a reoptimization algorithm for the shortest path problem with time windows abstract the shortest path problem with time windows spptw occurs in the construction of vehicle routes and schedules for which time window constraints must be satisfied the spptw is repeatedly solved to produce routes with disjoint schedules which form the solution of the original problem the cost of repeatedly solving the spptw can be reduced by reusing part of the solution of the preceding problem a primal dual reoptimization method which runs in pseudo polynomial time is proposed it can solve problems with up to 2500 nodes

optimal solution of vehicle routing problems using minimum k trees we consider the problem of optimally scheduling a fleet of k vehicles to make deliveries to n customers subject to vehicle capacity constraints given a graph with n 1 nodes a k tree is defined to be a set of n k edges that span the graph we show that the vehicle routing problem can be modeled as the problem of finding a minimum cost k tree with two k edges incident on the depot and subject to some side constraints that impose vehicle capacity and the requirement that each customer be visited exactly once the side constraints are dualized to obtain a lagrangian problem that provides lower bounds in a branch and bound algorithm this algorithm has produced proven optimal solutions for a number of difficult problems including a well known problem with 100 customers and several real problems with 25 71 customers

an exact algorithm for the pickup and delivery problem with time windows the pickup and delivery problem with time windows pdptw is a generalization of the vehicle routing problem with time windows in the pdptw a set of identical vehicles located at a central depot must be optimally routed to service a set of transportation requests subject to capacity time window pairing and precedence constraints in this paper we present a new exact algorithm for the pdptw based on a set partitioning like integer formulation and we describe a bounding procedure that finds a near optimal dual solution of the lp relaxation of the formulation by combining two dual ascent heuristics and a cut and column generation procedure the final dual solution is used to generate a reduced problem containing only the routes whose reduced costs are smaller than the gap between a known upper bound and the lower bound achieved if the resulting problem has moderate size it is solved by an integer programming solver otherwise a branch and cut and price algorithm is used to close the integrality gap extensive computational results over the main instances from the literature show the effectiveness of the proposed exact method

lifted polynomial size formulations for the homogeneous and heterogeneous vehicle routing problems abstract we propose compact formulations for the symmetric and asymmetric capacitated vehicle routing problems these formulations are obtained by lifting using the reformulation linearization technique a novel polynomial size ordered path based formulation we show that the strongest proposed formulation is equivalent to the strongest multi commodity flow formulation presented so far in addition we propose polynomial size valid inequalities that aim at further tightening the proposed formulations also the tightest formulation is extended to model the fleet size and mix vehicle routing problem with fixed costs we show that the new derived model is not comparable with a state of the art polynomial length formulation we present the results of computational experiments that demonstrate the tightness of the proposed formulations and the impact of the valid inequalities

set covering in fuel considered vehicle routing problems the paper studies set covering in fuel considered vehicle routing problems fvrp firstly we study the fvrp with distance constraint and time windows fvrp tw whose objective is to find a set covering with the minimum cardinality which means the number of used vehicles is minimized and hence the fuel consumption is minimized in the real logistics we give a bicriteria approximation algorithm for this problem secondly we study the set covering in the fvrp with distance constraint and constant time windows fvrp ctw which has a constant number of the time windows provided by logistics companies we give a bicriteria approximation algorithm with 2 o log 1 for this problem in which the first term is the approximation ratio on the distance constraint and the second term is the approximation ratio on the cardinality of the covering set thirdly we study the set covering in general fvrp and propose a lower bound for this problem which is based on total unimodularity finally we design an algorithm framework based on the lower bound for solving the set covering in general fvrp simulation results demonstrate the effectiveness of the algorithms for solving the set covering in fvrp tw and general fvrp

new developments in the primal dual column generation technique abstract the optimal solutions of the restricted master problems typically leads to an unstable behavior of the standard column generation technique and consequently originates an unnecessarily large number of iterations of the method to overcome this drawback variations of the standard approach use interior points of the dual feasible set instead of optimal solutions in this paper we focus on a variation known as the primal dual column generation technique which uses a primal dual interior point method to obtain well centered non optimal solutions of the restricted master problems we show that the method converges to an optimal solution of the master problem even though non optimal solutions are used in the course of the procedure also computational experiments are presented using linear relaxed reformulations of three classical integer programming problems the cutting stock problem the vehicle routing problem with time windows and the capacitated lot sizing problem with setup times the numerical results indicate that the appropriate use of a primal dual interior point method within the column generation technique contributes to a reduction of the number of iterations as well as the running times on average furthermore the results show that the larger the instance the better the relative performance of the primal dual column generation technique

lagrangean decomposition a model yielding stronger lagrangean bounds given a mixed integer programming problem with two matrix constraints it is possible to define a lagrangean relaxation such that the relaxed problem decomposes additively into two subproblems each having one of the two matrices of the original problem as its constraints there is one lagrangean multiplier per variable we prove that the optimal value of this new lagrangean dual dominates the optimal value of the lagrangean dual obtained by relaxing one set of constraints and give a necessary condition for a strict improvement we show on an example that the resulting bound improvement can be substantial we show on a complex practical problem how lagrangean decomposition may help uncover hidden special structures and thus yield better solution methodology

vehicle routing with time windows two optimization algorithms we describe two optimization methods for vehicle routing problems with time windows these are a k tree relaxation with time windows added as side constraints and a lagrangian decomposition in which variable splitting is used to divide the problem into two subproblems a semi assignment problem and a series of shortest path problems with time windows and capacity constraints we present optimal solutions to problems with up to 100 customers

