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This special issue of Mathematical Structures in Computer Science contains a selection of papers presented at three satellite events of CONCUR'09, which was held between 31 August and 5 September 2009 in Bologna (Italy). Specifically, it contains three papers from the 16th International Workshop on Expressiveness in Concurrency (EXPRESS'09), one paper from the 2nd Interaction and Concurrency Experience (ICE'09) and two papers from the 6th Workshop on Structural Operational Semantics (SOS'09). [ABSTRACT FROM PUBLISHER]

This paper focuses on the study of optimality conditions (both necessary and sufficient) for a weakly quasi e-Pareto solution to a multiobjective optimization problem by using a minimax programming approach. To establish necessary conditions for approximate solutions of minimax programming problems under a suitable constraint qualification, we use some advanced tools of variational analysis and generalized differentiation. Sufficient conditions for such solutions to the considered problem are also provided by using generalized convex functions defined in terms of the limiting subdifferential for locally Lipschitz functions. In addition, some duality results for minimax programming problems are also provided. [ABSTRACT FROM AUTHOR]

In this paper, a new group of optimization algorithms named Human Strategy Algorithm (HS) is proposed which is inspired by human strategies to problem solving. The main idea of HS is based on human actions to find the problem’s optima by means of accessible instruments. As the environment of an unknown problem assumed to be a black box, it is supposed that the environment of our problem is a dark room occupied by several men named blind men. The main mission of these men is to look for the optimum solution. Each man has at least one instrument as his assistance. Like real life, the instrument might be any tool such as stick, billy, rope, stone, yoyo, sweep. Any instrument by its unique features is suitable in some situations. In fact, this algorithm maps problem space and searches agents to dark room and people, respectively. In this paper, one sample algorithm of the group of human strategy, YOYO Blind Man Algorithm (YOYO-BMA), is introduced which uses yoyos as men’s accessible instruments. The performance of the YOYO-BMA is evaluated on a set of benchmark problems provided for CEC’2010 Special Session and Competition on Large-Scale Global Optimization (Tang et al. 2010). The results show superior performance of proposed algorithm in comparison with others. Moreover, the problem of designing urban traffic network is solve to evaluate the algorithm using a real complex problem. [ABSTRACT FROM AUTHOR]

The aim of this paper is building a mathematical model for Travelling salesman problem (TSP) with multi-objective; the model describes the problem of (TSP) with three objectives (cost, distance, time), Real data were collected with a sample of twenty states of United State of America, Three methods were used (Branch and Bound algorithm, Nearest neighbor and two-way exchange improvement heuristic), The comparison was conducted among results reached. To solve the problem multi-objective of (TSP), The weighted model demonstrated the effectiveness and flexibility to solve real problems of multi-objective (TSP), where it can be said that it is impossible to solve this problem without resorting to multiple -objective mathematical models, In other words, the number of possible rout for the 20 town is {(n -1)! =19! =121645100408832000}, to find the optimal routs among these routs it takes very long time and a lot of effort, here stand out importance of two-way exchange improvement heuristic algorithm, where this rout is satisfactory to the decision maker in terms of cost, distance and time. [ABSTRACT FROM AUTHOR]

Purpose – Simple assembly line balancing problem type 1 is the most studied assembly line problem and many procedures have been proposed to solve it. Ho and Emrouznejad proposed to add a novel set of constrains into a binary integer-programming model that is useful for breaking symmetries between equivalent solutions. The purpose of this paper is to compare this way of breaking symmetries with the usual ones existing in the literature (by means of the objective function and by means of additional constraints) and propose two novel ways of breaking symmetries which improve the existing ones. Design/methodology/approach – For the comparison, the authors solve the well-known benchmark instances. Findings – It was found that the most efficient model is one of the new models which has not been proposed in the literature to date. Moreover, the authors noticed that Ho and Emrouznejad attribute a mathematical model to Patterson and Albracht that is different from the original model proposed by Patterson and Albracht. Originality/value – There is not, in the literature, a comparison between classical and new mathematical models. The authors give an empirical comparison between them, together with two new ones that the authors propose. Moreover, the authors point out the mistake about the attribution model in Ho and Emrouznejad's, work attributing a mathematical model to Patterson and Albracht, with the aim of preventing its possible propagation in future researches. [ABSTRACT FROM AUTHOR]

