SAS/OWA:ordered weighted averaging in SAS optimization

This paper explores the use of the optimization procedures in SAS/OR software with application to the ordered weight averaging (OWA) operators of decision-making units (DMUs). OWA was originally introduced by Yager (IEEE Trans Syst Man Cybern 18(1):183-190, 1988) has gained much interest among researchers, hence many applications such as in the areas of decision making, expert systems, data mining, approximate reasoning, fuzzy system and control have been proposed. On the other hand, the SAS is powerful software and it is capable of running various optimization tools such as linear and non-linear programming with all type of constraints. To facilitate the use of OWA operator by SAS users, a code was implemented. The SAS macro developed in this paper selects the criteria and alternatives from a SAS dataset and calculates a set of OWA weights. An example is given to illustrate the features of SAS/OWA software. © Springer-Verlag 2009.

Evaluating productive efficiency:comparative study of commercial banks in Gulf countries

Financial institutes are an integral part of any modern economy. In the 1970s and 1980s, Gulf Cooperation Council (GCC) countries made significant progress in financial deepening and in building a modern financial infrastructure. This study aims to evaluate the performance (efficiency) of financial institutes (banking sector) in GCC countries. Since, the selected variables include negative data for some banks and positive for others, and the available evaluation methods are not helpful in this case, so we developed a Semi Oriented Radial Model to perform this evaluation. Furthermore, since the SORM evaluation result provides a limited information for any decision maker (bankers, investors, etc...), we proposed a second stage analysis using classification and regression (C&R) method to get further results combining SORM results with other environmental data (Financial, economical and political) to set rules for the efficient banks, hence, the results will be useful for bankers in order to improve their bank performance and to the investors, maximize their returns. Mainly there are two approaches to evaluate the performance of Decision Making Units (DMUs), under each of them there are different methods with different assumptions. Parametric approach is based on the econometric regression theory and nonparametric approach is based on a mathematical linear programming theory. Under the nonparametric approaches, there are two methods: Data Envelopment Analysis (DEA) and Free Disposal Hull (FDH). While there are three methods under the parametric approach: Stochastic Frontier Analysis (SFA); Thick Frontier Analysis (TFA) and Distribution-Free Analysis (DFA). The result shows that DEA and SFA are the most applicable methods in banking sector, but DEA is seem to be most popular between researchers. However DEA as SFA still facing many challenges, one of these challenges is how to deal with negative data, since it requires the assumption that all the input and output values are non-negative, while in many applications negative outputs could appear e.g. losses in contrast with profit. Although there are few developed Models under DEA to deal with negative data but we believe that each of them has it is own limitations, therefore we developed a Semi-Oriented-Radial-Model (SORM) that could handle the negativity issue in DEA. The application result using SORM shows that the overall performance of GCC banking is relatively high (85.6%). Although, the efficiency score is fluctuated over the study period (1998-2007) due to the second Gulf War and to the international financial crisis, but still higher than the efficiency score of their counterpart in other countries. Banks operating in Saudi Arabia seem to be the highest efficient banks followed by UAE, Omani and Bahraini banks, while banks operating in Qatar and Kuwait seem to be the lowest efficient banks; this is because these two countries are the most affected country in the second Gulf War. Also, the result shows that there is no statistical relationship between the operating style (Islamic or Conventional) and bank efficiency. Even though there is no statistical differences due to the operational style, but Islamic bank seem to be more efficient than the Conventional bank, since on average their efficiency score is 86.33% compare to 85.38% for Conventional banks. Furthermore, the Islamic banks seem to be more affected by the political crisis (second Gulf War), whereas Conventional banks seem to be more affected by the financial crisis.

Multi-criteria logistics distribution network design using SAS/OR

This paper explores the use of the optimization procedures in SAS/OR software with application to the contemporary logistics distribution network design using an integrated multiple criteria decision making approach. Unlike the traditional optimization techniques, the proposed approach, combining analytic hierarchy process (AHP) and goal programming (GP), considers both quantitative and qualitative factors. In the integrated approach, AHP is used to determine the relative importance weightings or priorities of alternative warehouses with respect to both deliverer oriented and customer oriented criteria. Then, a GP model incorporating the constraints of system, resource, and AHP priority is formulated to select the best set of warehouses without exceeding the limited available resources. To facilitate the use of integrated multiple criteria decision making approach by SAS users, an ORMCDM code was implemented in the SAS programming language. The SAS macro developed in this paper selects the chosen variables from a SAS data file and constructs sets of linear programming models based on the selected GP model. An example is given to illustrate how one could use the code to design the logistics distribution network.

