Abstract: In this paper we have introduced a computational method for a class of Telegraph Equation change to two-dimensional nonlinear Volterra integral equations, based on the expansion of the solution as a series of Haar functions. Also, by using the Banach fixed point theorem, we get an upper bound for the error of our method. Since our examples in this article are selected from different references, so the numerical results obtained here can be compared with other numerical methods.

• Publication Date: 13-Mar-2016
• DOI: 10.15224/978-1-63248-086-6-55
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Abstract: In recent years, a great number of Data Envelopment Analysis (DEA) studies have focused on Decision Making Units (DMUs) with two-stage structures, where all outputs from the first stage are intermediate products that are applied as the inputs of the second stage. In many situations, some inputs and outputs are shared between two stages. For this type of two-stage process, the conventional two-stage DEA models have some limitations e.g. efficiency formulation and linearizing transformation. In this paper, we introduce a relational DEA model for the two-stage process with shared inputs and outputs that the overall efficiency is illustrated as a convex combination of efficiencies of its two stages. The linearity of DEA models is preserved in our model. A numerical example of Malaysian Palm Oil refineries is used to explain the model.

• Publication Date: 13-Mar-2016
• DOI: 10.15224/978-1-63248-086-6-59
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