We focus our study on a discussion of duality relationships of a minimax fractional programming problem with its two types of second-order dual models under the second-order generalized convexity type assumptions. Results obtained in this paper naturally unify and extend some previously known results on minimax fractional programming in the literature. [ABSTRACT FROM AUTHOR]

In this paper, a model of a linear multilevel programming problem with dominated objective functions (LMPPD(l)) is proposed, where multiple reactions of the lower levels do not lead to any uncertainty in the upper-level decision making. Under the assumption that the constrained set is nonempty and bounded, a necessary optimality condition is obtained. Two types of geometric properties of the solution sets are studied. It is demonstrated that the feasible set of LMPPD(l) is neither necessarily composed of faces of the constrained set nor necessarily connected. These properties are different from the existing theoretical results for linear multilevel programming problems. [ABSTRACT FROM AUTHOR]

In this paper, the property of a necessary second-order optimality condition to hold with the same Lagrange multiplier for all critical vectors is investigated. It is limited to nonconvex optimization problems in &IRlig;n with equality and inequality constraints; the Mangasarian-Fromovitz constraint qualification is assumed to hold. A counterexample was given recently by Anitescu. We give some sufficient conditions and we prove that this property holds if n ≤ 2 or if the number of active inequality constraints is at most two. For three active inequality constraints and n = 3, a counterexample is given. [ABSTRACT FROM AUTHOR]

The article features the author's comments on the research paper "A New Product Analysis and Decision Model." The author acknowledges the important applications of the paper for sequential decision theory in the field of management science, but expresses concern as to generalizations made in the text. It is suggested that the demand function component of the mathematical analysis discussed in the paper. The author proposes that the functional analysis overlooks some main difficulties associated with the featured decision making variables. The industrial product development process is discussed. A heuristic programming approach is also examined.

In this paper we present a mathematical programming model for the Kanban system in a deterministic multi-stage capacitated assembly-tree-structure production setting. We discuss solution procedures to the problem and address three special cases of practical interest. [ABSTRACT FROM AUTHOR]

Purchasing managers face a complex problem when determining order quantities for multiple items in the presence of quantity discounts and resource limitations. In this paper, the problem is formulated as a mathematical programming model. An efficient solution algorithm is developed utilizing the Lagrangian relaxation approach. Extensive computational experiments are performed and the results are presented. [ABSTRACT FROM AUTHOR]

This paper points out the abstract similarities between problems arising in programming, discrete systems analysis in engineering, and network flow problems in operations research. The highly developed techniques of analyzing discrete systems of two terminal elements in electrical engineering become applicable to analyzing the complexity and execution time of computer programs. Similarly, the concept of the cost-oriented flows in network flow problems has significance in determining execution times in program segments. The abstract similarities explored in this paper are predicated on the concept of a flowgraph, which is a dual graph of a more traditional view of a computer program as a control graph. This slightly different view- point of computer programs results in the abstract similarity to discrete systems which suggests many new ideas and permits the use of results from the well-developed fields of electrical engineering and operations research. [ABSTRACT FROM AUTHOR]

In a recent paper, Lippman presents sufficient conditions for Denardo's N-stage contraction in discounted semi-Markov decision processes with unbounded rewards. In this note it is demonstrated that Lippman's conditions may be replaced by weaker conditions which even imply l-stage contraction. The verification of the conditions of this note is somewhat easier. [ABSTRACT FROM AUTHOR]

The author responds to the paper "The Loading Problem," by Eilon and Christofides. He focuses on suggesting a solution to the problem. The recommended solution involves a heuristic algorithm that allegedly requires fewer computations than the one proposed by Eilon and Christofides. It is suggested that the simpler algorithm offered by the author reaches mathematical optimization as often as the aforementioned algorithm. It is further proposed that the algorithm presented by Eilon and Christofides cannot be used to solve multi-dimensional programming problems. The author goes on to discuss a numerical analysis that can be used for the allocation of industrial resources. Related mathematical models are discussed in detail. A table comparing the results of the two algorithms is also presented.

