minimizing total tardiness on one machine is np hard the problem of minimizing the total tardiness for a set of independent jobs on one machine is considered lawler has given a pseudo polynomial time algorithm to solve this problem in spite of extensive research efforts for more than a decade the question of whether it can be solved in polynomial time or it is np hard in the ordinary sense remained open in this paper the problem is shown to be np hard in the ordinary sense

scheduling orders for multiple product types with due date related objectives abstract we consider m machines in parallel with each machine capable of producing one specific product type there are n orders with each one requesting specific quantities of the various different product types order j has a release date rj and a due date dj the different product types for order j can be produced at the same time we consider various due date related objectives such as the minimization of the maximum lateness lmax and the total number of late orders u j we present polynomial time algorithms for the easy cases and heuristics for np hard cases for minimizing u j we also propose an exact algorithm based on constraint propagation and bounding strategy the effectiveness of the algorithms is demonstrated through an empirical study

scheduling problems with two competing agents to minimize minmax and minsum earliness measures abstract a relatively new class of scheduling problems consists of multiple agents who compete on the use of a common processor we focus in this paper on a two agent setting each of the agents has a set of jobs to be processed on the same processor and each of the agents wants to minimize a measure which depends on the completion times of its own jobs the goal is to schedule the jobs such that the combined schedule performs well with respect to the measures of both agents we consider measures of minmax and minsum earliness specifically we focus on minimizing maximum earliness cost or total weighted earliness cost of one agent subject to an upper bound on the maximum earliness cost of the other agent we introduce a polynomial time solution for the minmax problem and prove np hardness for the weighted minsum case the unweighted minsum problem is shown to have a polynomial time solution

minimizing total tardiness in permutation flowshops we consider the permutation flowshop scheduling problem with the objective of minimizing total tardiness presented are several properties that are used to calculate lower bounds on total tardiness of jobs for a given partial sequence and to identify sequences dominated by others we develop a branch and bound algorithm using these bounds and a dominance rule results of computational experiments on randomly generated problems are reported

a note on the equivalence of two heuristics to minimize total tardiness abstract over the last thirty years many researchers have studied single machine static and deterministic scheduling with the objective of minimizing total tardiness it has been established that the tardiness problem is np hard so it is unlikely that a polynomial time algorithm can be found for developing optimal solutions to this problem the modified due date rule mdd is generally considered to be an efficient heuristic that deals with the tardiness problem recently panwalkar et al have proposed the psk rule as effective in dealing with tardiness the purpose of this paper is to show that the psk rule is an implementation of the mdd rule furthermore the relationship between the mdd rule and the wi wilkeson and irwin rule is clarified

asymptotic equivalence of spectral density estimation and gaussian white noise we consider the statistical experiment given by a sample y 1 y n of a stationary gaussian process with an unknown smooth spectral density f asymptotic equivalence in the sense of le cam s deficiency distance to two gaussian experiments with simpler structure is established the first one is given by independent zero mean gaussians with variance approximately f i where i is a uniform grid of points in nonparametric gaussian scale regression this approximation is closely related to well known asymptotic independence results for the periodogram and corresponding inference methods the second asymptotic equivalence is to a gaussian white noise model where the drift function is the log spectral density this represents the step from a gaussian scale model to a location model and also has a counterpart in established inference methods that is log periodogram regression the problem of simple explicit equivalence maps markov kernels allowing to directly carry over inference appears in this context but is not solved here

scheduling on parallel identical machines to minimize total tardiness this paper focuses on the problem of scheduling n independent jobs on m identical parallel machines for the objective of minimizing total tardiness of the jobs we develop dominance properties and lower bounds and develop a branch and bound algorithm using these properties and lower bounds as well as upper bounds obtained from a heuristic algorithm computational experiments are performed on randomly generated test problems and results show that the algorithm solves problems with moderate sizes in a reasonable amount of computation time

