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

the proportionate flow shop total tardiness problem abstract we consider the proportionate flow shop total tardiness problem and show how to implement lawler s 1977 pseudo polynomial dynamic programming dp algorithm for the single machine total tardiness problem to the multi machine environment of proportionate flow shop we also present solvable special cases including one with small big jobs that has not been considered for the corresponding single machine problem we then convert the dp algorithm for the proportionate flow shop to a fully polynomial time approximation scheme fptas finally we show by a counterexample that pinedo s 2002 p 140 statement that the elimination criteria for the single machine total weighted tardiness problem also apply to the proportionate flow shop total weighted tardiness problem does not always hold and present an appropriately revised statement

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

precedence theorems and dynamic programming for the single machine weighted tardiness problem abstract we tackle precedence constrained sequencing on a single machine in order to minimize total weighted tardiness classic dynamic programming dp methods for this problem are limited in performance due to excessive memory requirements particularly when the precedence network is not sufficiently dense over the last decades a number of precedence theorems have been proposed which distinguish dominant precedence constraints for a job pool that is initially without precedence relation in this paper we connect and extend the findings of the foregoing two strands of literature we develop a framework for applying the precedence theorems to the precedence constrained problem to tighten the search space and we propose an exact dp algorithm that utilizes a new efficient memory management technique our procedure outperforms the state of the art algorithm for instances with medium to high network density we also empirically verify the computational gain of using different sets of precedence theorems

strongly polynomial algorithms for the high multiplicity scheduling problem a high multiplicity scheduling problem consists of many jobs which can be partitioned into relatively few groups where all the jobs within each group are identical polynomial and even strongly polynomial algorithms for the standard scheduling problem in which all jobs are assumed to be distinct become exponential for the corresponding high multiplicity problem in this paper we study various high multiplicity problems of scheduling unit time jobs on a single machine we provide strongly polynomial algorithms for constructing optimal schedules with respect to several measures of efficiency completion time lateness tardiness the number of tardy jobs and their weighted counterparts the algorithms require a number of operations that are polynomial in the number of groups rather than in the total number of jobs as a by product we identify a new family of nxn transportation problems which are solvable in o n log n time by a simple greedy algorithm

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

non permutation flow shop scheduling with order acceptance and weighted tardiness model the problem of non permutation flow shop scheduling with order acceptance the model is transformed to linear mip that is optimally solved by commercial solver theorems that are favorable for developing algorithms are presented an efficient two phase genetic algorithm tp ga is proposed the heuristic yields high quality non permutation solutions this paper studies the non permutation solution for the problem of flow shop scheduling with order acceptance and weighted tardiness fss oawt we formulate the problem as a linear mixed integer programming lmip model that can be optimally solved by ampl cplex for small sized problems in addition a non linear integer programming nip model is presented to design heuristic algorithms a two phase genetic algorithm tp ga is developed to solve the problem of medium and large sizes based on the nip model the properties of fss oawt are investigated and several theorems for permutation and non permutation optimum are provided the performance of the tp ga is studied through rigorous computational experiments using a large number of numeric instances the lmip model is used to demonstrate the differences between permutation and non permutation solutions to the fss oawt problem the results show that a considerably large portion of the instances have only an optimal non permutation schedule e g 43 3 for small sized and the proposed tp ga algorithms are effective in solving the fss oawt problems of various scales small medium and large with both permutation and non permutation solutions

schemes to compute unsteady flashing flows some ways to compute flashing flows in variable cross section ducts are provided focusing on the homogeneous relaxation model the basic numerical method relies on a splitting technique that is consistent with the overall entropy inequality the cross section is assumed to he continuous and the finite volume approach is applied to approximate homogeneous equations several suitable schemes to account for complex equation of state are discussed namely the rusanov scheme an approximate form of the roe scheme and the volumes finis roe vfroe scheme with the help of nonconservative variables to evaluate respective accuracy the homogeneous euler equations are computed first and the l1 error norm of transient solutions of shock tube experiments are plotted it is shown that the rusanov scheme is indeed less accurate which balances its interesting properties inasmuch as it preserves the positivity of the mean density and the maximum principle for the vapor quality computations of real cases are presented which account for the mass transfer term and the time space dependent cross sections