A framework of concepts is developed which helps to unify a substantial portion of the literature on large-scale mathematical programming. These concepts fall into two categories. The first category consists of problem manipulations that can be used to derive what are often referred to as "master" problems; the principal manipulations discussed are Projection, Inner Linearization, and Outer Linearization. The second category consists of solution strategies that can be used to solve the master problems, often with the result that "subproblems" arise which can then be solved by specialized algorithms. The Piecewise, Restriction, and Relaxation strategies are the principal ones discussed. Numerous algorithms found in the literature are classified according to the manipulation/strategy pattern they can be viewed as using, and the usefulness of the framework is demonstrated by using it (see Part II of this paper) to rederive a representative selection of algorithms. The material presented is listed in the following order: The first section is introductory in nature, and discusses types of large-scale problems, the scope of discussion and the literature, and the notation used. The second section, entitled "Problem Manipulation: Source of 'Master' Problems" covers the subjects of projection, inner linearization and outer linearization. The third section, "Solution Strategies: Source of 'Subproblems'," discusses piecewise strategy, restriction and relaxation. The fourth section is entitled "Synthesizing Known Algorithms from Manipulations and Strategies," and is followed by a concluding section and an extensive bibliography. [ABSTRACT FROM AUTHOR]

A series of probabilistic models are formulated for the credit granting policy of a firm. First, a single-period analysis is presented for the two-action problem, "give credit or do not give credit." Then a multi-period analysis for the same problem is presented, showing that the single-period analysis ignores important future benefits. The multi-period analysis contains a Bayesian approach to revisions of the probability of collection as collection experience is gained. The multi-period analysis is modified by adding discounting to reflect the time value of money and a probability that the customer will cease purchasing. Next, a dynamic programming formulation of the multi-media problem is presented, and this formulation is then adapted to include a decision on how much credit to offer. The paper closes with a series of remarks concerning the practical application of the analysis. A series of probabilistic models are formulated for the credit granting policy of a firm. First, a single-period analysis is presented for the two-action problem, "give credit or do not give credit." Then a multi-period analysis for the same problem is presented, showing that the single-period analysis ignores important future benefits. The multi-period analysis contains a Bayesian approach to revisions of the probability of collection as collection experience is gained. The multi-period analysis is modified by adding discounting to reflect the time value of money and a probability that the customer will cease purchasing. Next, a dynamic programming formulation of the multi-media problem is presented, and this formulation is then adapted to include a decision on how much credit to offer. The paper closes with a series of remarks concerning the practical application of the analysis. [ABSTRACT FROM AUTHOR]

In this paper the Fiacco-McCormick SUMT technique is embedded in a class of inside-out algorithms. Convergence is demonstrated for the nonlinear programming problem under fairly general conditions and the algorithms are interpreted in a geometric structure. [ABSTRACT FROM AUTHOR]

As interest grows rapidly in industry on the potentialities of mathematical programming techniques, it appears worthwhile to have a paper devoted to some of the more promoting developments which may speed up the transition from interest to use. Three topics have been selected (in three sections that follow) which have recently come into prominence: uncertainty, combinatorial problems, and large scale systems. The reader will find in the course of their dissensions that a survey--though perhaps not a systematic survey--has been made of current techniques in the linear programming field. [ABSTRACT FROM AUTHOR]

Generalized models provide a framework for the study of evolution equations without specifying all functional forms in the defining vector field. The generalized formulation of problems has been shown to facilitate the analytical investigation of local dynamics and has been used successfully to answer applied questions. Yet their potential to facilitate analytical computations has not been realized in the mathematical literature. In the present paper, we introduce the method of generalized modelling in mathematical terms, supporting the key steps of the procedure by rigorous proofs. Further, we point out open questions that are in the scope of present mathematical research and if answered could greatly increase the predictive power of generalized models. [ABSTRACT FROM AUTHOR]