an optimization algorithm for the vehicle routing problem with time windows based on lagrangian relaxation our paper presents a new optimization method for the vehicle routing problem with time windows vrptw the vrptw is a generalization of the vehicle routing problem where the service of a customer must start within a given time interval a so called time window our method is based on a lagrangian relaxation of the constraint set requiring that each customer must be serviced the master problem consists of finding the optimal lagrangian multipliers and the subproblem is a shortest path problem with time windows and capacity constraints the optimal multipliers are found using a method exploiting the benefits of subgradient methods as well as a bundle method the method has been implemented and tested on a series of well known benchmark problems of size up to 100 customers our algorithm turns out to be very competitive compared to algorithms considered in the literature and we have succeeded in solving several previously unsolved problems

a hierarchical bayesian statistical framework for response time distributions this paper provides a statistical framework for estimating higher order characteristics of the response time distribution such as the scale variability and shape consideration of these higher order characteristics often provides for more rigorous theory development in cognitive and perceptual psychology e g luce 1986 rt distribution for a single participant depends on certain participant characteristics which in turn can be thought of as arising from a distribution of latent variables the present work focuses on the three parameter weibull distribution with parameters for shape scale and shift initial value bayesian estimation in a hierarchical framework is conceptually straightforward parameter estimates both for participant quantities and population parameters are obtained through markov chain monte carlo methods the methods are illustrated with an application to response time data in an absolute identification task the behavior of the bayes estimates are compared to maximum likelihood ml estimates through monte carlo simulations for small sample size there is an occasional tendency for the ml estimates to be unreasonably extreme in contrast by borrowing strength across participants bayes estimation shrinks extreme estimates the results are that the bayes estimators are more accurate than the corresponding ml estimators

on the distance constrained vehicle routing problem we analyze the vehicle routing problem with constraints on the total distance traveled by each vehicle two objective functions are considered minimize the total distance traveled by vehicles and minimize the number of vehicles used we demonstrate a close relationship between the optimal solutions for the two objective functions and perform a worst case analysis for a class of heuristics we present a heuristic that provides a good worst case result when the number of vehicles used is relatively small

branch and price column generation for solving huge integer programs we discuss formulations of integer programs with a huge number of variables and their solution by column generation methods i e implicit pricing of nonbasic variables to generate new columns or to prove lp optimality at a node of the branch and bound tree we present classes of models for which this approach decomposes the problem provides tighter lp relaxations and eliminates symmetry we then discuss computational issues and implementation of column generation branch and bound algorithms including special branching rules and efficient ways to solve the lp relaxation we also discuss the relationship with lagrangian duality

on the flexibility of constraint programming models from single to multiple time windows for the traveling salesman problem one of the major strengths of constraint programming is the flexibility and expressiveness of models in that computational paradigm which make it easy to add problem dependent constraints without having to modify the solution strategy we show here what needs to be done in order to adapt a constraint programming algorithm for the traveling salesman problem with time windows so that it can handle multiple time windows computational results are also presented on a set of instances created for that little studied problem

classification of dantzig wolfe reformulations for binary mixed integer programming problems abstract in this note we provide a classification of dantzig wolfe reformulations for binary mixed integer programming problems we specifically focus on modeling the binary conditions in the convexification approach to the dantzig wolfe decomposition for a general binary mixed integer programming problem an extreme point of the overall problem does not necessarily correspond to an extreme point of the subproblem therefore the binary conditions cannot in general be imposed on the new master problem variables but must be imposed on the original binary variables in some cases however it is possible to impose the binary restrictions directly on the new master problem variables the issue of imposing binary conditions on the original variables versus the master problem variables has not been discussed systematically for mip problems in general in the literature and most of the research has been focused on the pure binary case the classification indicates in which cases you can and cannot impose binary conditions on the new master problem variables

a note on the reliability coefficients for item response model based ability estimates assuming item parameters on a test are known constants the reliability coefficient for item response theory irt ability estimates is defined for a population of examinees in two different ways as a the product moment correlation between ability estimates on two parallel forms of a test and b the squared correlation between the true abilities and estimates due to the bias of irt ability estimates the parallel forms reliability coefficient is not generally equal to the squared correlation reliability coefficient it is shown algebraically that the parallel forms reliability coefficient is expected to be greater than the squared correlation reliability coefficient but the difference would be negligible in a practical sense

local search with annealing like restarts to solve the vrptw abstract in this paper we propose a metaheuristic based on annealing like restarts to diversify and intensify local searches for solving the vehicle routing problem with time windows vrptw using the solomon s benchmark instances for the problem our method obtained seven new best results and equaled 19 other best results extensive comparisons indicate that our method is comparable to the best in published literature this approach is flexible and can be extended to handle other variants of vehicle routing problems and other combinatorial optimization problems

a cluster based optimization approach for the multi depot heterogeneous fleet vehicle routing problem with time windows this paper presents a novel three phase heuristic algorithmic approach for the multi depot routing problem with time windows and heterogeneous vehicles it has been derived from embedding a heuristic based clustering algorithm within a vrptw optimization framework to this purpose a rigorous milp mathematical model for the vrptw problem is first introduced likewise other optimization approaches the new formulation can efficiently solve case studies involving at most 25 nodes to optimality to overcome this limitation a preprocessing stage clustering nodes together is initially performed to yield a more compact cluster based milp problem formulation in this way a hierarchical hybrid procedure involving one heuristic and two algorithmic phases was developed phase i aims to identifying a set of cost effective feasible clusters while phase ii assigns clusters to vehicles and sequences them on each tour by using the cluster based milp formulation ordering nodes within clusters and scheduling vehicle arrival times at customer locations for each tour through solving a small milp model is finally performed at phase iii numerous benchmark problems featuring different sizes clustered random customer locations and time window distributions have been solved at acceptable cpu times