new precedence theorems for one machine weighted tardiness in an earlier paper by emmons emmons h 1969 one machine sequencing to minimize certain functions of job tardiness oper res 17 701 715 the problem of sequencing jobs on a single machine in order to minimize total tardiness was analyzed emmons provided three theorems for specifying precedence relations for pairs of jobs his theorems apply when the tardiness penalty for each job grows at the same rate rinnooy kan et al rinnooy kan a h g b j lageweg j k lenstra 1975 minimizing total costs in one machine scheduling oper res 23 908 927 later extended emmons s theorems to the case when job tardiness penalties can grow at different rates for different jobs provided here is a set of theorems stronger than those of rinnooy kan et al that more fully exploits the special properties of the weighted tardiness function allowing for greater reduction of the solution space

increasing the rooted connectivity of a digraph by one in order to unify these approaches here we describe a two phase greedy algorithm working on a slight extension of lattice polyhedra this framework includes the rooted node connectivity augmentation problem as well and hence the resulting algorithm when appropriately specialized finds a minimum cost of new edges whose addition to a digraph increases its rooted connectivity by one the only known algorithm for this problem used submodular flows actually the specialized algorithm solves an extension of the rooted edge connectivity and node connectivity augmentation problem

chain constrained spanning trees we consider the problem of finding a spanning tree satisfying a family of additional constraints several settings have been considered previously the most famous being the problem of finding a spanning tree with degree constraints since the problem is hard the goal is typically to find a spanning tree that violates the constraints as little as possible iterative rounding has become the tool of choice for constrained spanning tree problems however iterative rounding approaches are very hard to adapt to settings where an edge can be part of more than a constant number of constraints we consider a natural constrained spanning tree problem of this type namely where upper bounds are imposed on a family of cuts forming a chain our approach reduces the problem to a family of independent matroid intersection problems leading to a spanning tree that violates each constraint by a factor of at most 9 we also present strong hardness results among other implications these are the first to show in the setting of a basic constrained spanning tree problem a qualitative difference between what can be achieved when allowing multiplicative as opposed to additive constraint violations

two dimensional computation of gas flow in a porous bed characterized by a porosity jump a finite volume method based on a vfroe solver to simulate the flow of compressible gas in a variable porous medium for two dimensional geometries is proposed the modeling is based on the euler system where a non conservative term is added to take the porosity variation into account a detailed presentation of the scheme is given the main point is the construction of non conservative fluxes to reproduce the non conservation aspect of the problem we compare the numerical method with an exact solution of the riemann problem and we check that the method preserves steady state situations even if we use a discontinuous jump for the porosity finally we present two simulations involving a two dimensional gas flow

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

on the solution to the riemann problem for the compressible duct flow the quasi one dimensional euler equations in a duct of variable cross section form probably one of the simplest nonconservative systems we consider the riemann problem for it and discuss its properties in particular for some initial conditions the solution to the riemann problem appears to be nonunique in order to rule out the nonphysical solutions we provide two dimensional computations of the euler equations in a duct of corresponding geometry and compare them with the one dimensional 1d results then the physically relevant 1d solutions satisfy a kind of entropy rate admissibility criterion

a branch and bound algorithm for the total weighted tardiness problem this paper presents a new branch and bound algorithm for the single machine total weighted tardiness problem it obtains lower bounds using a lagrangian relaxation approach with subproblems that are total weighted completion time problems the well known subgradient optimization technique is replaced by a multiplier adjustment method that leads to an extremely fast bound calculation the method incorporates various devices for checking dynamic programming dominance in the search tree extensive computational results for problems with up to 50 jobs show the superiority of the algorithm over existing methods

approximating min cost chain constrained spanning trees a reduction from weighted to unweighted problems we study the min cost chain constrained spanning tree mccst problem find a min cost spanning tree in a graph subject to degree constraints on a nested family of node sets we devise the first polytime algorithm that finds a spanning tree that i violates the degree constraints by at most a constant factor and ii whose cost is within a constant factor of the optimum previously only an algorithm for unweighted ccst was known olver and zenklusen in proceedings of the 16th ipco pp 324 335 2013 which satisfied i but did not yield any cost bounds this also yields the first result that obtains an o 1 factor for both the cost approximation and violation of degree constraints for any spanning tree problem with general degree bounds on node sets where an edge participates in a super constant number of degree constraints a notable feature of our algorithm is that we reduce mccst to unweighted ccst and then utilize olver and zenklusen in proceedings of the 16th ipco pp 324 335 2013 via a novel application of lagrangian duality to simplify the cost structure of the underlying problem and obtain a decomposition into certain uniform cost subproblems we show that this lagrangian relaxation based idea is in fact applicable more generally and for any cost minimization problem with packing side constraints yields a reduction from the weighted to the unweighted problem we believe that this reduction is of independent interest as another application of our technique we consider the k budgeted matroid basis problem where we build upon a recent rounding algorithm of bansal and nagarajan proceedings of ipco 2016 arxiv 1512 02254 2015 to obtain an improved n o k 1 5 epsilon time algorithm that returns a solution that satisfies any one of the budget constraints exactly and incurs a 1 epsilon violation of the other budget constraints