saddlepoint approximations for short and long memory time series a frequency domain approach abstract saddlepoint techniques provide numerically accurate small sample approximations to the distribution of estimators and test statistics except for a few simple models these approximations are not available in the framework of stationary time series we contribute to fill this gap under short or long range serial dependence for gaussian and non gaussian processes we show how to derive and implement saddlepoint approximations for two relevant classes of frequency domain statistics ratio statistics and whittle s estimator we compare our new approximations to the ones obtained by the standard asymptotic theory and by two widely applied bootstrap methods the numerical exercises for whittle s estimator show that our approximations yield accuracy s improvements while preserving analytical tractability a real data example concludes the paper

central limit theorem for fourier transforms of stationary processes we consider asymptotic behavior of fourier transforms of stationary ergodic sequences with finite second moments we establish a central limit theorem clt for almost all frequencies and also an annealed clt the theorems hold for all regular sequences our results shed new light on the foundation of spectral analysis and on the asymptotic distribution of periodogram and it provides a nice blend of harmonic analysis theory of stationary processes and theory of martingales

effective integration of the nonlinear vector schrodinger equation abstract a comprehensive algebro geometric integration of the two component nonlinear vector schrodinger equation manakov system is developed the allied spectral variety is a trigonal riemann surface which is described explicitly and the solutions of the equations are given in terms of functions of the surface the final formulae are effective in the sense that all entries like transcendental constants in exponentials winding vectors etc are expressed in terms of the prime form of the curve and well algorithmized operations on them that made the result available for direct calculations in applied problems implementing the manakov system the simplest solutions in jacobian functions are given as a particular case of general formulae and are discussed in detail

the single machine total tardiness scheduling problem review and extensions abstract we review the latest theoretical developments for the single machine total tardiness 1 t scheduling problem and propose extensions to some of them we also review and in some cases extend exact algorithms fully polynomial time approximation schemes heuristic algorithms special cases and generalizations of the 1 t problem our findings indicate that the 1 t problem continues to attract significant research interest from both a theoretical and a practical perspective even though the problem is ordinary np hard the current state of the art algorithms are capable of solving problems with up to 500 jobs

single machine scheduling under the job rejection constraint in this paper we consider single machine scheduling problems under the job rejection constraint a job is either rejected in which case a rejection penalty has to be paid or accepted and processed on the single machine however the total rejection penalty of the rejected jobs cannot exceed a given upper bound the objective is to find a schedule such that a given criterion f is minimized where f is a non decreasing function on the completion times of the accepted jobs we analyze the computational complexities of the problems for distinct objective functions and present pseudo polynomial time algorithms in addition we provide a fully polynomial time approximation scheme for the makespan problem with release dates for other objective functions related to due dates we point out that there is no approximation algorithm with a bounded approximation ratio

a necessary and sufficient condition for asymptotic independence of discrete fourier transforms under short and long range dependence let x t be a stationary time series and let d t denote the discrete fourier transform dft of x 0 x t 1 with a data taper the main results of this paper provide a characterization of asymptotic independence of the dfts in terms of the distance between their arguments under both short and long range dependence of the process x t further asymptotic joint distributions of the dfts d t 1t and d t 2t are also established for the cases t 1t 2t o 1 as t asymptotically close ordinates and t 1t 2t as t asymptotically distant ordinates some implications of the main results on the estimation of the index of dependence are also discussed

isospectral hamiltonian flows in finite and infinite dimensions the approach to isospectral hamiltonian flow introduced in part i is further developed to include integration of flows with singular spectral curves the flow on finite dimensional ad invariant poisson submanifolds of the dual widetilde gl r of the positive part of the loop algebra widetilde gl r is obtained through a generalization of the standard method of linearization on the jacobi variety of the invariant spectral curves these curves are embedded in the total space of a line bundlet p1 c allowing an explicit analysis of singularities arising from the structure of the image of a moment map tilde j r m n r times m n r to widetilde gl r from the space of rank r deformations of a fixedn n matrixa it is shown how the linear flow of line bundles e t to tilde s over a suitably desingularized curve tilde s may be used to determine both the flow of matricial polynomialsl and the hamiltonian flow in the spacemn r mn r in terms of functions the resulting flows are proved to be completely integrable the reductions to subalgebras developed in part i are shown to correspond to invariance of the spectral curves and line bundles e t to tilde s under certain linear or anti linear involutions the integration of two examples from part i is given to illustrate the method the rosochatius system and the cnls coupled non linear schrodinger equation

