by extending the modified Block-pulse functions(MBPFs) on the Volterra integral equation of the second kind obtained from Volterra integral equation of the first kind, we obtain the approximate solution. Some theorems are proved to provide an error analysis for proposed method. Numerical examples show that the proposed scheme has a suitable degree of accuracy.

In the present work, first a Polytropic-Based Blowby Model (PBBM) was validated using a Thermodynamic Simulation Code (TSC). Then, using the results extracted from a single-cylinder SI research engine, the P- of an Ensemble Average Cycle (EAC) was calculated the experimental cycles. The crevice flow rates of the EAC were estimated using both codes. The results showed a good agreement between them.

Benchmarking is a tool for evaluating organizational performance with a learning approach from others. The importance of benchmarking in every industry is clear for anyone. In the automotive industry, the performance of after-sales service agencies in Iran is evaluated every year by Iran Standard and Quality Inspection company. One of the ways to continuously improve in after-sales service agencies is benchmarking of successful and efficient examples in the network. In this paper, a benchmarking model is developed considering that the repair index and customer satisfaction are interdependent. To improve the accuracy and operationality of benchmarking, some constraints have been added to the model with the opinion of experts. Considering the dependent parameters, a data envelopment analysis model has been proposed and this model has been implemented to benchmark 20 after-sales service agencies of a car company. By solving the model and comparing it with the results of the original model, it was observed that the considered conditions changed the benchmarking and increased the accuracy. This paper discusses the concept of the impact and importance of dependent parameters in benchmarking, and with this concept, a benchmarking model for automotive after-sales service agencies is presented.

This work presents the generalized nonlinear multi-terms fractional variable-order differential equation with proportional delays. In this paper, a novel shifted Jacobi operational matrix technique is introduced to solve a class of these equations mentioned, so that the main problem becomes a system of algebraic equations that we can solve numerically. The suggested technique is successfully developed for the aforementioned problem. Comprehensive numerical tests are provided to demonstrate the generality, efficiency, accuracy of presented scheme and the flexibility of this technique. The numerical experiments compared it with other existing methods such as Reproducing Kernel Hilbert Space method ($ RKHSM $). Comparing the results of these methods as well as comparing the current method ($NSJOM$) with the true solution, indicating the validity and efficiency of this scheme. Note that the procedure is easy to implement and this technique will be considered as a generalization of many numerical schemes. Furthermore, the error and its bound are estimated.

The goal of this paper is to calculate the order reduction of the generalized mKdV equation with constant coefficients (gmKdVcc) and the generalized mKdV equation with variable-coefficients (gmKdVvc) using the mu-symmetry method. Moreover we obtain Lagrangian and mu-conservation law of the gmKdVcc equation and the gmKdVvc equation using the variational problem method.

Determining and measuring efficiency is an important strategy in decision making. Due to the lack of transparency in the efficiency of production stages in Butter production units, the purpose of this study is to design a data envelopment analysis model to evaluate the efficiency of production stages of these units. The contribution of this research is to develop a model for evaluating the efficiency of a two-stage production system with both desirable and undesirable output using the network model of Khalili and Shahmir (2015). The developed two-stage model has been conducted using accurate and certain data of twenty Butter manufacturing factories in 1399, which can evaluate efficiency separately and in an integrated manner. At the end of the first stage, there are two types of desired output. There is a desired output of breakfast cream that does not enter the second stage of production and it is supplied to market for sale, and another desirable output is the pasteurized cream that is transferred to the second stage of production. At the end of the second stage, a desirable output, which is the packaged butter and an undesirable output, which is butter dough are obtained. The efficiency of all twenty units was evaluated and compared. Depending on the efficiency of the whole process, there was only one efficient unit. According to the efficiency of the first stage, there was only one efficient unit out of twenty units, and according to the second stage, there are two efficient units. The conclusion is that this industry has a high inefficiency in the factories located in provinces of Tehran and Alborz on their production process. Thus, it is necessary for the managers of this industry to increase efficiency of their production process.

In conventional DEA methods, all inputs and outputs are assumed to be continuous. However, the implied presumption of continuous data may not maintain an acceptable level of precision in practical data. Many practical situations such as number of teachers in a school, number of students in a college, or research papers only take integer values. Presented work presumes subsets of input and output variables in traditional five-pronged axioms in DEA model to be integer values for the first time in the field. An additional effort in this work expands axioms and a new model is presented. This paper presents a novel two phase model that in the first phase produces more precise efficiency values and the best benchmark in its second phase, i.e. the nearest integer point to the efficiency boundary is selected based on constant returns to scale. A case study is presented that demonstrates a comparison of efficiency values obtained with this model compared to prior models that is show in table 1. And in Table 2, the values of the slack are compared with each other.

Data envelopment analysis (DEA), is a non-parametric mathematical programming technique to evaluate the efficiency of a set of homogeneous decision-making units (DMUs), so that DMUs are evaluated into two groups, efficient and inefficient. According to the staggering costs in order to managing DMUs or organizations, maintaining some loss-making organizations are not cost-effective. Therefore, one of the concerns of managers in the discussion related to the financial problems of organizations is the maintenance or merger or elimination of inefficient organizations (inefficient DMUs). However, this article focuses on the performance of inefficient units. Therefore, we measure the productivity of inefficient DMUs using the revised Malmquist productivity index (MPI) to make a decision based on the maintenance or merger or elimination of these DMUs by decision makers (DMs).

In the latest decade, the concept of service delivery and software-as-a-service have evolved into two important evolution paradigms which have affected the information systems area. A paradigm shift in software development has been triggered by this change, in which software is developed through the use of ready-made services in the cloud. Since service composition in the cloud environment must be done on-the-fly, realizing this requires a trade-off between the optimality of the composite service and the time it takes. As QoS-aware service composition has several potential solutions, some of which are usually considered optimal, which should be considered an NP-hard problem. A growing number of services leads to a larger problem search space, which is why in recent years many researchers have looked into methods that use meta-heuristic algorithms to solve the problem of service composition in a cloud environment. Thus, it is crucial that researchers have access to up-to-date and specialized review articles. Based on a systematic review of the research literature, the paper aims to extract important questions that are relevant to meta-heuristic QoS-aware service composition methods. Then, after classifying the studies and studying the proposed methods, goals, and priorities of researchers in articles, useful results and statistics for future research in this field are presented.

This paper develops an efficient non-dominated sorting genetic algorithm (NSGA-II) to solve the redundancy allocation problem (RAP) of series-parallel systems. The system consists of subsystem in series, where components are used in parallel for each subsystem. Both the system and its subsystems can only take two states of complete perfect and complete failure. Identical redundant components are included to achieve a desirable reliability. The components of each subsystem, which are chosen from a list that is available in the market, are characterized by their cost, weight, and reliability. To find the optimum combination of the number of components for each subsystem, the mathematical formulation for the maximal reliability and minimal cost of the system configuration under cost constraint is first obtained. Then, a modified NSGA-II is proposed to solve the model. In this algorithm, a heuristic method of generating a primary solution is integrated to achieve better solutions. Moreover, design of experiment approach is employed to calibrate the parameters of the algorithm. At the end, some numerical examples are used to validate the solution, to assess the performance of the proposed methodology under different configurations, and to compare the performance with the ones of two other meta-heuristic algorithms. The results of experiments are generally in favor of the proposed solution algorithm.