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

a matter of degree improved approximation algorithms for degree bounded minimum spanning trees in this paper we present a new bicriteria approximation algorithm for the degree bounded minimum spanning tree problem in this problem we are given an undirected graph a nonnegative cost function on the edges and a positive integer b and the goal is to find a minimum cost spanning tree t with maximum degree at most b in an n node graph our algorithm finds a spanning tree with maximum degree o b logn and cost o optb where optb is the minimum cost of any spanning tree whose maximum degree is at most b our algorithm uses ideas from lagrangean duality we show how a set of optimum lagrangean multipliers yields bounds on both the degree and the cost of the computed solution

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

additive guarantees for degree bounded directed network design we present polynomial time approximation algorithms for some degree bounded directed network design problems our main result is for intersecting supermodular connectivity requirements with degree bounds given a directed graph g v e with nonnegative edge costs a connectivity requirement specified by an intersecting supermodular function f and upper bounds a v b v v in v on in degrees and out degrees of vertices find a minimum cost f connected subgraph of g that satisfies the degree bounds we give a bicriteria approximation algorithm for this problem using the natural lp relaxation and show that our guarantee is the best possible relative to this lp relaxation we also obtain similar results for the more general class of crossing supermodular requirements in the absence of edge costs our result gives the first additive o 1 approximation guarantee for degree bounded intersecting crossing supermodular connectivity problems we also consider the minimum crossing spanning tree problem given an undirected edge weighted graph g edge subsets e i i 1 k and nonnegative integers b i i 1 k find a minimum cost spanning tree if it exists in g that contains at most b i edges from each set e i we obtain a r 1 additive approximation for this problem when each edge lies in at most r sets a special case of this problem is the degree bounded minimum spanning tree and our techniques give a substantially shorter proof of the recent 1 approximation of singh and lau in proceedings of the 40th annual acm symposium on theory of computing 2007 pp 661 670

primal dual meets local search approximating msts with nonuniform degree bounds we present a new bicriteria approximation algorithm for the degree bounded minimum cost spanning tree mst problem given an undirected graph with nonnegative edge weights and a degree bound b find a spanning tree of maximum node degree b and minimum total edge cost our algorithm outputs a tree of maximum degree at most a constant times b and total edge cost at most a constant times that of a minimum cost degree b bounded spanning tree while our new algorithm is based on ideas from lagrangian relaxation as is our previous work siam j comput 31 2002 pp 1783 1793 it does not rely on computing a solution to a linear program instead it uses a repeated application of kruskal s mst algorithm interleaved with a combinatorial update of approximate lagrangian node multipliers maintained by the algorithm these updates cause subsequent repetitions of the spanning tree algorithm to run for longer and longer times leading to overall progress and a proof of the performance guarantee a second useful feature of our algorithm is that it can handle nonuniform degree bounds on the nodes given distinct bounds bv for every node v in v the output tree has degree at most o bv log v for every v in v as before the cost of the tree is at most a constant times that of a minimum cost tree obeying all degree bounds

a faster fully polynomial approximation scheme for the single machine total tardiness problem abstract lawler e l lawler a fully polynomial approximation scheme for the total tardiness problem operations research letters 1 1982 207 208 proposed a fully polynomial approximation scheme for the single machine total tardiness problem which runs in o n 7 e time where n is the number of jobs and e is the desired level of approximation a faster fully polynomial approximation scheme running in o n 5 log n n 5 e time is presented in this note by applying an alternative rounding scheme in conjunction with implementing kovalyov s m y kovalyov improving the complexities of approximation algorithms for optimization problems operations research letters 17 1995 85 87 bound improvement procedure