on the effectiveness of set covering formulations for the vehicle routing problem with time windows the vehicle routing problem with time windows vrptw is one of the most important problems in distribution and transportation a classical and recently popular technique that has proven effective for solving these problems is based on formulating them as a set covering problem the method starts by solving its linear programming relaxation via column generation and then uses a branch and bound strategy to find an integer solution to the set covering problem a solution to the vrptw an empirically observed property is that the optimal solution value of the set covering problem is very close to its linear programming relaxation which makes the branch and bound step extremely efficient in this paper we explain this behavior by demonstrating that for any distribution of service times time windows customer loads and locations the relative gap between fractional and integer solutions of the set covering problem becomes arbitrarily small as the number of customers increases

multi phase dynamic constraint aggregation for set partitioning type problems dynamic constraint aggregation is an iterative method that was recently introduced to speed up the linear relaxation solution process of set partitioning type problems this speed up is mostly due to the use at each iteration of an aggregated problem defined by aggregating disjoint subsets of constraints from the set partitioning model this aggregation is updated when needed to ensure the exactness of the overall approach in this paper we propose a new version of this method called the multi phase dynamic constraint aggregation method which essentially adds to the original method a partial pricing strategy that involves multiple phases this strategy helps keeping the size of the aggregated problem as small as possible yielding a faster average computation time per iteration and fewer iterations we also establish theoretical results that provide some insights explaining the success of the proposed method tests on the linear relaxation of simultaneous bus and driver scheduling problems involving up to 2 000 set partitioning constraints show that the partial pricing strategy speeds up the original method by an average factor of 4 5

speed accuracy response models scoring rules based on response time and accuracy starting from an explicit scoring rule for time limit tasks incorporating both response time and accuracy and a definite trade off between speed and accuracy a response model is derived since the scoring rule is interpreted as a sufficient statistic the model belongs to the exponential family the various marginal and conditional distributions for response accuracy and response time are derived and it is shown how the model parameters can be estimated the model for response accuracy is found to be the two parameter logistic model it is found that the time limit determines the item discrimination and this effect is illustrated with the amsterdam chess test ii

a new optimization algorithm for the vehicle routing problem with time windows the vehicle routing problem with time windows vrptw is a generalization of the vehicle routing problem where the service of a customer can begin within the time window defined by the earliest and the latest times when the customer will permit the start of service in this paper we present the development of a new optimization algorithm for its solution the lp relaxation of the set partitioning formulation of the vrptw is solved by column generation feasible columns are added as needed by solving a shortest path problem with time windows and capacity constraints using dynamic programming the lp solution obtained generally provides an excellent lower bound that is used in a branch and bound algorithm to solve the integer set partitioning formulation our results indicate that this algorithm proved to be successful on a variety of practical sized benchmark vrptw test problems the algorithm was capable of optimally solving 100 customer problems this problem size is six times larger than any reported to date by other published research

exact algorithms for the vehicle routing problem based on spanning tree and shortest path relaxations we consider the problem of routing vehicles stationed at a central facility depot to supply customers with known demands in such a way as to minimize the total distance travelled the problem is referred to as the vehicle routing problem vrp and is a generalization of the multiple travelling salesman problem that has many practical applications we present tree search algorithms for the exact solution of the vrp incorporating lower bounds computed from i shortest spanning k degree centre tree k dct and ii q routes the final algorithms also include problem reduction and dominance tests computational results are presented for a number of problems derived from the literature the results show that the bounds derived from the q routes are superior to those from k dct and that vrps of up to about 25 customers can be solved exactly

on the nucleolus of the basic vehicle routing game in the vehicle routing cost allocation problem the aim is to find a good cost allocation method i e a method that according to specified criteria allocates the cost of an optimal route configuration among the customers we formulate this problem as a co operative game in characteristic function form and give conditions for when the core of the vehicle routing game is nonempty one specific solution concept to the cost allocation problem is the nucleolus which minimizes maximum discontent among the players in a co operative game the class of games we study is such that the values of the characteristic function are obtained from the solution of a set of mathematical programming problems we do not require an explicit description of the characteristic function for all coalitions instead by applying a constraint generation approach we evaluate information about the function only when it is needed for the computation of the nucleolus

selected topics in column generation dantzig wolfe decomposition and column generation devised for linear programs is a success story in large scale integer programming we outline and relate the approaches and survey mainly recent contributions not yet found in textbooks we emphasize the growing understanding of the dual point of view which has brought considerable progress to the column generation theory and practice it stimulated careful initializations sophisticated solution techniques for the restricted master problem and subproblem as well as better overall performance thus the dual perspective is an ever recurring concept in our selected topics

paradoxical results in multidimensional item response theory in multidimensional item response theory mirt it is possible for the estimate of a subject s ability in some dimension to decrease after they have answered a question correctly this paper investigates how and when this type of paradoxical result can occur we demonstrate that many response models and statistical estimates can produce paradoxical results and that in the popular class of linearly compensatory models maximum likelihood estimates are guaranteed to do so in light of these findings the appropriateness of multidimensional item response methods for assigning scores in high stakes testing is called into question

