A feasibility conjecture related to the Hirsch conjecture.

Photocopy. [Washington?] Clearinghouse for Federal Scientific and Technical Information of the U. S. Dept. of Commerce [1966?]

Density evolution and power profile optimization for iterative multiuser decoders based on individually optimum multiuser detectors

Iterative multiuser joint decoding based on exact Belief Propagation (BP) is analyzed in the large system limit by means of the replica method. It is shown that performance can be improved by appropriate power assignment to the users. The optimum power assignment can be found by linear programming in most technically relevant cases. The performance of BP iterative multiuser joint decoding is compared to suboptimum approximations based on Interference Cancellation (IC). While IC receivers show a significant loss for equal-power users, they yield performance close to BP under optimum power assignment.

Selecting the most preferable alternatives in a group decision making problem using DEA

Group decision making is the study of identifying and selecting alternatives based on the values and preferences of the decision maker. Making a decision implies that there are several alternative choices to be considered. This paper uses the concept of Data Envelopment Analysis to introduce a new mathematical method for selecting the best alternative in a group decision making environment. The introduced model is a multi-objective function which is converted into a multi-objective linear programming model from which the optimal solution is obtained. A numerical example shows how the new model can be applied to rank the alternatives or to choose a subset of the most promising alternatives.

An extended minimax disparity to determine the OWA operator weights

This paper contributes to extend the minimax disparity to determine the ordered weighted averaging (OWA) model based on linear programming. It introduces the minimax disparity approach between any distinct pairs of the weights and uses the duality of linear programming to prove the feasibility of the extended OWA operator weights model. The paper finishes with an open problem. © 2006 Elsevier Ltd. All rights reserved.

A note on DEA models in technology selection:an improvement of Karsak and Ahiska's approach

This paper introduces a compact form for the maximum value of the non-Archimedean in Data Envelopment Analysis (DEA) models applied for the technology selection, without the need to solve a linear programming (LP). Using this method the computational performance the common weight multi-criteria decision-making (MCDM) DEA model proposed by Karsak and Ahiska (International Journal of Production Research, 2005, 43(8), 1537-1554) is improved. This improvement is significant when computational issues and complexity analysis are a concern.

PCB assembly line assignment:a genetic algorithm approach

Purpose – This paper sets out to study a production-planning problem for printed circuit board (PCB) assembly. A PCB assembly company may have a number of assembly lines for production of several product types in large volume. Design/methodology/approach – Pure integer linear programming models are formulated for assigning the product types to assembly lines, which is the line assignment problem, with the objective of minimizing the total production cost. In this approach, unrealistic assignment, which was suffered by previous researchers, is avoided by incorporating several constraints into the model. In this paper, a genetic algorithm is developed to solve the line assignment problem. Findings – The procedure of the genetic algorithm to the problem and a numerical example for illustrating the models are provided. It is also proved that the algorithm is effective and efficient in dealing with the problem. Originality/value – This paper studies the line assignment problem arising in a PCB manufacturing company in which the production volume is high.

A multi-depot travelling salesman problem and its iterative and integrated approaches

This paper formulates a logistics distribution problem as the multi-depot travelling salesman problem (MDTSP). The decision makers not only have to determine the travelling sequence of the salesman for delivering finished products from a warehouse or depot to a customer, but also need to determine which depot stores which type of products so that the total travelling distance is minimised. The MDTSP is similar to the combination of the travelling salesman and quadratic assignment problems. In this paper, the two individual hard problems or models are formulated first. Then, the problems are integrated together, that is, the MDTSP. The MDTSP is constructed as both integer nonlinear and linear programming models. After formulating the models, we verify the integrated models using commercial packages, and most importantly, investigate whether an iterative approach, that is, solving the individual models repeatedly, can generate an optimal solution to the MDTSP. Copyright © 2006 Inderscience Enterprises Ltd.

On the solution of a class of capital investment problems

In this work the solution of a class of capital investment problems is considered within the framework of mathematical programming. Upon the basis of the net present value criterion, the problems in question are mainly characterized by the fact that the cost of capital is defined as a non-decreasing function of the investment requirements. Capital rationing and some cases of technological dependence are also included, this approach leading to zero-one non-linear programming problems, for which specifically designed solution procedures supported by a general branch and bound development are presented. In the context of both this development and the relevant mathematical properties of the previously mentioned zero-one programs, a generalized zero-one model is also discussed. Finally,a variant of the scheme, connected with the search sequencing of optimal solutions, is presented as an alternative in which reduced storage limitations are encountered.

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.