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

a well balanced scheme for the numerical processing of source terms in hyperbolic equations in a variety of physical problems one encounters source terms that are balanced by internal forces and this balance supports multiple steady state solutions that are stable typical of these are gravity driven flows such as those described by the shallow water equations over a nonuniform ocean bottom 1 10 qquad h t hu x 0 text and hu t left hu 2 frac gh 2 2 right x ga x x h 0 many classic numerical schemes cannot maintain these steady solutions or achieve them in the long time limit with an acceptable level of accuracy because they do not preserve the proper balance between the source terms and internal forces we propose here a numerical scheme adapted to a scalar conservation law that preserves this balance and that can it is hoped be extended to more general hyperbolic systems the proof of convergence of this scheme toward the entropy solution is given and some numerical tests are reported

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

on the complexity of preemptive openshop scheduling problems abstract we investigate the complexity status of the preemptive openshop scheduling problem after reviewing recent studies of the shop with various objective functions we define the concept of preempting job w r to a schedule and state some general results for the preemptive openshop environment these results are then used to show by reduction from the 3 partition that the n job 2 machine mean flow time problem with ready times and job preemption is unary np hard

a parallel repetition theorem we show that a parallel repetition of any two prover one round proof system mip 2 1 decreases the probability of error at an exponential rate no constructive bound was previously known the constant in the exponent in our analysis depends only on the original probability of error and on the total number of possible answers of the two provers the dependency on the total number of possible answers is logarithmic which was recently proved to be almost the best possible u feige and o verbitsky proc 11th annual ieee conference on computational complexity ieee computer society press los alamitos ca 1996 pp 70 76

new results for single machine scheduling with past sequence dependent setup times and due date related objectives abstract we show that the single machine scheduling problem with past sequence dependent p s d setup times and either the minimum maximum lateness or the minimum maximum tardiness objective is solvable in o n2 time by an index priority rule followed by backward insertions of certain qualifying jobs we also show that the problem with the minimum number of tardy jobs objective is solvable in o n2 time by a variant of moore s algorithm we then show how to modify a general purpose dynamic programming algorithm to solve the problem with other due date related objectives such as the total weighted tardiness the weighted number of tardy jobs and in the case of an unrestricted common due date the total weighted earliness tardiness we also present heuristic decomposition algorithms for the np hard scheduling problems with p s d setup times and the objectives of total weighted tardiness weighted number of tardy jobs and total weighted earliness tardiness around an unrestricted common due date these algorithms decompose the respective problem heuristically into smaller sub problems which are then solved optimally by dynamic programming we show experimentally that the heuristic performs well with extended job due dates close to the makespan because in those cases the heuristic is capable of locating the optimal solution with either zero total weighted tardiness or with only a few tardy jobs in the remaining cases the quality of the ds solutions is superior with normally distributed data compared to the corresponding solutions with uniformly distributed data this is because sampling from the normal distribution reduces the variability among processing times and weights which in turn decreases the hardness of the problem finally we show that the heuristic s performance deteriorates as the problem size increases

on generalizations of network design problems with degree bounds iterative rounding and relaxation have arguably become the method of choice in dealing with unconstrained and constrained network design problems in this paper we extend the scope of the iterative relaxation method in two directions 1 by handling more complex degree constraints in the minimum spanning tree problem namely laminar crossing spanning tree and 2 by incorporating degree bounds in other combinatorial optimization problems such as matroid intersection and lattice polyhedra we give new or improved approximation algorithms hardness results and integrality gaps for these problems our main result is a 1 b o log n approximation algorithm for the minimum crossing spanning tree mcst problem with laminar degree constraints the laminar mcst problem is a natural generalization of the well studied bounded degree mst and is a special case of general crossing spanning tree we give an additive log c m hardness of approximation for general mcst even in the absence of costs c 0 is a fixed constant and m is the number of degree constraints this also leads to a multiplicative log c m hardness of approximation for the robust k median problem anthony et al in math oper res 35 79 101 2010 improving over the previously known factor 2 hardness we then consider the crossing contra polymatroid intersection problem and obtain a 2 2b 1 approximation algorithm where is the maximum element frequency this models for example the degree bounded spanning set intersection in two matroids finally we introduce the crossing latticep olyhedron problem and obtain a 1 b 2 1 approximation algorithm under certain condition this result provides a unified framework and common generalization of various problems studied previously such as degree bounded matroids

