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Abstract: Data envelopment analysis (DEA) is defined based on observed units and by finding the distance of each unit to the border of estimated production possibility set (PPS). The convexity is one of the underlying assumptions of the PPS. This paper shows some difficulties of using standard DEA models in the presence of input-ratios and/or output-ratios. The paper defines a new convexity assumption when data includes a ratio variable. Then it proposes a series of modified DEA models which are capable to rectify this problem. [Copyright &y& Elsevier]

Abstract: This paper focuses on multi-objective large-scale non-linear programming (MOLSNLP) problems with block angular structure. We extend the technique for order preference by similarity ideal solution (TOPSIS) to solve them. Compromise (TOPSIS) control minimizes the measure of distance, provided that the closest solution should have the shortest distance from the positive ideal solution (PIS) as well as the longest distance from the negative ideal solution (NIS). As the measure of “closeness”L P -metric is used. Thus, we reduce a q-dimensional objective space to a two-dimensional space by a first-order compromise procedure. The concept of a membership function of fuzzy set theory is used to represent the satisfaction level for both criteria. Moreover, we derive a single objective large-scale non-linear programming (LSNLP) problem using the max–min operator for the second-order compromise operation. Finally, a numerical illustrative example is given to clarify the main results developed in this paper. [Copyright &y& Elsevier]

Abstract: Ghatee and Hashemi [M. Ghatee, S.M. Hashemi, Ranking function-based solutions of fully fuzzified minimal cost flow problem, Inform. Sci. 177 (2007) 4271–4294] transformed the fuzzy linear programming formulation of fully fuzzy minimal cost flow (FFMCF) problems into crisp linear programming formulation and used it to find the fuzzy optimal solution of balanced FFMCF problems. In this paper, it is pointed out that the method for transforming the fuzzy linear programming formulation into crisp linear programming formulation, used by Ghatee and Hashemi, is not appropriate and a new method is proposed to find the fuzzy optimal solution of multi-objective FFMCF problems. The proposed method can also be used to find the fuzzy optimal solution of single-objective FFMCF problems. To show the application of proposed method in real life problems an existing real life FFMCF problem is solved. [Copyright &y& Elsevier]

Abstract: Curve fitting is an interesting and important subject in mathematics and engineering. It has been studied extensively and a number of approaches, mostly based on polynomials and piecewise polynomials, have been employed. In the usual setting, some data points are given and one wants to find a polynomial function with the minimum violations measured by a norm in the given data points. In these approaches, norms are applied to aggregate all violations as a scalar. In this paper, the polynomial curve fitting problem is considered from the viewpoint of decision making. Taking into account some weaknesses of the norm-based approaches, a multiobjective programming model for curve fitting is given in which the violations are minimized simultaneously as a vector. This approach is more flexible for the curve fitting problem. Indeed, using the concept of efficiency in multiobjective programming, it enables us to impose some additional helpful secondary preferences. Especially, this approach can obtain a fitted curve with efficient violations and minimum average curvature or minimum average slope. [ABSTRACT FROM AUTHOR]

Abstract: Data envelopment analysis (DEA) and multiple objective linear programming (MOLP) can be used as tools in management control and planning. The existing models have been established during the investigation of the relations between the output-oriented dual DEA model and the minimax reference point formulations, namely the super-ideal point model, the ideal point model and the shortest distance model. Through these models, the decision makers’ preferences are considered by interactive trade-off analysis procedures in multiple objective linear programming. These models only consider the output-oriented dual DEA model, which is a radial model that focuses more on output increase. In this paper, we improve those models to obtain models that address both inputs and outputs. Our main aim is to decrease total input consumption and increase total output production which results in solving one mathematical programming model instead of n models. Numerical illustration is provided to show some advantages of our method over the previous methods. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a partial enumeration algorithm is developed for a class of pure IP problems. Then, a computational algorithm, named PE_SPEEDUP (partial enumeration speedup), has been developed to use whatever explicit linear constraints are present to speedup the search for a solution. The method is easy to understand and implement, yet very effective in dealing with many pure IP problems, including knapsack problems, reliability optimization, and spare allocation problems. The algorithm is based on monotonicity properties of the problem functions, and uses function values only; it does not require continuity or differentiability of the problem functions. This allows its use on problems whose functions cannot be expressed in closed algebraic form. The reliability and efficiency of the proposed algorithm and the PE_SPEEDUP algorithm has been demonstrated on some integer optimization problems taken from the literature. [Copyright &y& Elsevier]

Abstract: This paper considers the scenario of supply chain with multiple products and multiple suppliers, all of which have limited capacity. We assume that received items from suppliers are not of perfect quality. Items of imperfect quality, not necessarily defective, could be used in another inventory situation. Imperfect items are sold as a single batch, prior to receiving the next shipment, at a discounted price. The demand over a finite planning horizon is known, and an optimal procurement strategy for this multi-period horizon is to be determined. Each of products can be sourced from a set of approved suppliers, a supplier-dependent transaction cost applies for each period in which an order is placed on a supplier. A product-dependent holding cost per period applies for each product in the inventory that is carried across a period in the planning horizon. Also a maximum storage space for the buyer in each period is considered. The decision maker, the buyer, needs to decide what products to order, in what quantities, with which suppliers, and in which periods. Finally, a genetic algorithm (GA) is used to solve the model. [Copyright &y& Elsevier]

Abstract: One of the interesting, important and attractive problems in applied mathematics is approximation of functions in a given space. In this paper the problem is considered for fuzzy data and fuzzy functions using the defuzzification function of Fortemps and Roubens. Approximation of a fuzzy function on some given points for i =1,2,…, m is considered by some researchers as interpolation problem. But in interpolation problem we find a polynomial of degree at most n = m −1 where m is the number of points. But when we have lots of points (m is very large) it is not good or even possible to find such polynomials. In this case we want to find a polynomial of arbitrary degree which is an approximation to original function. One of the works has done is regression by some researchers and we introduced a different method. In this case we have m points but we want to find a polynomial of degree at most n < m but not n = m −1 necessarily. We introduce a fuzzy polynomial approximation as universal approximation of a fuzzy function on a discrete set of points and we present a method to compute it. We show that this approximation can be non-unique, however we choose one of them with the smallest amount of fuzziness. [Copyright &y& Elsevier]

Abstract: This paper presents dynamic programming algorithms for generating optimal guillotine-cutting patterns of equal rectangles. The algorithms are applicable for solving the unconstrained problem where the blank demand is unconstrained, the constrained problem where the demand is exact, the unconstrained problem with blade length constraint, and the constrained problem with blade length constraint. The algorithms are able to generate the simplest optimal patterns to simplify the cutting process. When the sheet length is longer than the blade length of the guillotine shear used, the dynamic programming algorithm is applied to generate optimal layouts on segments of lengths no longer than the blade length, and the knapsack algorithm is employed to find the optimal layout of the segments on the sheet. The computational results indicate that the algorithms presented are more efficient than the branch-and-bound algorithms, which are the best algorithms so far that can guarantee the simplest patterns. [Copyright &y& Elsevier]