In 2010, Zou et al in [5] paper indicated the lower Bounds on the Minimum eigenvalue of M-matrices. In this paper we first with an example show that this bound is incorrect, and then we exhibit the new and better bound for the Minimum eigenvalue of M-matrices. [ABSTRACT FROM AUTHOR]

Fuzzy logic programming tries to introduce fuzzy logic into logic programming in order to provide new generation computer languages which incorporate comfortable programming resources for helping the development of applications where uncertainty could play an important role. In this sense, the mathematical concept of multi-adjoint lattice has been successfully exploited into the so-called Multi-Adjoint Logic Programming approach, MALP in brief, for modelling flexible notions of truth-degrees beyond the simpler case of true and false. In this paper, we focus on two relevant mathematical concepts for this kind of domains useful for evaluating MALP. On the one side, we adapt the classical notion of Dedekind–MacNeille completion in order to relax some usual hypothesis on such kind of ordered sets, and next we study the advantages of generating multi-adjoint lattices as the Cartesian product of previous ones. On the practical side, we show that the formal mechanisms described before have direct correspondences with interesting debugging tasks into the ‘Fuzzy Logic Programming Environment for Research’, FLOPER in brief, developed in our research group. [ABSTRACT FROM PUBLISHER]

While data envelopment analysis (DEA) models are very sensitive to possible data errors, in many real applications, the data of production processes cannot be precisely measured. Fuzzy DEA is asuccessful method that allows to deal with imprecise data in DEA. In this paper, we develop fuzzy version of the input relaxation model introduced in Jahahshahloo and Khodabakhshi [15] by using some ranking methods based on the comparison of α-cuts. The resulting auxiliary crisp problems can be solved by the usual DEA software. It is shown that, using a numerical example, how the proposed model become specially useful for detecting sensitive decision-making units. [ABSTRACT FROM AUTHOR]

Abstract  In this paper, we study the weighted (x(q + 1), x; 2, q)-minihypers. These are weighted sets of x(q + 1) points in PG(2, q) intersecting every line in at least x points. We investigate the decomposability of these minihypers, and define a switching construction which associates to an (x(q + 1), x; 2, q)-minihyper, with x ≤ q 2 − q, not decomposable in the sum of another minihyper and a line, a (j(q + 1), j; 2, q)-minihyper, where j = q 2 − q − x, again not decomposable into the sum of another minihyper and a line. We also characterize particular (x(q + 1), x; 2, q)-minihypers, and give new examples. Additionally, we show that (x(q + 1), x; 2, q)-minihypers can be described as rational sums of lines. In this way, this work continues the research on (x(q + 1), x; 2, q)-minihypers by Hill and Ward (Des Codes Cryptogr 44:169–196, 2007), giving further results on these minihypers. [ABSTRACT FROM AUTHOR]

A reformulation of a mathematical program is a formulation which shares some properties with, but is in some sense better than, the original program. Reformulations are important with respect to the choice and efficiency of the solution algorithms; furthermore, it is desirable that reformulations can be carried out automatically. Reformulation techniques are widespread in mathematical programming but interestingly they have never been studied under a unified framework. This paper attempts to move some steps in this direction. We define a framework for storing and manipulating mathematical programming formulations and give several fundamental definitions categorizing useful reformulations in essentially four types (opt-reformulations, narrowings, relaxations and approximations). We establish some theoretical results and give reformulation examples for each type. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of frequency-filtering IBLU decompositions that use continued-fraction approximation for the diagonal blocks. This technique allows us to construct efficient frequency-filtering preconditioners for discretizations of elliptic partial differential equations on domains with non-trivial geometries. We prove theoretically for a class of model problems that the application of the proposed preconditioners leads to a convergence rate of up to 1-O(h1/4) of the CG iteration. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this paper is to establish that there exist suitable objective functions for mathematical programming formulations of dynamic user equilibrium assignment in the sense of . Recently, showed that we cannot necessarily calculate a dynamic user equilibrium assignment by minimising the integral over time of Beckmann’s objective function that is widely used to solve for static user equilibrium assignment. In the present paper, two distinct objective functions are presented that result from formulations of assignment either as a variational inequality or as an infinitesimal optimisation: each of these formulations can be solved as a forward dynamic programme. With these formulations and solution approaches, we solve an example based upon Lin and Lo’s one correctly. [Copyright &y& Elsevier]