an outer approximate subdifferential method for piecewise affine optimization piecewise affine functions arise from lagrangian duals of integer programming problems and optimizing them provides good bounds for use in a branch and bound method methods such as the subgradient method and bundle methods assume only one subgradient is available at each point but in many situations there is more information available we present a new method for optimizing such functions which is related to steepest descent but uses an outer approximation to the subdifferential to avoid some of the numerical problems with the steepest descent approach we provide convergence results for a class of outer approximations and then develop a practical algorithm using such an approximation for the compact dual to the linear programming relaxation of the uncapacitated facility location problem we make a numerical comparison of our outer approximation method with the projection method of conn and cornuejols and the bundle method of schramm and zowe

a flexible latent trait model for response times in tests latent trait models for response times in tests have become popular recently one challenge for response time modeling is the fact that the distribution of response times can differ considerably even in similar tests in order to reduce the need for tailor made models a model is proposed that unifies two popular approaches to response time modeling proportional hazard models and the accelerated failure time model with log normally distributed response times this is accomplished by resorting to discrete time the categorization of response time allows the formulation of a response time model within the framework of generalized linear models by using a flexible link function item parameters of the proposed model can be estimated with marginal maximum likelihood estimation applicability of the proposed approach is demonstrated with a simulation study and an empirical application additionally means for the evaluation of model fit are suggested

information matrices and standard errors for mles of item parameters in irt the paper clarifies the relationship among several information matrices for the maximum likelihood estimates mles of item parameters it shows that the process of calculating the observed information matrix also generates a related matrix that is the middle piece of a sandwich type covariance matrix monte carlo results indicate that standard errors ses based on the observed information matrix are robust to many but not all conditions of model distribution misspecifications ses based on the sandwich type covariance matrix perform most consistently across conditions results also suggest that ses based on other matrices are either not consistent or perform not as robust as those based on the sandwich type covariance matrix or the observed information matrix

two interpretations of the discrimination parameter in this paper we propose two interpretations for the discrimination parameter in the two parameter logistic model 2plm the interpretations are based on the relation between the 2plm and two stochastic models in the first interpretation the 2plm is linked to a diffusion model so that the probability of absorption equals the 2plm the discrimination parameter is the distance between the two absorbing boundaries and therefore the amount of information that has to be collected before a response to an item can be given for the second interpretation the 2plm is connected to a specific type of race model in the race model the discrimination parameter is inversely related to the dependency of the information used in the decision process extended versions of both models with person to person variability in the difficulty parameter are considered when fitted to a data set it is shown that a generalization of the race model that allows for dependency between choices and response times rts is the best fitting model

an accelerated branch and price algorithm for multiple runway aircraft sequencing problems abstract this paper presents an effective branch and price b p algorithm for multiple runway aircraft sequencing problems this approach improves the tractability of the problem by several orders of magnitude when compared with solving a classical 0 1 mixed integer formulation over a set of computationally challenging instances central to the computational efficacy of the b p algorithm is solving the column generation subproblem as an elementary shortest path problem with aircraft time windows and non triangular separation times using an enhanced dynamic programming procedure we underscore in our computational study the algorithmic features that contribute in our experience to accelerating the proposed dynamic programming procedure and hence the overall b p algorithm

an interpolation approximation for the mean workload in a gi g 1 queue this paper develops a closed form approximation for the mean steady state workload or virtual waiting time in a gi g 1 queue using the first two moments of the service time distribution and the first three moments plus the density at the origin of the interarrival time distribution with default values provided in case information is unavailable the approximation is based on light and heavy traffic limiting behavior the essential ideas are exposed by using s l brumelle s formula to relate the mean workload to the mean waiting time and k t marshall s formula to relate the mean waiting time to the first two moments of the idle period both formulas extend to general single server models without independence conditions so this approach provides a basis for extensions but a convenient exact expression for the second order heavy traffic term is evidently not possible even for gi g 1 for the gi g 1 second order heavy traffic term an approximation is proposed based on the relatively nice expression est

rendezvous search on the line with more than two players suppose n blind speed one players are placed by a random permutation onto the integers 1 to n and each is pointed randomly to the right or left what is the least expected time required form m n of them to meet together at a single point if they must all use the same strategy we call this time the symmetric rendezvous value rn ms otherwise the asymmetric value rn ma we show that r3 2a 47 48 and that rn ns is asymptotic to n 2 these results respectively extend those for two players given by alpern and gal alpern s s gal 1995 rendezvous search on the line with distinguishable players siam j control optim 33 1270 1276 and anderson and essegaier anderson e j s essegaier 1995 rendezvous search on the line with indistinguishable players siam j control optim 33 1637 1642

asymmetry matters dynamic half way points in bidirectional labeling for solving shortest path problems with resource constraints faster abstract with their paper symmetry helps bounded bi directional dynamic programming for the elementary shortest path problem with resource constraints discrete optimization 3 2006 pp 255 273 righini and salani introduced bounded bidirectional dynamic programming dp as an acceleration technique for solving variants of the shortest path problem with resource constraints spprc spprcs must be solved iteratively when vehicle routing and scheduling problems are tackled via lagrangian relaxation or column generation techniques righini and salani and several subsequent works have shown that bounded bidirectional dp algorithms are often superior to their monodirectional counterparts since the former can mitigate the fact that the number of labels increases strongly with the path length bidirectional dp has become a quasi standard for solving spprcs with general resource extension functions in computational experiments however one can still observe that the number of forward and backward label extensions is very unbalanced despite a symmetric bounding of a critical resource in the middle of its feasible domain we exploit this asymmetry in forward and backward label extensions to reduce the overall workload by introducing a so called dynamic half way point which is a dynamic bounding criterion based on the current state of the simultaneously solved forward and backward dps experiments with the standard and the electric vehicle routing problem with time windows as well as the vehicle routing and truck driver scheduling problem confirm that dynamic half way points better balance forward and backward labeling and reduce the overall runtime