Fuzzy data envelopment analysis:a discrete approach

Data envelopment analysis (DEA) as introduced by Charnes, Cooper, and Rhodes (1978) is a linear programming technique that has widely been used to evaluate the relative efficiency of a set of homogenous decision making units (DMUs). In many real applications, the input-output variables cannot be precisely measured. This is particularly important in assessing efficiency of DMUs using DEA, since the efficiency score of inefficient DMUs are very sensitive to possible data errors. Hence, several approaches have been proposed to deal with imprecise data. Perhaps the most popular fuzzy DEA model is based on a-cut. One drawback of the a-cut approach is that it cannot include all information about uncertainty. This paper aims to introduce an alternative linear programming model that can include some uncertainty information from the intervals within the a-cut approach. We introduce the concept of "local a-level" to develop a multi-objective linear programming to measure the efficiency of DMUs under uncertainty. An example is given to illustrate the use of this method.

An integer-valued data envelopment analysis model with bounded outputs

Integer-valued data envelopment analysis (DEA) with alternative returns to scale technology has been introduced and developed recently by Kuosmanen and Kazemi Matin. The proportionality assumption of their introduced "natural augmentability" axiom in constant and nondecreasing returns to scale technologies makes it possible to achieve feasible decision-making units (DMUs) of arbitrary large size. In many real world applications it is not possible to achieve such production plans since some of the input and output variables are bounded above. In this paper, we extend the axiomatic foundation of integer-valuedDEAmodels for including bounded output variables. Some model variants are achieved by introducing a new axiom of "boundedness" over the selected output variables. A mixed integer linear programming (MILP) formulation is also introduced for computing efficiency scores in the associated production set. © 2011 The Authors. International Transactions in Operational Research © 2011 International Federation of Operational Research Societies.

An aggregate measure of financial ratios using a multiplicative DEA model

This paper examines the problems in the definition of the General Non-Parametric Corporate Performance (GNCP) and introduces a multiplicative linear programming as an alternative model for corporate performance. We verified and tested a statistically significant difference between the two models based on the application of 27 UK industries using six performance ratios. Our new model is found to be a more robust performance model than the previous standard Data Envelopment Analysis (DEA) model.

Benefits of retailer-supplier partnership initiatives under time-varying demand:a comparative analytical study

This paper aims to help supply chain managers to determine the value of retailer-supplier partnership initiatives beyond information sharing (IS) according to their specific business environment under time-varying demand conditions. For this purpose, we use integer linear programming models to quantify the benefits that can be accrued by a retailer, a supplier and system as a whole from shift in inventory ownership and shift in decision-making power with that of IS. The results of a detailed numerical study pertaining to static time horizon reveal that the shift in inventory ownership provides system-wide cost benefits in specific settings. Particularly, when it induces the retailer to order larger quantities and the supplier also prefers such orders due to significantly high setup and shipment costs. We observe that the relative benefits of shift in decision-making power are always higher than the shift in inventory ownership under all the conditions. The value of the shift in decision-making power is greater than IS particularly when the variability of underlying demand is low and time-dependent variation in production cost is high. However, when the shipment cost is negligible and order issuing efficiency of the supplier is low, the cost benefits of shift in decision-making power beyond IS are not significant. © 2012 Taylor & Francis.

Fully probabilistic control design in an adaptive critic framework

Optimal stochastic controller pushes the closed-loop behavior as close as possible to the desired one. The fully probabilistic design (FPD) uses probabilistic description of the desired closed loop and minimizes Kullback-Leibler divergence of the closed-loop description to the desired one. Practical exploitation of the fully probabilistic design control theory continues to be hindered by the computational complexities involved in numerically solving the associated stochastic dynamic programming problem. In particular very hard multivariate integration and an approximate interpolation of the involved multivariate functions. This paper proposes a new fully probabilistic contro algorithm that uses the adaptive critic methods to circumvent the need for explicitly evaluating the optimal value function, thereby dramatically reducing computational requirements. This is a main contribution of this short paper.