This paper presents a hybridization of a Constraint Programming (CP) model and search techniques with Local Search (LS) and some ideas borrowed from Genetic Algorithms (GA). The context is the physician rostering problem, whose instances can vary greatly and for which almost no general tool has been developed. It is hoped that the combination of the three techniques will lead to an algorithm that has sufficient flexibility to solve most instances with a small amount of customization. To achieve this goal we also introduce Generic constraints: these constraints are used to model several types of ergonomic constraints that are found amongst physician rostering problems. [ABSTRACT FROM AUTHOR]

We provide a new construction of rationality for cubic fourfolds via Mori's theory and the minimal model program. As an application we present the solution of the Kuznetsov conjecture for d D 42 (the first open case). Our methods also show an explicit connection between the rationality of cubic fourfolds belonging to the first four admissible families Cd with d D 14; 26; 38, and 42 and some birational models of K3 surfaces of degree d contained in well known rational Fano fourfolds. [ABSTRACT FROM AUTHOR]

In a recent paper, Petersen (1990) proposed to relax the convexity assumptions invoked in JL traditional Data Envelopment Analysis (DEA). Unfortunately, the new approach is not consistent with the relaxed assumptions. Also, the efficiency evaluations in input and output spaces are based on different technological assumptions. The aim of this paper is to clarify which assumptions are actually involved and to develop modifications such that the input and output based measures are consistent. In effect, a family of DEA methods based on relaxed convexity assumptions is identified. [ABSTRACT FROM AUTHOR]

The Linear Programming Problem is by far the most widely used optimization model. Its impact on economic and government modeling is immense. The Simplex Method for solving the Linear Programming (LP) Problem, due to George Dantzig, has been an extremely efficient computational tool for almost four decades. The method has been the subject of intense investigations for many years, but some major aspects of its behavior are not fully understood yet. The purpose of this paper is to survey the body of knowledge on the efficiency of the Simplex Method, from both practical and theoretical points of view. Adopting the number of iterations (pivot steps) as the yardstick for efficiency, we survey four aspects of the issue: 1. Reports on practical experience of the method's performance on real-life LP problems. 2. Results on controlled (Monte-Carlo) experiments solving LP problems which were randomly generated according to some predetermined distributions. 3. Complexity results, including theoretical analyses on both upper and lower bounds for the performance of the Simplex as well as non-Simplex algorithms for LP. 4. Results of recent theoretical studies using probabilistic analysis to derive bounds on the average behavior of the Simplex Method. We discuss the consequences and limitations of the various studies. Special emphasis is given to open questions. [ABSTRACT FROM AUTHOR]

Data Envelopment Analysis has now been extensively applied in a range of empirical settings to identify relative inefficiencies, and provide targets for improvements. It accomplishes this by developing peer groups for each unit being operated. The use of categorical variables is an important extension which can improve the peer group construction process and incorporate "on-off" characteristics, e.g., presence of drive-in window or not in a banking network. It relaxes the stringent need for factors to display piecewise constant marginal productivities. In so doing, it substantially strengthens the credibility of the insights obtained. The paper treats the cases when the categorical variable can be controllable or uncontrollable by the manager, for the cases of technical and scale inefficiency. The approach is illustrated using real data. [ABSTRACT FROM AUTHOR]

Multiobjective mathematical programming has been one of the fastest growing areas of OR/MS during the last 15 years. This paper presents: 1. some reasons for the rapidly growing increase in interest in multiobjective mathematical programming. 2. a discussion of the advantages and disadvantages of the three general approaches (articulation of the decision maker's preference structure over the multiple objectives prior to, during, or after the optimization) towards multiobjective mathematical programming, 3. a nontechnical overview of many of the specific solution techniques for multiobjective mathematical programming, and 4. a discussion of important areas for further research. The overview concentrates on those techniques which require an articulation of the decision maker's preference structure either during or after the optimization, since these are the areas where most of the recent research has been conducted. It differs from previous overviews in that, in addition to the timing of the elicited preference information, the techniques are also classified according to the types of decision variables contained in the model (i.e., only continuous decision variables, or at least some discrete decision variables). In addition, the types of preference information (e.g., a ranking of outcomes) required of the various techniques are also discussed. [ABSTRACT FROM AUTHOR]