lp models for bin packing and cutting stock problems abstract we review several linear programming lp formulations for the one dimensional cutting stock and bin packing problems namely the models of kantorovich gilmore gomory onecut models as in the dyckhoff stadtler approach position indexed models and a model derived from the vehicle routing literature we analyse some relations between the corresponding lp relaxations and their relative strengths and refer how to derive branching schemes that can be used in the exact solution of these problems using branch and price

a generalized speed accuracy response model for dichotomous items we propose a generalization of the speed accuracy response model sarm introduced by maris and van der maas psychometrika 77 615 633 2012 in these models the scores that result from a scoring rule that incorporates both the speed and accuracy of item responses are modeled our generalization is similar to that of the one parameter logistic or rasch model to the two parameter logistic or birnbaum model in item response theory an expectation maximization em algorithm for estimating model parameters and standard errors was developed furthermore methods to assess model fit are provided in the form of generalized residuals for item score functions and saddlepoint approximations to the density of the sum score the presented methods were evaluated in a small simulation study the results of which indicated good parameter recovery and reasonable type i error rates for the residuals finally the methods were applied to two real data sets it was found that the two parameter sarm showed improved fit compared to the one parameter sarm in both data sets

record breaking optimization results using the ruin and recreate principle a new optimization principle is presented solutions of problems are partly but significantly ruined and rebuilt or recreated afterwards performing this type of change frequently one can obtain astounding results for classical optimization problems the new method is particularly suited for more complex optimization problems discontinuous ones problems with hard to find admissible solutions problems with complex objectives or many constraints the method is an all purpose heuristic numerical results are given for the traveling salesman problem for the vehicle routing problem with time windows and for network optimization numerical evidence for the quality of the proposed principle is given for most of the instances of a research library of problems the ruin and recreate r r implementation achieved the best published results for many instances better or much better solutions could be found

lattice boltzmann simulation of steady non newtonian blood flow in a 3d generic stenosis case a lattice boltzmann simulation of blood flow using the carreau yasuda model to calculate the non newtonian viscosity is described in this paper the carreau yasuda model is implemented in the lattice boltzmann software by adjusting the shear dependent viscosity over the relaxation parameter which is locally computed each time step by applying the newton iteration within the flow solver a scheme to compare the non newtonian and newtonian flow effects is proposed finally a comparison has been made between non newtonian and newtonian flow in a 3d generic stenosis

routing optimization with time windows under uncertainty we study an a priori traveling salesman problem with time windows tsptw in which the travel times along the arcs are uncertain and the goal is to determine within a budget constraint a route for the service vehicle in order to arrive at the customers locations within their stipulated time windows as well as possible in particular service at customer s location cannot commence before the beginning of the time window and any arrival after the end of the time window is considered late and constitutes to poor customer service in articulating the service level of the tsptw under uncertainty we propose a new decision criterion called the essential riskiness index which has the computationally attractive feature of convexity that enables us to formulate and solve the problem more effectively as a decision criterion for articulating service levels it takes into account both the probability of lateness and its magnitude and can be applied in contexts where either the distributional information of the uncertain travel times is fully or partially known we propose a new formulation for the tsptw where we explicitly express the service starting time at each customer s location as a convex piecewise affine function of the travel times which would enable us to obtain the tractable formulation of the corresponding distributionally robust problem we also show how to optimize the essential riskiness index via benders decomposition and present cases where we can obtain closed form solutions to the subproblems we also illustrate in our numerical studies that this approach scales well with the number of samples used for the sample average approximation the approach can be extended to a more general setting including vehicle routing problem with time windows with uncertain travel times and customers demands

note on the complexity of the shortest path models for column generation in vrptw in this note we prove that the relaxation approach in designing the subproblem of pricing out only the feasible routes for the set partition formulation of the vrptw is justified on complexity grounds that is the first dynamic programming model presented in m desrochers j desrosiers and m solomon 1992 that is able to price out all feasible routes is np hard in the strong sense

stabilized stress velocity pressure finite element formulations of the navier stokes problem for fluids with non linear viscosity abstract the three field stress velocity pressure mixed formulation of the incompressible navier stokes problem can lead to two different types of numerical instabilities the first is associated with the incompressibility and loss of stability in the calculation of the stress field and the second with the dominant convection the first type of instabilities can be overcome by choosing an interpolation for the unknowns that satisfies the appropriate inf sup conditions whereas the dominant convection requires a stabilized formulation in any case this paper proposes two stabilized schemes of sub grid scale sgs type differing in the definition of the space of the sub grid scales and both allowing to use the same interpolation for the variables u p deviatoric stress velocity and pressure even in problems where the convection component is dominant and the velocity stress gradients are high another aspect considered in this work is the non linearity of the viscosity modeled with constitutive models of quasi newtonian type this paper includes a description of the proposed methods some of their implementation issues and a discussion about benefits and drawbacks of a three field formulation several numerical examples serve to justify our claims

branch and price and cut for the multiple traveling repairman problem with distance constraints abstract in this paper we extend the multiple traveling repairman problem by considering a limitation on the total distance that a vehicle can travel the resulting problem is called the multiple traveling repairmen problem with distance constraints mtrpd in the mtrpd a fleet of identical vehicles is dispatched to serve a set of customers each vehicle that starts from and ends at the depot is not allowed to travel a distance longer than a predetermined limit and each customer must be visited exactly once the objective is to minimize the total waiting time of all customers after the vehicles leave the depot to optimally solve the mtrpd we propose a new exact branch and price and cut algorithm where the column generation pricing subproblem is a resource constrained elementary shortest path problem with cumulative costs an ad hoc label setting algorithm armed with bidirectional search strategy is developed to solve the pricing subproblem computational results show the effectiveness of the proposed method the optimal solutions to 179 out of 180 test instances are reported in this paper our computational results serve as benchmarks for future researchers on the problem