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

two phase shock tube problems and numerical methods of solution the study involves the flow of compressible gas in a porous bed we are interested in exploring the solution to a shock tube problem that also includes a discontinuous jump in the porosity of the bed the averaging process that is used to derive the governing system of equations introduces terms that prevent the equations taking a standard conservation form the purpose of this work is to explore how the porosity jump effects the solution to the riemann problem and to assess whether standard conservative and nonconservative numerical methods can provide the correct solution to the riemann problem the study illustrates serious shortfalls in the numerical solution to these problems using standard techniques by exploring the exact solution the author suggests how the standard numerical methods can be modified to provide the correct solution to these systems

a multiphase godunov method for compressible multifluid and multiphase flows we propose a new model and a solution method for two phase compressible flows the model involves six equations obtained from conservation principles applied to each phase completed by a seventh equation for the evolution of the volume fraction this equation is necessary to close the overall system the model is valid for fluid mixtures as well as for pure fluids the system of partial differential equations is hyperbolic hyperbolicity is obtained because each phase is considered to be compressible two difficulties arise for the solution one of the equations is written in non conservative form non conservative terms exist in the momentum and energy equations we propose robust and accurate discretisation of these terms the method solves the same system at each mesh point with the same algorithm it allows the simulation of interface problems between pure fluids as well as multiphase mixtures several test cases where fluids have compressible behavior are shown as well as some other test problems where one of the phases is incompressible the method provides reliable results is able to compute strong shock waves and deals with complex equations of state

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

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

first and second order finite volume methods for the one dimensional nonconservative euler system gas flow in porous media with a nonconstant porosity function provides a nonconservative euler system we propose a new class of schemes for such a system for the one dimensional situations based on nonconservative fluxes preserving the steady state solutions we derive a second order scheme using a splitting of the porosity function into a discontinuous and a regular part where the regular part is treated as a source term while the discontinuous part is treated with the nonconservative fluxes we then present a classification of all the configurations for the riemann problem solutions in particularly we carefully study the resonant situations when two eigenvalues are superposed based on the classification we deal with the inverse riemann problem and present algorithms to compute the exact solutions we finally propose new sod problems to test the schemes for the resonant situations where numerical simulations are performed to compare with the theoretical solutions the schemes accuracy first and second order is evaluated comparing with a nontrivial steady state solution with the numerical approximation and convergence curves are established

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 new discrete particle swarm optimization approach for the single machine total weighted tardiness scheduling problem with sequence dependent setup times in this paper we present a new discrete particle swarm optimization dpso approach to face the np hard single machine total weighted tardiness scheduling problem in presence of sequence dependent setup times differently from previous approaches the proposed dpso uses a discrete model both for particle position and velocity and a coherent sequence metric we tested the proposed dpso mainly over a benchmark originally proposed by cicirello in 2003 and available online the results obtained show the competitiveness of our dpso which is able to outperform the best known results for the benchmark in addition we also tested the dpso on a set of benchmark instances from orlib for the single machine total weighted tardiness problem and we analysed the role of the dpso swarm intelligence mechanisms as well as the local search intensification phase included in the algorithm

survivable network design with degree or order constraints we present algorithmic and hardness results for network design problems with degree or order constraints the first problem we consider is the survivable network design problem with degree constraints on vertices the objective is to find a minimum cost subgraph which satisfies connectivity requirements between vertices and also degree upper bounds b v on the vertices this includes the well studied minimum bounded degree spanning tree problem as a special case our main result is a 2 2b v 3 approximation algorithm for the edge connectivity survivable network design problem with degree constraints where the cost of the returned solution is at most twice the cost of an optimum solution satisfying the degree bounds and the degree of each vertex v is at most 2b v 3 this implies the first constant factor bicriteria approximation algorithms for many degree constrained network design problems including the minimum bounded degree steiner forest problem our results also extend to directed graphs and provide the first constant factor bicriteria approximation algorithms for the minimum bounded degree arborescence problem and the minimum bounded degree strongly k edge connected subgraph problem in contrast we show that the vertex connectivity survivable network design problem with degree constraints is hard to approximate even when the cost of every edge is zero a striking aspect of our algorithmic result is its simplicity it is based on the iterative relaxation method which is an extension of jain s iterative rounding method this provides an elegant and unifying algorithmic framework for a broad range of network design problems we also study the problem of finding a minimum cost lambda edge connected subgraph with at least k vertices which we call the k lambda subgraph problem this generalizes some well studied classical problems such as the k mst and the minimum cost lambda edge connected subgraph problems we give a polylogarithmic approximation for the k 2 subgraph problem however by relating it to the densest k subgraph problem we provide evidence that the k lambda subgraph problem might be hard to approximate for arbitrary lambda