a tabu search algorithm for the single machine total weighted tardiness problem abstract in this study a tabu search ts approach to the single machine total weighted tardiness problem smtwt is presented the problem consists of a set of independent jobs with distinct processing times weights and due dates to be scheduled on a single machine to minimize total weighted tardiness the theoretical foundation of single machine scheduling with due date related objectives reveal that the problem is np hard rendering it a challenging area for meta heuristic approaches this paper presents a totally deterministic ts algorithm with a hybrid neighborhood and dynamic tenure structure and investigates the strength of several candidate list strategies based on problem specific characteristics in increasing the efficiency of the search the proposed ts approach yields very high quality results for a set of benchmark problems obtained from the literature

asymptotic spectral theory for nonlinear time series we consider asymptotic problems in spectral analysis of stationary causal processes limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given instead of the commonly used strong mixing conditions in our asymptotic spectral theory we impose conditions only involving conditional moments which are easily verifiable for a variety of nonlinear time series

weighted tardiness scheduling on parallel machines with proportional weights in this paper we address the problem of scheduling a number of jobs on a bank of parallel machines to minimize the total weighted tardiness under the assumption that the weight of each job is proportional to its processing time the version of the problem that has general weights has been shown to be strongly np complete we prove this version of the problem to be np complete and give a pseudopolynomial time algorithm for solving it we study a family of simple sequencing rules in which the jobs are sequenced in increasing order of i di pi where di is the due date of job i pi its processing time wi its weight and 0 1 this family of sequencing rules generalizes the earliest due date sequencing rule we obtain bounds on the ratio c c iwipi where c and c are the costs of the heuristic and optimal schedules respectively the denominator is the cost of having each job be late by its own processing time it is intended to measure what is or is not a large deviation from optimali

quasiperiodic solutions for matrix nonlinear schrodinger equations the adler kostant symes theorem yields isospectral hamiltonian flows on the dual erm g of a lie subalgebra erm g of a loop algebra erm g a general approach relating the method of integration of krichever novikov and dubrovin to such flows is used to obtain finite gap solutions of matrix nonlinear schrodinger equations in terms of quotients of functions

a possibilistic approach to sequencing problems with fuzzy parameters in this paper a possibilistic approach to sequencing is proposed for each parameter whose value is not precisely known a possibility distribution is given the objective is to calculate a sequence of jobs for which the possibility necessity of delays of jobs is minimal five sequencing problems are formulated and the computational complexity of all of them is explored

affine lie algebraic origin of constrained kp hierarchies an affine sl n 1 algebraic construction of the basic constrained kp hierarchy is presented this hierarchy is analyzed using two approaches namely linear matrix eigenvalue problem on hermitian symmetric space and constrained kp lax formulation and it is shown that these approaches are equivalent the model is recognized to be the generalized non linear schrodinger gnls hierarchy and it is used as a building block for a new class of constrained kp hierarchies these constrained kp hierarchies are connected via similarity backlund transformations and interpolate between gnls and multi boson kp toda hierarchies our construction uncovers the origin of the toda lattice structure behind the latter hierarchy

some new efficient methods to solve the n 1 ri ϵti scheduling problem abstract in this paper we prove a sufficient condition for local optimality to solve the n 1 r i t i scheduling problem which is known to be np hard we then define a new dominant subset of schedules on the basis of this condition and propose several new approximate algorithms to construct schedules belonging to this subset numerical experiments enable us to compare them with classical approximate algorithms

hierarchies of evolution equations associated with certain symmetric spaces hierarchies of evolution equations associated with certain symmetric spaces are presented main examples of such symmetric spaces are hermitian symmetric spaces and the obtained evolution equations include generalized nonlinear schrodinger equations those results are obtained by extending the lie algebra in the ablowitz kaup newell segur scheme from sl 2 c to more general one

