International Journal of Industrial Mathematics
Volume:14 Issue: 1, Winter 2022

Our aim at this paper is to estimate the parameters of extended Burr XII (EBXII) based on krecords with corrected bias. To get this goal maximum likelihood estimator (MLE) is applied and bias correction for ML estimation is considered to get better and improved estimator. Numerical results for comparison of performances of estimators are also presented.

This paper deals with benchmarking for a three-stage DMU. After investigating and eliminating congestion, adjustment of intermediate products and initial inputs have achieved by utilizing an Inverse DEA model, which dominates the current vectors and serve as a benchmark that is to the best of this paper knowledge. This process has two cases. First, the overall efficiency stays fixed, and the second case, is corresponded to the overall efficiency ‎improvement.‎

Data Envelopment Analysis is a technique based on mathematical planning for specifying the efficiency of decision making units (DMUs). In some cases, manager is not going to add a new resource but to reallocate one of the previous resources. Reallocating a resource may be done for different purposes and has different benefits. For example, without adding a new resource and only using the same resources, is it possible to increase the efficiency of one unit or even increase the efficiency of the whole system? In this paper, a mathematical model is presented that can be used to reallocate one of the previous available resources between units in such a way that the total efficiency of decision-making units reaches the maximum possible value. In this model, in order to prevent excessive reduction of the share of each unit of the desired source, restrictions have been considered. In these constraints, a lower bound for the share of each unit is specified. Also, reallocating a resource is likely to lead some changes in output values of decision-making units. In the presented model, some constraints are considered that specify an upper bound for outputs produced by the units. There are other restrictions in this model. The first is that the total share of units from the desired resource should not exceed the amount available of it and the second is that the total output produced by all units should be at least equal to the total output produced before reallocation. The model presented in this article, in addition to considering the restrictions described, all of which are unavoidable, has been transformed into a linear programming model that can be solved by many existing software.

Identification of various sources of inefficiency plays an important role in the performance analysis aimed at developing plans for the improvement of decision making. In this regard, not only technical, cost, and allocative efficiency can be estimated by information on inputs and outputs and their prices, but losses due to the lack of profit and revenue and optimal cost can also be calculated based on the relevant inefficiency. The present paper aimed at providing new estimation of cost efficiency and sources of losses in the total efficiency in a non-competitive environment where there is the possibility of change in prices of inputs and outputs from one DMU to another. In line with studies (Tone .K, "A Strange Case of the Cost and Allocative Efficiencies in DEA". Journal of the Operational Research Society 53, (2002), pp.1225-1231) and (Tone. K., Tsutsui, M. "Decomposition of Cost Efficiency and its Application to Japanese-Us Electric Utility Comparisons". Socio-Economic Planning Sciences 47 (2007), pp.91-106), the present study sought to introduce new sources of inefficiency and related losses by presenting new price-based and cost-based production possibility sets.

The hub location problems are highly crucial due to their applications in the transportation and distribution area. Today, the complexities of solving the real world problems using the single-objective techniques are challenging. For a more real model, the present study considers a bi-objective capacitated single-allocation hub location problem assuming the reliability of paths. In addition to the capacity, the fixed costs for the hubs are considered, as well. Furthermore, while minimizing the cost, the reliability of the weakest path is making maximized. Three mathematical models are proposed for this problem. The performance of single-objective models is evaluated and then, the proposed bi-objective model is solved using the ε-constraint method. In the present study, the fixed cost is calculated using two different one is based on the distance from the center of mass and another one depends on the hub capacity. The results reveal that the third model with the fixed cost based on the distance from the center of mass has the best performance.

The numerical solution of linear integral equations of third kind is discussed in various studies, but in the previous researches on this kind of equations only the analytical solution was investigated. Due to some limitations for this kind of solutions, in this paper we propose a new method for numerical solution of linear integral equations of third kind. The proposed method is based on the approximation of the unknown function with Krall-Laguerre polynomials. This method has a simple computation with a quite acceptable approximate solution. Moreover, we obtain an estimate of the error bound for suggested method. Two examples are also presented to show the efficiency of the proposed method.

We study the independent Jeffreys' prior of the unknown location, scale and skewness parameters of truncated-exponential skew-symmetric distributions(TESSD). We show that this prior is symmetric and improper but it yields a proper posterior distribution for some densities. A simulation study using Monte Carlo methods is presented to compare the efficiency of Bayesian estimators in TESSD with Azzalinis' skew models under square error loss and Linex loss functions.

In this paper, we study a class of second-order fuzzy initial value problems that are known as the Cauchy-Euler differential equations, in the crisp case. This work begins by studying the structure of solution function in the crisp case and providing a requirement space of the generalized differentiable functions. In sequel, the process of production and construction of the solution formula are discussed, in details. Finally, the obtained formulas are applied and illustrated by solving some examples.

In this research work, we have shown that it is possible to use fuzzy transform method (FTM) for approximate solution of space-time fractional advection-dispersion equation. In numerical methods, in order to approximate a function on a particular interval, only a restricted number of points are employed. However, what makes the F-transform preferable to other methods is that it makes use of all points in the interval.

Dynamical systems with delay are widespread in nature. The study of time-delay induced changes in the collective behavior of systems of coupled nonlinear oscillators is a subject of great interest, both because of its fundamental importance from the point of view of dynamical systems and because of its practical applications. In this paper, an explicit technique is proposed for numerical solution of nonlocal dynamical systems with time delay. The proposed method is adopted quadratic spline interpolation. Then, the error analysis of the developed method is discussed. It is exploited in the discussion of nonlocal delay Ikeda and Hutchinson models. Finally, the performance of the presented approach is verified by applying the error and convergence study for different values of fractional order parameters.