A general approach for optimizing regular criteria in the job-shop scheduling problem

Even though a very large number of solution methods has been developed for the job-shop scheduling problem, a majority has been designed for the makespan criterion. In this paper, we propose a general approach for optimizing any regular criterion in the job-shop scheduling problem. The approach is a local search method that uses a disjunctive graph model and neighborhoods generated by swapping critical arcs. The connectivity property of the neighborhood structure is proved and a novel efficient method for evaluating moves is presented. Besides its generality, another prominent advantage of the proposed approach is its simple implementation that only requires to tune the range of one parameter. Extensive computational experiments carried out on various criteria (makespan, total weighted flow time, total weighted tardiness, weighted sum of tardy jobs, maximum tardiness) show the efficiency of the proposed approach. Best results were obtained for some problem instances taken from the literature.     

The multiple judge,multiple criteria ranking problem: A fuzzy set approach

This paper investigates the problem of selecting, from a set of issues, those which best satisfy a collection of criteria. A group of judges have fuzzy sets defined over the issues, for each criterion, whose values lie in a finite linearly ordered set $\text{L}$. These judges also have fuzzy sets defined over the set of criteria. The paper discusses methods of aggregating all the fuzzy sets into one fuzzy set μ, defined on the issues, so that μA?L gives the final ranking for issue A.     

A discrete dynamic convexized method for the max-cut problem

The max-cut problem is a classical NP-hard problem in graph theory. In this paper, we adopt a local search method, called MCFM, which is a simple modification of the Fiduccia-Mattheyses heuristic method in Fiduccia and Mattheyses (Proc. ACM/IEEE DAC, pp. 175?C181, 1982) for the circuit partitioning problem in very large scale integration of circuits and systems. The method uses much less computational cost than general local search methods. Then, an auxiliary function is presented which has the same global maximizers as the max-cut problem. We show that maximization of the function using MCFM can escape successfully from previously converged discrete local maximizers by taking increasing values of a parameter. An algorithm is proposed for the max-cut problem, by maximizing the auxiliary function using MCFM from random initial solutions. Computational experiments were conducted on three sets of standard test instances from the literature. Experimental results show that the proposed algorithm is effective for the three sets of standard test instances.     

A remark on max-cut problem with an application to digital-analogue convertors

We introduce notions of a distance-decreasing weight function and of an alternating cut. For a class of distance-decreasing weights we solve the max-cut problem. In general, we prove that alternating cuts are near optimal. This has application to digital-analogue convertors.     

A Bayesian-martingale approach to the general disorder problem

We consider a Bayesian-martingale approach to the general change-point detection problem. In our setting the change-point represents a random time of bifurcation of two probability measures given on the space of right-continuous functions. We derive a reflecting backward stochastic differential equation (RBSDE) for the value process related to the disorder problem and show that in classical cases of the Wiener and Poisson disorder problems this RBSDE is equivalent to free-boundary problems for parabolic differential and differential–difference operators respectively.     

A multiple criteria approach to data envelopment analysis

In this paper, we present a Multiple Criteria Data Envelopment Analysis (MCDEA) model which can be used to improve discriminating power of DEA methods and also effectively yield more reasonable input and output weights without a priori information about the weights. In the proposed model, several different efficiency measures, including classical DEA efficiency, are defined under the same constraints. Each measure serves as a criterion to be optimized. Efficiencies are then evaluated under the framework of multiple objective linear programming (MOLP). The method is illustrated through three examples in which data sets are taken from previous research on DEA's discriminating power and weight restriction.     

A visual interactive method for solving the multiple criteria problem

This paper proposes a new method for solving multiple criteria mathematical programming problems. The method does not rely on explicit knowledge of the properties of the utility function. However, if the utility function is assumed to be pseudoconcave and differentiable when the procedure terminates, sufficient conditions for optimality can be established.The method has some features in common with the well-known GDF method of Geoffrion, Dyer and Feinberg (1972). However, our method operates solely in terms of efficient solutions contrary to the GDF method. Moreover, the original procedure of the GDF method for solving the direction-finding problem has been abandoned, since it has turned out that it is not very workable in practice. Instead, the idea of using reference goals or aspiration levels, originated by Wierzbicki, is utilized for determining a direction of improvement. The step-size problem is dealt with in a manner analogous to the GDF method. Computer graphics are used as an aid in solving the step-size problem.The method is easy to implement and convenient to use. Any standard LP package with a parametric optimization routine can be used. In addition, a graphical display device is required.     