isospectral hamiltonian flows in finite and infinite dimensions i generalized moser systems and moment maps into loop algebras a moment map jr jia gl r is constructed from the poisson manifold j a of rank r perturbations of a fixed n xn matrix a to the dual r f e positive part of the formal loop algebra i r g r c 1 the adler kostant symes theorem is used to give hamiltonians which generate commutative isospectral flows on g r the pull back of these hamiltonians by the moment map gives rise to commutative isospectral hamiltonian flows in j a the latter may be identified with flows on finite dimensional coadjoint orbits in g and linearized on the jacobi variety of an invariant spectral curve xr which generically is an r sheeted riemann surface reductions of j a are derived corresponding to subalgebras of gl r c and sl r c determined as the fixed point set of automorphism groupes generated by involutions i e jdl the classical algebras as well as reductions to twisted subalgebras of s r c the theory is illustrated by a number of examples of finite dimensional isospectral flows defining integrable hamiltonian systems and their embeddings as finite gap solutions to integrable systems of pde s

a frequency domain bootstrap for ratio statistics in time series analysis the asymptotic properties of the bootstrap in the frequency domain based on studentized periodogram ordinates are studied it is proved that this bootstrap approximation is valid for ratio statistics such as autocorrelations by using edgeworth expansions it is shown that the bootstrap approximation even outperforms the normal approximation the results carry over to whittle estimates in a simulation study the behavior of the bootstrap is studied for empirical correlations and whittle estimates

one machine sequencing to minimize total tardiness a fourth theorem for emmons in 1969 h emmons provided three theorems emmons 1 3 for determining precedence relations between pairs of jobs for the single machine tardiness problem we show here a fourth straightforward theorem that uses the information when the jobs in the pair are both known to precede a third job in an optimum sequence the new theorem augments the three emmons theorems and is shown to be a generalization of a theorem by elmaghraby

matrix nonlinear schrodinger equations and moment maps into loop algebras it is shown how darboux coordinates on a reduced symplectic vector space may be used to parametrize the phase space on which the finite gap solutions of matrix nonlinear schrodinger equations are realized as isospectral hamiltonian flows the parametrization follows from a moment map embedding of the symplectic vector space reduced by suitable group actions into the dual g of the algebra g of positive frequency loops in a lie algebra g the resulting phase space is identified with a poisson subspace of g consisting of elements that are rational in the loop parameter reduced coordinates associated to the various hermitian symmetric lie algebras g k corresponding to the classical lie algebras are obtained

a parallel multiple reference point approach for multi objective optimization this paper presents a multiple reference point approach for multi objective optimization problems of discrete and combinatorial nature when approximating the pareto frontier multiple reference points can be used instead of traditional techniques these multiple reference points can easily be implemented in a parallel algorithmic framework the reference points can be uniformly distributed within a region that covers the pareto frontier an evolutionary algorithm is based on an achievement scalarizing function that does not impose any restrictions with respect to the location of the reference points in the objective space computational experiments are performed on a bi objective flow shop scheduling problem results quality measures as well as a statistical analysis are reported in the paper

a frequency domain empirical likelihood method for irregularly spaced spatial data this paper develops empirical likelihood methodology for irregularly spaced spatial data in the frequency domain unlike the frequency domain empirical likelihood fdel methodology for time series on a regular grid the formulation of the spatial fdel needs special care due to lack of the usual orthogonality properties of the discrete fourier transform for irregularly spaced data and due to presence of nontrivial bias in the periodogram under different spatial asymptotic structures a spatial fdel is formulated in the paper taking into account the effects of these factors the main results of the paper show that wilks phenomenon holds for a scaled version of the logarithm of the proposed empirical likelihood ratio statistic in the sense that it is asymptotically distribution free and has a chi squared limit as a result the proposed spatial fdel method can be used to build nonparametric asymptotically correct confidence regions and tests for covariance parameters that are defined through spectral estimating equations for irregularly spaced spatial data in comparison to the more common studentization approach a major advantage of our method is that it does not require explicit estimation of the standard error of an estimator which is itself a very difficult problem as the asymptotic variances of many common estimators depend on intricate interactions among several population quantities including the spectral density of the spatial process the spatial sampling density and the spatial asymptotic structure results from a numerical study are also reported to illustrate the methodology and its finite sample properties

