International Journal of Industrial Mathematics
Year:2022 | Volume:14 | Issue:4|Papers Count:7

In this work, we present a simple e, cient modi, ed Block-Pulse functions (MBPFs) for numerical solution of class of linear Volterra integral equation of , rst kind. The peresent method is based on converting Volterra integral equation of the , rst kind into Volterra integral equation of the second kind. Some theorems are included to show the convergence and advantage of this method. Numerical results show that the approximate solutions have a good degree of accuracy.

Due to the required clearance between the cylinder liner and piston of a reciprocating IC engine, a few crevices appear among compression rings and cylinder-piston. Although the gas leakage into the crankcase can be controlled substantially via the use of two or three compression rings, it is impossible to remove the existing crevices and the ring ori, ces of the cylinder-piston-ring pack. Escape of unburned mixture into the crevices can result in a serious impact on the work done per cycle, fuel conversion e, ciency, and pollutant emission, which are all important in the , ring cycle. In the present work, , rst a Polytropic-Based Blowby Model (PBBM) was validated using a Thermodynamic Simulation Code (TSC) equipped with a blowby sub-model. Then, using the experimental results extracted from a single-cylinder SI research engine in skip-, re and NG fuel mode, the P ,of an Ensemble Average Cycle (EAC) was calculated from the P , s of 200 experimental cycles. The crevice ow rates of the EAC were estimated using TSC and PBBM. The results showed a good agreement between them. The study of blowby in 200 experimental cycles via the use of PBBM revealed that the existing cyclic variations of the cylinder pressure caused corresponding cyclic changes in Net Cylinder Mass Lost (NCML) and Net Mass Passed (NMP) through the ring ori, ces and the pressure inside the crevices. A linear correlation was observed between maximum NCML and cylinder peak pressure while an inverse correlation was detected between cylinder peak pressure and NCML at the EVO position.

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 e, cient 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 di, erential 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, e, ciency, accuracy of presented scheme and the exibility 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 e, ciency 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-coe, cients (gmKdVcc) and the generalized mKdV equation with variable-coe, cients (gmKdVvc) using the ,-symmetry method. Moreover we obtain Lagrangian and ,-conservation law of the gmKdVcc equation and the gmKdVvc equation using the variational problem method.

Determining and measuring e, ciency is an important strategy in decision making. Due to the lack of transparency in the e, ciency of production stages in Butter production units, the purpose of this study is to design a data envelopment analysis model to evaluate the e, ciency of production stages of these units. The contribution of this research is to develop a model for evaluating the e, ciency 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 e, ciency separately and in an integrated manner. At the end of the , rst 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 e, ciency of all twenty units was evaluated and compared. Depending on the e, ciency of the whole process, there was only one e, cient unit. According to the e, ciency of the , rst stage, there was only one e, cient unit out of twenty units, and according to the second stage, there are two e, cient units. The conclusion is that this industry has a high ine, ciency 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 e, ciency 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 , ve-pronged axioms in DEA model to be integer values for the , rst time in the , eld. An additional e, ort in this work expands axioms and a new model is presented. This paper presents a novel two phase model that in the , rst phase produces more precise e, ciency values and the best benchmark in its second phase, i. e. the nearest integer point to the e, ciency boundary is selected based on constant returns to scale. A case study is presented that demonstrates a comparison of e, ciency 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.