A multiple criteria decision-making approach for the selection of stocks

A fundamental principle of modern portfolio theory is that portfolio selectiondecisions are generally made using two criteria, corresponding to the first twomoments of return distributions, namely the expected returnportfolio variance.One criticism over this theory, which has often been addressed both bypractitioners and academics, is that it fails to embody all thedecision-maker's objectives, through the various stages of the decisionprocess. The aim of this paper is to present an alternative methodologicalapproach for modeling one of the most crucial phases of the portfolio managementprocess, the security selection phase. The main characteristic of the proposedapproach is that it fully takes into account the inherent multi-dimensionalnature of the problem, although allowing the decision-maker to incorporate hispreferences in the decision process. The validity of the proposed approach istested through an illustrative application in Athens Stock Exchange. Besides, adetailed categorized bibliography is provided, relative to the application ofthe techniques of multiple criteria decision making to the problems and issuesof portfolio management.     

A time-dependent multiple criteria single-machine scheduling problem

We introduce a nonpreemptive single-machine scheduling model with time-dependent multiple criteria. We formulate the problem as a knapsack problem and propose a dynamic programming (DP)-based algorithm to finding all efficient schedules. An illustrative example is enclosed.     

Generalised 2-circulant inequalities for the max-cut problem

The max-cut problem is a fundamental combinatorial optimisation problem, with many applications. Poljak and Turzik found some facet-defining inequalities for the associated polytope, which we call 2-circulant inequalities. We present a more general family of facet-defining inequalities, an exact separation algorithm that runs in polynomial time, and some computational results.     

A general approach to nonlinear multiple control problems with perturbation consideration

In this paper, we consider a general nonlinear optimal control problem involving multiple criteria. We show that the problem can be transformed into a standard optimal control problem, and hence, is solvable by conventional techniques. However, the optimal control so obtained is of open loop nature and is rather sensitive to perturbations. Based on the first-order approximation, neighboring extremal approach is used to obtain a local linear feedback correction control law, leading to a combined controller. Two numerical examples are solved using the proposed method to demonstrate the effectiveness of the combined control.     

An extreme-distance approach to multiple criteria ranking

A distance approach based on extreme points, or predefined ideal and anti-ideal points, is proposed to improve on the TOPSIS (Technique for Order Performance [or Ordered Preference] by Similarity to Ideal Solution) method of multiple criteria ranking. Two case studies demonstrate how the analysis procedure works, and provide a basis for comparison of the proposed method to the original TOPSIS and similar methods. In applications, the new method produces results that are generally consistent with the original technique, but offers new features such as a clear interpretation of extreme points, more flexibility in setting extreme points, no normalization distortion, and the ability to handle non-monotonic criteria.     

Novel stability criteria for neutral systems with multiple time delays

Based on the eigenvalues of characteristic equations, some new criteria are derived to ensure the asymptotic stability for a class of neutral differential equations with multiple time delays. Conditions obtained here are independent of the time delays and easy to be checked. When suitable f_j(·) (j = 1, 2, … , m) are chosen, the model studied in this paper will reduce to a simple form. Moreover, our results can resolve some nonlinear neutral problems which are seldom discussed. Finally, an example with numerical simulation is given to show the effectiveness of our method.     

A visual interactive approach for multiple criteria decision making with monotone utility functions

We consider the problem of choosing the best of a set of alternatives where each alternative is evaluated on multiple criteria. We develop a visual interactive approach assuming that the decision maker (DM) has a general monotone utility function. The approach partitions the criteria space into nonoverlapping cells. The DM uses various graphical aids to move between cells and to further manipulate selected cells with the goal of creating cells that have ideal points less preferred than an alternative. When the DM identifies such cells, all alternatives in those cells are eliminated from further consideration. The DM may also compare pairs of alternatives. The approach terminates with the most preferred alternative of the DM.     

A visual reference direction approach to solving discrete multiple criteria problems

In this paper, we propose a new visual interactive method for solving discrete multiple criteria problems. The method is based on the use of a reference direction, which is determined by the aspiration levels for the criteria specified by the decision maker. The reference direction is projected onto the set of efficient alternatives. A subset found in this way is presented to a decision maker in a visual form using computer graphics. He can choose any efficient alternatives he pleases.We need notmake any assumptions about the properties of the utility function.The method has been implemented on an IBM/PC1 microcomputer. The name of the program is Vimda (a Visual Interactive Method for Discrete Alternatives).     

A multiple objective goal programming approach to the truckload routing problem

Truckload (TL) routing has always been a challenge. The TL routing problem (TRP) itself is hard, but the complexity of solving the problem increases due to the stochastic nature of TL demand. It is traditionally approached using single objective solution methodologies that range from linear programming to dynamic programming techniques. This paper presents a deterministic multiple objective formulation of the TRP. A ‘route algebra’ is developed to facilitate the solution procedure, paving the way for the use of goal programming and tabu search techniques.     

A multiple criteria socio-technical approach for the Portuguese Army Special Forces recruitment

4OR - Cat-SD (Categorization by Similarity-Dissimilarity) is a method developed for handling nominal classification problems in the context of Multiple Criteria Decision Aiding (MCDA). This paper...