The decomposition of a finite partially ordered set of elements as a union of chains was considered by Dilworth [2]. Dantzig and Hoffman [1] formulated this problem as a linear programming problem and obtained Dilworth's theorem from duality theory. For some practical applications and for a method to obtain a minimal decomposition see Ford & Fulkerson [3]. In this paper we generalise this problem to the case when the set is not necessarily partially ordered and obtain a method of finding a minimal chain decomposition of the set. [ABSTRACT FROM AUTHOR]

If the constraint matrix of a linear program has special structure it may be possible to speed computation. Techniques have been developed to take advantages of such special structures as generalized networks, generalized upper bounding, and decomposition. For these matrix structures, it is shown in this paper how to extend the techniques to Zangwill's mathematical programming algorithm, the convex simplex method. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for the solution of the knapsack problem. The method involves searching the nodes of a tree along a single branch at a time. The algorithm eliminates the computational drawbacks inherent in the usual branch and bound schemes. [ABSTRACT FROM AUTHOR]

This paper treats a Markov decision problem with an infinite planning horizon and no discounting. This model is analyzed by application, perhaps repeated, of a simple linear program. [ABSTRACT FROM AUTHOR]

Let us consider some particular optimization problem. Most of its data is determined by the economic "environment". However, this environment is evolutive, and may be the subject of an optimization research. The particular problem first considered then appears to be a suboptimization, and its results will be valid only if it is separable from its environment. This point of view can be expressed in mathematical terms by considering a "principal" programming problem from which one tries to separate a "reduced" subproblem. The concept of "separability" is defined and studied in the first part of this paper. In the second part, it is used to justify the "Method of Extended Models" as a tool for building optimization models. [ABSTRACT FROM AUTHOR]

A machine is to be bought, used for productive purposes for a length of time, and then sold. It is possible to do preventive maintenance while the machine is being used, if desired, in order to slow down the degradation of the machine's capability. The value of owning the machine is the sum of the discounted value of its production while it is owned plus its discounted value when sold. In this paper a modification of a model due to B. Naslund for the problem is discussed. Using Pontryagin's maximum principle, the problem is treated as one of optimal control with the control variables being the use or nonuse of preventive maintenance and the selection of the sale date. It is shown that the optimal maintenance policy is bang-bang, and methods for finding the optimal sale date are determined. Simply examples show the various kinds of solutions that can be obtained with varying assumptions concerning the actual functions used in the model. [ABSTRACT FROM AUTHOR]

This paper describes a simple calculation for the assignment and transportation problems which is "dual to" the well-known Hungarian Method. While the Hungarian is a dual method, this method is primal and so gives a feasible assignment at each stage of the calculation. Bounds on the number of steps required for the assignment and transportation problems are given. They are the same as the best bounds known for the Hungarian Method. [ABSTRACT FROM AUTHOR]

Job shop scheduling problem is very important one in real application of many kind of industries. In the real world applications, there exist many different kinds of disruptions with different sizes. In this situation, beyond the optimality of the final solution, its ability to absorb disruptions is vital, so that the final solution remains feasible in the case of occurring predicted disruptions. In this paper a robust job shop scheduling problem under disruptions is considered. It is intended to generate robust schedules which are able to absorb a predefined range of disruptions. For this reason, two robustness indices are proposed and the related formulas for computing the required buffer times to reach the desired robustness level are proposed. For this purpose, four methods are proposed to solve the variant defined robust job shop scheduling problem, including (1) a mathematical model, (2) a Branch and Bound algorithm, (3) a beam search algorithm, and (4) a meta-heuristic algorithm based on the particle swarm optimization (PSO) method. The first and second methods result in optimum solution. As the size of the problem increases, the required time to find the optimum solutions raises, so that no solutions can be achieved in rational amount of time, e.g. one hour. Therefore, the third and fourth methods are proposed to find good solutions even for large-scale problem in a limited amount of time. Finally, the algorithms are compared using some randomly generated instances. The results show that each algorithm can outperform the others in different conditions. [ABSTRACT FROM AUTHOR]