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

approximate multi matroid intersection via iterative refinement we introduce a new iterative rounding technique to round a point in a matroid polytope subject to further matroid constraints this technique returns an independent set in one matroid with limited violations of the constraints of the other matroids in addition to the classical steps of iterative relaxation approaches we iteratively refine involved matroid constraints this leads to more restrictive constraint systems whose structure can be exploited to prove the existence of constraints that can be dropped hence throughout the iterations we both tighten constraints and later relax them by dropping constraints under certain conditions due to the refinement step we can deal with considerably more general constraint classes than existing iterative relaxation and rounding methods which typically involve a single matroid polytope with additional simple cardinality constraints that do not overlap too much we show that our rounding method combined with an application of a matroid intersection algorithm yields the first 2 approximation for finding a maximum weight common independent set in 3 matroids moreover our 2 approximation is lp based and settles the integrality gap for the natural relaxation of the problem prior to our work no upper bound better than 3 was known for the integrality gap which followed from the greedy algorithm we also discuss various other applications of our techniques including an extension that allows us to handle a mixture of matroid and knapsack constraints

a plant location guide for the unsure approximation algorithms for min max location problems this paper studies an extension of the k median problem under uncertain demand we are given an n vertex metric space v d and m client sets documentclass aastex usepackage amsbsy usepackage amsfonts usepackage amssymb usepackage bm usepackage mathrsfs usepackage pifont usepackage stmaryrd usepackage textcomp usepackage portland xspace usepackage amsmath amsxtra pagestyle empty declaremathsizes 10 9 7 6 begin document s i subseteq v i 1 m end document the goal is to open a set of k facilities f such that the worst case connection cost over all the client sets is minimized i e documentclass aastex usepackage amsbsy usepackage amsfonts usepackage amssymb usepackage bm usepackage mathrsfs usepackage pifont usepackage stmaryrd usepackage textcomp usepackage portland xspace usepackage amsmath amsxtra pagestyle empty declaremathsizes 10 9 7 6 begin document min f subseteq v f k max i in m left sum j in s i d

a well balanced approximate riemann solver for compressible flows in variable cross section ducts a well balanced approximate riemann solver is introduced in this paper in order to compute approximations of one dimensional euler equations in variable cross section ducts the interface riemann solver is grounded on the vfroe ncv scheme and it enforces the preservation of riemann invariants of the steady wave the main properties of the scheme are detailed we provide numerical results to assess the validity of the scheme even when the cross section is discontinuous a first series is devoted to analytical test cases and the last results correspond to the simulation of a bubble collapse

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

local search heuristics for k median and facility location problems we analyze local search heuristics for the metric k median and facility location problems we define the locality gap of a local search procedure for a minimization problem as the maximum ratio of a locally optimum solution obtained using this procedure to the global optimum for k median we show that local search with swaps has a locality gap of 5 furthermore if we permit up to p facilities to be swapped simultaneously then the locality gap is 3 2 p this is the first analysis of a local search for k median that provides a bounded performance guarantee with only k medians this also improves the previous known 4 approximation for this problem for uncapacitated facility location we show that local search which permits adding dropping and swapping a facility has a locality gap of 3 this improves the bound of 5 given by m korupolu c plaxton and r rajaraman analysis of a local search heuristic for facility location problems technical report 98 30 dimacs 1998 we also consider a capacitated facility location problem where each facility has a capacity and we are allowed to open multiple copies of a facility for this problem we introduce a new local search operation which opens one or more copies of a facility and drops zero or more facilities we prove that this local search has a locality gap between 3 and 4

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

weighted tardiness single machine scheduling with proportional weights this paper considers arkin and roundy s single machine weighted tardiness scheduling model with tardiness penalties proportional to the processing times it presents a two stage decomposition mechanism that proves to be powerful in solving the problem completely or reducing it to a much smaller problem three types of orderings of adjacent jobs are derived that play a crucial role in problem decomposition the decomposition method solves 155 out of 320 test problems with job sizes ranging from 20 to 150 it reduces 163 unsolved problems to smaller subproblems with sizes not exceeding 25 jobs the job sizes of the remaining two unsolved subproblems are 30 and 45