real time vehicle rerouting problems with time windows this paper introduces and studies real time vehicle rerouting problems with time windows applicable to delivery and or pickup services that undergo service disruptions due to vehicle breakdowns in such problems one or more vehicles need to be rerouted in real time to perform uninitiated services with the objective to minimize a weighted sum of operating service cancellation and route disruption costs a lagrangian relaxation based heuristic is developed which includes an insertion based algorithm to obtain a feasible solution for the primal problem a dynamic programming based algorithm solves heuristically the shortest path problems with resource constraints that result from the lagrangian relaxation computational experiments show that the developed lagrangian heuristic performs very well

probabilistic analysis of a combined aggregation and math programming heuristic for a general class of vehicle routing and scheduling problems we propose and analyze a heuristic that uses region partitioning and an aggregation scheme for customer attributes load size time windows etc to create a finite number of customer types a math program is solved based on these aggregated customer types to generate a feasible solution to the original problem the problem class we address is quite general and defined by a number of general consistency properties problems in this class include vrps with general distance norms capacitated problems time window vrps pick up and delivery problems combined inventory control and routing problems and arc routing we provide a probabilistic analysis of this heuristic under very general probabilistic assumptions in particular we do not require independence between customer locations and their various attributes the heuristic is a s optimal as the number of customers n tends to infinity further it runs in o n log n time for a fixed relative error and can be designed to be asymptotically optimal w

vehicle routing problem with fuzzy time windows in this paper a vehicle routing problem with fuzzy time windows vrpftw is proposed and solved in the transportation business time windows are not always strictly obeyed and the deviation of service time from the customer specific time window determines the customer s satisfaction level which can also be regarded as the supplier s service level this paper applies fuzzy membership functions to characterize the service level issues associated with time window violation in a vehicle routing problem and proposes vrpftw vrpftw is formulated as a multi objective model with two goals 1 to minimize the travel distance and 2 to maximize the service level of the supplier to customers to solve this multi objective model a two stage algorithm is developed to obtain a pareto solution for vrpftw using the two stage algorithm vrpftw is decomposed into two subproblems namely a traditional vehicle routing problem with time windows email protected and a service improvement problem and each of the objectives is sequentially solved the service improvement problem is solved under two different scenarios when the fuzzy membership function is linear it is shown that the service improvement problem can be solved by the cutting plane algorithm within finite iterations and when the fuzzy membership function is concave the service improvement problem can be solved by a subgradient based algorithm moreover an alternative formulation of vrpftw is also proposed and analyzed experiments are conducted to compare different models of vehicle routing problems with time windows in situations where violation of time windows is allowed and the results show that the vrpftw model can achieve considerable cost savings while at the same time maintaining an acceptable service level

characterizing the manifest probability distributions of three latent trait models for accuracy and response time in this paper we study the statistical relations between three latent trait models for accuracies and response times the hierarchical model hm of van der linden psychometrika 72 3 287 308 2007 the signed residual time model sm proposed by maris and van der maas psychometrika 77 4 615 633 2012 and the drift diffusion model dm as proposed by tuerlinckx and de boeck psychometrika 70 4 629 650 2005 one important distinction between these models is that the hm and the dm either assume or imply that accuracies and response times are independent given the latent trait variables while the sm does not in this paper we investigate the impact of this conditional independence property or a lack thereof on the manifest probability distribution for accuracies and response times we will find that the manifest distributions of the latent trait models share several important features such as the dependency between accuracy and response time but we also find important differences such as in what function of response time is being modeled our method for characterizing the manifest probability distributions is related to the dutch identity holland in psychometrika 55 6 5 18 1990

parallel machine scheduling linear programming and parameter list scheduling heuristics in this paper we consider a class of parallel machine scheduling problems and their associated set partitioning formulations we show that the tightness of the linear programming relaxation of these formulations is directly related to the performance of a class of heuristics called parameter list scheduling heuristics this makes it possible to characterize the worst possible gap between optimal solutions for the scheduling problems and the corresponding linear programming relaxations in the case of the classical parallel machine weighted completion time model we also show that the solution to the linear programming relaxation of the set partitioning formulation is asymptotically optimal under mild assumptions on the distribution of job weights and processing times finally we extend most of the results to the time discretized formulation of machine scheduling problems

a generalized insertion heuristic for the traveling salesman problem with time windows this article describes a generalized insertion heuristic for the traveling salesman problem with time windows in which the objective is the minimization of travel times the algorithm gradually builds a route by inserting at each step a vertex in its neighbourhood on the current route and performing a local reoptimization this is done while checking the feasibility of the remaining part of the route backtracking is sometimes necessary once a feasible route has been determined an attempt is made to improve it by applying a post optimization phase based on the successive removal and reinsertion of all vertices tests performed on 375 instances indicate that the proposed heuristic compares very well with alternative methods and very often produces optimal or near optimal solutions

