مجله بین المللی محاسبات و مدل سازی ریاضی
سال سیزدهم شماره 1 (Winter 2023)

The original DEA models were applicable only to technologies characterized by positive inputs/outputs. We consider the interval scale (IS) variables especially when the IS variable is a difference of two different variables (like sales etc.) have been used as inputs and/or outputs. We measure Preferred Efficiency (PE) in Data Envelopment Analysis (DEA) with negative data when these data derived from IS variables. The PE is an efficiency concept that takes into account the decision maker’s (DM) preferences. We search the Most Preferred combination of inputs and outputs of Decision Making Units (DMUs) which are efficient in DEA. Also, we approximate indifference contour of the unknown Preferred Function (PF) at Most Preference Solution (MPS) with supporting hyperplane on PPS at MPS. We propose a way to obtain this the supporting hyperplane and also assume this the hyperplane is tangent on the indifference contour of PF. We use from the radial DEA problems with Variable Returns to Scale (VRS) (BCC models) at the combination orientation (both outputs are maximized and inputs are minimized). Also, We decompose each IS variable into two Ratio Scale (RS) variables and then utilizing from a compromise solution approach generate Common Weights (CW) for the decomposed input/output variables. In other to, we will introduce an MOLP model which its objective functions are input/output variables subject to the defining constraints of production possibility set (PPS) of DEA models. Lastly, the procedure and the resulting PE scores are applicable to solving practical problems by the mentioned models.

Decisions are based on information. To be useful, information must be reliable. The concept of a Z-number relates to the issue of reliability of the information. the fully Z-number linear programming problems (FZLPP) in which all the parameters, as well as the variables, are represented by fully Z-numbers is a good topic for readers. and in this study, we proposed a practical method to solve fully Z-numbers linear programming by using the fuzzy ranking method for constraints and converting objective function to a multi-objective function, and finding their optimal solution with Z-number.

In this paper, the concept of partial pseudo-triangular entropy as a superior measure of indeterminacy for uncertain random variables is proposed. It is first proved that partial entropy and partial triangular entropy sometimes fail to measure the indeterminacy of an uncertain random variable. Then, the concept of partial pseudo-triangular entropy and its mathematical properties are investigated. To illustrate the outperformance of partial pseudo-triangular entropy as a measure of risk, a portfolio optimization problem is optimized via different types of entropy. Furthermore, a genetic algorithm (GA) is implemented in MATLAB to solve the corresponding problem. Numerical results show that partial pseudo-triangular entropy as a quantifier of portfolio risk outperforms partial entropy and partial triangular entropy in the uncertain random portfolio optimization problem.

This work considers a numerical method based on the 2D-hybrid block-pulse functions and normalized Bernstein polynomials to solve 2D-nonlinear Fredholm integral equations of the second type. These problems are reduced to a system of nonlinear algebraic equations and solved by Newton's iterative method along with the numerical integration and collocation methods. Also, the convergence theorem for this algorithm is proved. Finally, some numerical examples are given to show the effectiveness and simplicity of the proposed method.

Optimum cropping pattern in vineyard irrigated farming is one of the vital tasks for obtaining the best irrigation water reserves of the command. In this article the linear programming model was developed for optimal use of water and land resources. The model was tested by the data from Chinangali irrigated farmland with 120 cultivated hectares found in Dodoma, Tanzania. The results show that, the savings of 16 470.40 m3 of water per annum will be observed if the planting of 14.18 hectares of Chardonnay, 27.97 hectares of Cabernet sauvignon, 56.14 hectares of Riesling and 21.39 hectares of Chenin blanc. Thus, it was recommended that 1 173 359.60 m3 of water should be released to the irrigated farmland per annum for the best irrigation planning versus the 1 189 830 m3 of water supplied currently per annum.

The multi-parametric programming (mp-P) is designed to minimize the number of unnecessary calculations to obtain the optimal solution under uncertainty, and since we widely encounter that kind of problem in mathematical models, its importance is increased. Although mp-P under uncertainty in objective function coefficients (OFC) and right-hand sides of constraints (RHS) has been highly considered and numerous methods have been proposed to solve them so far, uncertainty in the coefficient matrix (i.e., left-hand side (LHS) uncertainty) has been less considered. In this work, a new method for solving multi-parametric mixed integer linear programming (mp-MILP) problems under simultaneous uncertainty OFC, RHS, and LHS is presented. The method consists of two stages which in the first step, using tightening McCormick relaxation, the boundaries of the bilinear terms in the original mp-MILP problem are improved, the approximate model of the problem is obtained based on the improved boundaries of the first stage, and finally, an algorithm is presented to solve these kinds of problems. The efficiency of the proposed algorithm is investigated via different examples and the number of required calculations for solving the problem in different partitioning factors is compared. Also, model predictive control (MPC) using mp-P is designed for an example of an urban traffic network to examine the practical application of the proposed algorithm.