complexity of single machine multi criteria scheduling problems abstract we examine the complexity of scheduling problems when more than one measure of performance is appropriate the criteria we study are maximal tardiness flowtime number of tardy jobs tardiness and the weighted counterparts of the last three measures the machine environment is restricted to a single machine complexity results are given for secondary criterion bicriteria and weighted criteria approaches for all combinations of measures of the problems examined only six remain open

algorithms for single machine total tardiness scheduling with sequence dependent setups abstract we consider the problem of scheduling a single machine to minimize total tardiness with sequence dependent setup times we present two algorithms a problem space based local search heuristic and a greedy randomized adaptive search procedure grasp for this problem with respect to grasp our main contributions are a new cost function in the construction phase a new variation of variable neighborhood search in the improvement phase and path relinking using three different search neighborhoods the problem space based local search heuristic incorporates local search with respect to both the problem space and the solution space we compare our algorithms with simulated annealing genetic search pairwise interchange branch and bound and ant colony search on a set of test problems from literature showing that the algorithms perform very competitively

k ppm a new exact method to solve multi objective combinatorial optimization problems in this paper we propose an exact method able to solve multi objective combinatorial optimization problems this method is an extension for any number of objectives of the 2 parallel partitioning method 2 ppm we previously proposed like 2 ppm this method is based on splitting of the search space into several areas leading to elementary searches the efficiency of the proposed method is evaluated using a multi objective flow shop problem

on the complexity of generalized due date scheduling problems abstract we study the recently identified class of generalized due date scheduling problems these are machine scheduling problems for which due dates are specified according to the position in which a job is completed rather than the identity of that job flexible manufacturing environments and public sector planning problems provide applications we study a wide variety of these problems with a view to determining their computational complexity in several instances a problem which is np hard under a traditional due date definition admits an efficient algorithm under the new definition as well as determining the complexity of many generalized due date scheduling problems including one published open problem we also describe several problems the complexity of which is still unresolved

on bootstrapping kernel spectral estimates an approach to bootstrapping kernel spectral density estimates is described which is based on resampling from the periodogram of the original data we show that it is asymptotically valid under suitable conditions and we illustrate its performance for a medium sized time series sample with a small simulation study

an exact parallel method for a bi objective permutation flowshop problem in this paper we propose a parallel exact method to solve bi objective combinatorial optimization problems this method has been inspired by the two phase method which is a very general scheme to optimally solve bi objective combinatorial optimization problems here we first show that applying such a method to a particular problem allows improvements secondly we propose a parallel model to speed up the search experiments have been carried out on a bi objective permutation flowshop problem for which we also propose a new lower bound

a fully polynomial approximation scheme for the single machine weighted total tardiness problem with a common due date we develop a fully polynomial time approximation scheme fptas for minimizing the weighted total tardiness on a single machine provided that all due dates are equal the fptas is obtained by converting an especially designed pseudopolynomial dynamic programming algorithm

nonlinear schrodinger equations and simple lie algebras we associate a system of integrable generalised nonlinear schrodinger nls equations with each hermitian symmetric space these nls equations are considered as reductions of more general systems this time associated with a reductive homogeneous space the nonlinear terms are related to the curvature and torsion tensors of the appropriate geometrical space the hamiltonian structure is investigated using r matrix techniques and shown to be canonical for all these equations throughout the reduction procedure this hamiltonian structure does not degenerate each of the above systems of equations is gauge equivalent to a generalised ferromagnet reductions of the latter are discussed in terms of the corresponding nls type equations

scheduling preemptive open shops to minimize total tardiness this article considers the problem of scheduling preemptive open shops to minimize total tardiness the problem is known to be np hard an efficient constructive heuristic is developed for solving large sized problems a branch and bound algorithm that incorporates a lower bound scheme based on the solution of an assignment problem as well as various dominance rules are presented for solving medium sized problems computational results for the 2 machine case are reported the branch and bound algorithm can handle problems of up to 30 jobs in size within a reasonable amount of time the solution obtained by the heuristic has an average deviation of less than 2 from the optimal value while the initial lower bound has an average deviation of less than 11 from the optimal value moreover the heuristic finds approved optimal solutions for over 65 of the problems actually solved