a new dantzig wolfe reformulation and branch and price algorithm for the capacitated lot sizing problem with setup times although the textbook dantzig wolfe decomposition reformulation for the capacitated lot sizing problem as already proposed by manne manne a s 1958 programming of economic lot sizes management sci 4 2 115 135 provides a strong lower bound it also has an important structural deficiency imposing integrality constraints on the columns in the master program will not necessarily give the optimal integer programming solution manne s model contains only production plans that satisfy the wagner whitin property and it is well known that the optimal solution to a capacitated lot sizing problem will not necessarily satisfy this property the first contribution of this paper answers the following question unsolved for almost 50 years if manne s formulation is not equivalent to the original problem what is then a correct reformulation we develop an equivalent mixed integer programming mip formulation to the original problem and show how this results from applying the dantzig wolfe decomposition to the original mip formulation the set of extreme points of the lot size polytope that are needed for this mip dantzig wolfe reformulation is much larger than the set of dominant plans used by manne we further show how the integrality restrictions on the original setup variables translate into integrality restrictions on the new master variables by separating the setup and production decisions our new formulation gives the same lower bound as manne s reformulation second we develop a branch and price algorithm for the problem computational experiments are presented on data sets available from the literature column generation is accelerated by a combination of simplex and subgradient optimization for finding the dual prices the results show that branch and price is computationally tractable and competitive with other state of the art approaches found in the literature

saddlepoint approximations of the distribution of the person parameter in the two parameter logistic model large sample theory states the asymptotic normality of the maximum likelihood estimator of the person parameter in the two parameter logistic 2pl model in short tests however the assumption of normality can be grossly wrong as a consequence intended coverage rates may be exceeded and confidence intervals are revealed to be overly conservative methods belonging to the higher order theory more specifically saddlepoint approximations are a convenient way to deal with small sample problems confidence bounds obtained by these means hold the approximate confidence level for a broad range of the person parameter moreover an approximation to the exact distribution permits to compute median unbiased estimates mue that are as likely to overestimate as to underestimate the true person parameter additionally in small samples these mue are less mean biased than the often used maximum likelihood estimator

dynamic aggregation of set partitioning constraints in column generation column generation is often used to solve problems involving set partitioning constraints such as vehicle routing and crew scheduling problems when these constraints are in large numbers and the columns have on average more than 8 12 nonzero elements column generation often becomes inefficient because solving the master problem requires very long solution times at each iteration due to high degeneracy to overcome this difficulty we introduce a dynamic constraint aggregation method that reduces the number of set partitioning constraints in the master problem by aggregating some of them according to an equivalence relation to guarantee optimality this equivalence relation is updated dynamically throughout the solution process tests on the linear relaxation of the simultaneous vehicle and crew scheduling problem in urban mass transit show that this method significantly reduces the size of the master problem degeneracy and solution times especially for larger problems in fact for an instance involving 1 600 set partitioning constraints the master problem solution time is reduced by a factor of 8

worst case analyses linear programming and the bin packing problem in this paper we consider the familiar bin packing problem and its associated set partitioning formulation we show that the optimal solution to the bin packing problem can be no larger than 4 3 zlp wherezlp is the optimal solution value of the linear programming relaxation of the set partitioning formulation an example is provided to show that the bound is tight a by product of our analysis is a new worst case bound on the performance of the well studied first fit decreasing and best fit decreasing heuristics

an optimal algorithm for the traveling salesman problem with time windows this paper presents the development of new elimination tests which greatly enhance the performance of a relatively well established dynamic programming approach and its application to the minimization of the total traveling cost for the traveling salesman problem with time windows the tests take advantage of the time window constraints to significantly reduce the state space and the number of state transitions these reductions are performed both a priori and during the execution of the algorithm the approach does not experience problems stemming from increasing problem size wider or overlapping time windows or an increasing number of states nearly as rapidly as other methods our computational results indicate that the algorithm was successful in solving problems with up to 200 nodes and fairly wide time windows when the density of the nodes in the geographical region was kept constant as the problem size was increased the algorithm was capable of solving problems with up to 800 nodes for these problems the cpu time increased linearly with problem size these problem sizes are much larger than those of problems previously reported in the literature

using em to obtain asymptotic variance covariance matrices the sem algorithm abstract the expectation maximization em algorithm is a popular and often remarkably simple method for maximum likelihood estimation in incomplete data problems one criticism of em in practice is that asymptotic variance covariance matrices for parameters e g standard errors are not automatic byproducts as they are when using some other methods such as newton raphson in this article we define and illustrate a procedure that obtains numerically stable asymptotic variance covariance matrices using only the code for computing the complete data variance covariance matrix the code for em itself and code for standard matrix operations the basic idea is to use the fact that the rate of convergence of em is governed by the fractions of missing information to find the increased variability due to missing information to add to the complete data variance covariance matrix we call this supplemented em algorithm the sem algorithm theory and particular examples reinforce the conclusion that the sem alg

a hierarchical framework for modeling speed and accuracy on test items current modeling of response times on test items has been strongly influenced by the paradigm of experimental reaction time research in psychology for instance some of the models have a parameter structure that was chosen to represent a speed accuracy tradeoff while others equate speed directly with response time also several response time models seem to be unclear as to the level of parametrization they represent a hierarchical framework for modeling speed and accuracy on test items is presented as an alternative to these models the framework allows a plug and play approach with alternative choices of models for the response and response time distributions as well as the distributions of their parameters bayesian treatment of the framework with markov chain monte carlo mcmc computation facilitates the approach use of the framework is illustrated for the choice of a normal ogive response model a lognormal model for the response times and multivariate normal models for their parameters with gibbs sampling from the joint posterior distribution

a branch and price algorithm for the generalized assignment problem the generalized assignment problem examines the maximum profit assignment of jobs to agents such that each job is assigned to precisely one agent subject to capacity restrictions on the agents a new algorithm for the generalized assignment problem is presented that employs both column generation and branch and bound to obtain optimal integer solutions to a set partitioning formulation of the problem