Multiple criteria optimization of contemporary logistics distribution network problems

In the contemporary customer-driven supply chain, maximization of customer service plays an equally important role as minimization of costs for a company to retain and increase its competitiveness. This article develops a multiple-criteria optimization approach, combining the analytic hierarchy process (AHP) and an integer linear programming (ILP) model, to aid the design of an optimal logistics distribution network. The proposed approach outperforms traditional cost-based optimization techniques because it considers both quantitative and qualitative factors and also aims at maximizing the benefits of deliverer and customers. In the approach, the AHP is used to determine the relative importance weightings or priorities of alternative warehouses with respect to some critical customer-oriented criteria. The results of AHP prioritization are utilized as the input of the ILP model, the objective of which is to select the best warehouses at the lowest possible cost. In this article, two commercial packages are used: including Expert Choice and LINDO.

CAPS in Z(2,n)

We consider point sets in (Z^2,n) where no three points are on a line – also called caps or arcs. For the determination of caps with maximum cardinality and complete caps with minimum cardinality we provide integer linear programming formulations and identify some values for small n.

New Upper Bounds for Some Spherical Codes

The maximal cardinality of a code W on the unit sphere in n dimensions with (x, y) ≤ s whenever x, y ∈ W, x 6= y, is denoted by A(n, s). We use two methods for obtaining new upper bounds on A(n, s) for some values of n and s. We find new linear programming bounds by suitable polynomials of degrees which are higher than the degrees of the previously known good polynomials due to Levenshtein [11, 12]. Also we investigate the possibilities for attaining the Levenshtein bounds [11, 12]. In such cases we find the distance distributions of the corresponding feasible maximal spherical codes. Usually this leads to a contradiction showing that such codes do not exist.

Exact Discriminant Function Design Using Some Optimization Techniques

Some aspects of design of the discriminant functions that in the best way separate points of predefined final sets are considered. The concept is introduced of the nested discriminant functions which allow to separate correctly points of any of the final sets. It is proposed to apply some methods of non-smooth optimization to solve arising extremal problems efficiently.

A mixture density network approach to modelling and exploiting uncertainty in nonlinear control problems

In nonlinear and stochastic control problems, learning an efficient feed-forward controller is not amenable to conventional neurocontrol methods. For these approaches, estimating and then incorporating uncertainty in the controller and feed-forward models can produce more robust control results. Here, we introduce a novel inversion-based neurocontroller for solving control problems involving uncertain nonlinear systems which could also compensate for multi-valued systems. The approach uses recent developments in neural networks, especially in the context of modelling statistical distributions, which are applied to forward and inverse plant models. Provided that certain conditions are met, an estimate of the intrinsic uncertainty for the outputs of neural networks can be obtained using the statistical properties of networks. More generally, multicomponent distributions can be modelled by the mixture density network. Based on importance sampling from these distributions a novel robust inverse control approach is obtained. This importance sampling provides a structured and principled approach to constrain the complexity of the search space for the ideal control law. The developed methodology circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider. A nonlinear multi-variable system with different delays between the input-output pairs is used to demonstrate the successful application of the developed control algorithm. The proposed method is suitable for redundant control systems and allows us to model strongly non-Gaussian distributions of control signal as well as processes with hysteresis. © 2004 Elsevier Ltd. All rights reserved.

Motzkin Decomposable Sets

Theodore Motzkin proved, in 1936, that any polyhedral convex set can be expressed as the (Minkowski) sum of a polytope and a polyhedral convex cone. We have provided several characterizations of the larger class of closed convex sets, Motzkin decomposable, in finite dimensional Euclidean spaces which are the sum of a compact convex set with a closed convex cone. These characterizations involve different types of representations of closed convex sets as the support functions, dual cones and linear systems whose relationships are also analyzed. The obtaining of information about a given closed convex set F and the parametric linear optimization problem with feasible set F from each of its different representations, including the Motzkin decomposition, is also discussed. Another result establishes that a closed convex set is Motzkin decomposable if and only if the set of extreme points of its intersection with the linear subspace orthogonal to its lineality is bounded. We characterize the class of the extended functions whose epigraphs are Motzkin decomposable sets showing, in particular, that these functions attain their global minima when they are bounded from below. Calculus of Motzkin decomposable sets and functions is provided.

Spiral Walk Exposed

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2015