The development of a solid waste management strategy

This research is concerned with the application of operational research techniques in the development of a long- term waste management policy by an English waste disposal authority. The main aspects which have been considered are the estimation of future waste production and the assessment of the effects of proposed systems. Only household and commercial wastes have been dealt with in detail, though suggestions are made for the extension of the effect assessment to cover industrial and other wastes. Similarly, the only effects considered in detail have been costs, but possible extensions are discussed. An important feature of the study is that it was conducted in close collaboration with a waste disposal authority, and so pays more attention to the actual needs of the authority than is usual in such research. A critical examination of previous waste forecasting work leads to the use of simple trend extrapolation methods, with some consideration of seasonal effects. The possibility of relating waste production to other social and economic indicators is discussed. It is concluded that, at present, large uncertainties in predictions are inevitable; waste management systems must therefore be designed to cope with this uncertainty. Linear programming is used to assess the overall costs of proposals. Two alternative linear programming formulations of this problem are used and discussed. The first is a straightforward approach, which has been .implemented as an interactive computer program. The second is more sophisticated and represents the behaviour of incineration plants more realistically. Careful attention is paid to the choice of appropriate data and the interpretation of the results. Recommendations are made on methods for immediate use, on the choice of data to be collected for future plans, and on the most useful lines for further research and development.

Aircraft rotable inventory optimisation: development of a new solution

Analysis of the use of ICT in the aerospace industry has prompted the detailed investigation of an inventory-planning problem. There is a special class of inventory, consisting of expensive repairable spares for use in support of aircraft operations. These items, called rotables, are not well served by conventional theory and systems for inventory management. The context of the problem, the aircraft maintenance industry sector, is described in order to convey some of its special characteristics in the context of operations management. A literature review is carried out to seek existing theory that can be applied to rotable inventory and to identify a potential gap into which newly developed theory could contribute. Current techniques for rotable planning are identified in industry and the literature: these methods are modelled and tested using inventory and operational data obtained in the field. In the expectation that current practice leaves much scope for improvement, several new models are proposed. These are developed and tested on the field data for comparison with current practice. The new models are revised following testing to give improved versions. The best model developed and tested here comprises a linear programming optimisation, which finds an optimal level of inventory for multiple test cases, reflecting changing operating conditions. The new model offers an inventory plan that is up to 40% less expensive than that determined by current practice, while maintaining required performance.

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.

Applied operational research with SAS

Using a wide range of operational research (OR) optimization examples, Applied Operational Research with SAS demonstrates how the OR procedures in SAS work. The book is one of the first to extensively cover the application of SAS procedures to OR problems, such as single criterion optimization, project management decisions, printed circuit board assembly, and multiple criteria decision making. The text begins with the algorithms and methods for linear programming, integer linear programming, and goal programming models. It then describes the principles of several OR procedures in SAS. Subsequent chapters explain how to use these procedures to solve various types of OR problems. Each of these chapters describes the concept of an OR problem, presents an example of the problem, and discusses the specific procedure and its macros for the optimal solution of the problem. The macros include data handling, model building, and report writing. While primarily designed for SAS users in OR and marketing analytics, the book can also be used by readers interested in mathematical modeling techniques. By formulating the OR problems as mathematical models, the authors show how SAS can solve a variety of optimization problems.

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.

Structural optimization

The non-linear programming algorithms for the minimum weight design of structural frames are presented in this thesis. The first, which is applied to rigidly jointed and pin jointed plane frames subject to deflexion constraints, consists of a search in a feasible design space. Successive trial designs are developed so that the feasibility and the optimality of the designs are improved simultaneously. It is found that this method is restricted lo the design of structures with few unknown variables. The second non-linear programming algorithm is presented .in a general form. This consists of two types of search, one improving feasibility and the other optimality. The method speeds up the 'feasible direction' approach by obtaining a constant weight direction vector that is influenced by dominating constraints. For pin jointed plane and space frames this method is used to obtain a 'minimum weight' design which satisfies restrictions on stresses and deflexions. The matrix force method enables the design requirements to be expressed in a general form and the design problem is automatically formulated within the computer. Examples are given to explain the method and the design criteria are extended to include member buckling. Fundamental theorems are proposed and proved to confirm that structures are inter-related. These theorems are applicable to linear elastic structures and facilitate the prediction of the behaviour of one structure from the results of analysing another, more general, or related structure. It becomes possible to evaluate the significance of each member in the behaviour of a structure and the problem of minimum weight design is extended to include shape. A method is proposed to design structures of optimum shape with stress and deflexion limitations. Finally a detailed investigation is carried out into the design of structures to study the factors that influence their shape.