The object of the present paper is to study a Kenmotsu manifold admitting Ricci solitons and gradient Ricci solitons. [ABSTRACT FROM AUTHOR]

In a variety of discrete manufacturing environments, it is common to experience a nonlinear production rate. In particular, our interest is in the case of an increasing production rate, where learning creates efficiencies. This leads to greater output per unit time as the process continues. However, the advantages of an increasing production rate may be offset by other factors. For examples, JIT policies typically lead to smaller lot sizes, where the value of an increasing production rate is largely lost. We develop a general model that balances the impact of various competing effects. Our research focuses on determining lot sizes that satisfy demand requirements while minimising production and holding costs. We extend our prior work by developing a multi-product, multi-machine method for modelling and solving this class of production problems. The solution method is demonstrated using the production function from the PR#2 grinding process for a production plant in Carlisle, PA. The solution heuristic provides solution times that are on average only 0.22 to 0.55% above optimum as the solution parameters are varied and the ratio of heuristic solution times to optimal solution times varies from 18.16 to 14.15%. [ABSTRACT FROM AUTHOR]

We give a logic-independent semantics for predefined (data) types within the categorical abstract model theoretic framework of the theory of institutions. We develop a generic interpolation result for this semantics, which can be easily applied to various concrete situations from the theory and practice of specification and programming. Our study of interpolation is motivated by a number of important applications to computing science, especially in the area of structured specifications. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, new parametric prioritization methods (PPMs) to determine a family of priority vectors in an analytical hierarchy process (AHP) are proposed, pointing out the logical relation of elements in the comparative matrix. The scales and consistency cannot determine the priorities, but only the order of the alternatives. To derive the priorities of alternatives, a series of theorems and mathematical programming models is given based on a pairwise comparison matrix. This refers to parameters , by which there exists a family of priorities for the same judgment matrix. The discrimination of alternatives can be easily improved when using the proposed priority method by modifying the values of the parameters. Some false cognitions about how to determine the priority of an analytical hierarchy process are rectified. One should not elicit priority vectors from the judgment matrix; the information is incomplete, and the parameters must be considered. Finally, the meanings of parameters are explained in practical applications and an approach for determining the values of the parameters is proposed. Examples are also used to illustrate the features and applicability of the new approach in an AHP. [Copyright &y& Elsevier]

A new approach for obtaining the second order sufficient conditions for non-linear mathematical programming problems which makes use of second order derivative is presented. In the so-called second order η-approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order η-approximation of both the objective function and the constraint function constituting the original problem. The equivalence between the nonlinear original mathematical programming problem and its associated second order η-approximated optimization problem is established under second order invexity assumption imposed on the functions constituting the original optimization problem. [ABSTRACT FROM AUTHOR]

Abstract: Certain omissions have been pointed out in some papers on symmetric duality in multiobjective programming. Corrective measures have also been discussed. [Copyright &y& Elsevier]

Abstract: k-Restricted edge connectivity is an important parameter in measuring the reliability and fault tolerance of large interconnection networks. In this paper we present two families of graphs similar with the networks proposed by Chen et al. [Y.C. Chen, J.J.M. Tan, L.H. Hsu, S.S. Kao, Super-connectivity and super edge-connectivity for some interconnection networks, Applied Mathematics and Computation 140 (2003) 245–254] and study the -restricted edge connectivity of these graphs. In particular, as the applications of our results, the -restricted edge connectivity of the recursive circulant graphs and the n-ary k-cubes is given. [Copyright &y& Elsevier]

Abstract: In this paper, we obtained rich solutions for the discrete complex cubic Ginzburg–Landau equation by means of the extended tanh-function approach. These solutions include chirpless bright soliton, chirpless dark soliton, triangular function solutions and some solutions with alternating phases, and so on. Meanwhile, the range of parameters where some exact solution exists is given. [Copyright &y& Elsevier]