a column generation based decomposition algorithm for a parallel machine just in time scheduling problem we propose a column generation based exact decomposition algorithm for the problem of scheduling n jobs with an unrestrictively large common due date on m identical parallel machines to minimize total weighted earliness and tardiness we first formulate the problem as an integer program then reformulate it using dantzig wolfe decomposition as a set partitioning problem with side constraints based on this set partitioning formulation a branch and bound exact solution algorithm is developed for the problem in the branch and bound tree each node is the linear relaxation problem of a set partitioning problem with side constraints this linear relaxation problem is solved by column generation approach where columns represent partial schedules on single machines and are generated by solving two single machine subproblems our computational results show that this decomposition algorithm is capable of solving problems with up to 60 jobs in reasonable cpu time

generalized residuals for general models for contingency tables with application to item response theory generalized residuals are a tool employed in the analysis of contingency tables to examine possible sources of model error they have typically been applied to log linear models and to latent class models a general approach to generalized residuals is developed for a very general class of models for contingency tables to illustrate their use generalized residuals are applied to models based on item response theory irt models such models are commonly applied to analysis of standardized achievement or aptitude tests to obtain a realistic perspective on application of generalized residuals actual testing data are employed

an interpolation approximation for queueing systems with poisson input for many queueing systems of practical interest it is difficult to obtain exact analytical results it is however often possible to obtain asymptotic results for light and heavy traffic heavy traffic limit theorems yield expressions for normalized quantities of interest in light traffic we can obtain in addition to limits more sensitive information by calculating what are effectively derivatives of the quantity of interest with respect to the arrival rate we can then combine the light and heavy traffic results to yield a polynomial in the arrival rate as an approximation to the normalized quantity of interest for instance by utilizing the heavy traffic limit the light traffic limit and the first derivative we can obtain a quadratic approximation then by reversing the normalization process we can obtain an approximation for the original quantity of interest in this paper we present the details of the above approximation focusing via several examples on applications of the method we then compare the results of the approximation for the examples considered with exact and simulation results in addition we compare our results to some related approximations for the examples considered the approximation works extremely well

subset row inequalities applied to the vehicle routing problem with time windows this paper presents a branch and cut and price algorithm for the vehicle routing problem with time windows the standard dantzig wolfe decomposition of the arc flow formulation leads to a set partitioning problem as the master problem and an elementary shortest path problem with resource constraints as the pricing problem we introduce the subset row inequalities which are chvatal gomory rank 1 cuts based on a subset of the constraints in the master problem applying a subset row inequality in the master problem increases the complexity of the label setting algorithm used to solve the pricing problem because an additional resource is added for each inequality we propose a modified dominance criterion that makes it possible to dominate more labels by exploiting the step like structure of the objective function of the pricing problem computational experiments have been performed on the solomon benchmarks where we were able to close several instances the results show that applying subset row inequalities in the master problem significantly improves the lower bound and in many cases makes it possible to prove optimality in the root node

lattice boltzmann simulations of blood flow non newtonian rheology and clotting processes the numerical simulation of thrombosis in stented aneurysms is an important issue to estimate the efficiency of a stent in this paper we consider a lattice boltzmann lb approach to bloodflow modeling and we implement a non newtonian correction in order to reproduce more realistic flow profiles we obtain a good agreement between simulations and casson s model of blood rheology in a simple geometry finally we discuss how by using a passive scalar suspension model with aggregation on top of the lb dynamics we can describe the clotting processes in the aneurysm

assessing item fit for unidimensional item response theory models using residuals from estimated item response functions residual analysis e g hambleton swaminathan item response theory principles and applications kluwer academic boston 1985 hambleton swaminathan rogers fundamentals of item response theory sage newbury park 1991 is a popular method to assess fit of item response theory irt models we suggest a form of residual analysis that may be applied to assess item fit for unidimensional irt models the residual analysis consists of a comparison of the maximum likelihood estimate of the item characteristic curve with an alternative ratio estimate of the item characteristic curve the large sample distribution of the residual is proved to be standardized normal when the irt model fits the data we compare the performance of our suggested residual to the standardized residual of hambleton et al fundamentals of item response theory sage newbury park 1991 in a detailed simulation study we then calculate our suggested residuals using data from an operational test the residuals appear to be useful in assessing the item fit for unidimensional irt models

the tree representation for the pickup and delivery traveling salesman problem with lifo loading the feasible solutions of the traveling salesman problem with pickup and delivery tsppd are commonly represented by vertex lists however when the tsppd is required to follow a policy that loading and unloading operations must be performed in a last in first out lifo manner we show that its feasible solutions can be represented by trees consequently we develop a novel variable neighborhood search vns heuristic for the tsppd with last in first out loading tsppdl involving several search operators based on the tree data structure extensive experiments suggest that our vns heuristic is superior to the current best heuristics for the tsppdl in terms of solution quality while requiring no more computing time as the size of the problem increases

a neural network based approach to the double traveling salesman problem the double traveling salesman problem is a variation of the basic traveling salesman problem where targets can be reached by two salespersons operating in parallel the real problem addressed by this work concerns the optimization of the harvest sequence for the two independent arms of a fruit harvesting robot this application poses further constraints like a collision avoidance function the proposed solution is based on a self organizing map structure initialized with as many artificial neurons as the number of targets to be reached one of the key components of the process is the combination of competitive relaxation with a mechanism for deleting and creating artificial neurons moreover in the competitive relaxation process information about the trajectory connecting the neurons is combined with the distance of neurons from the target this strategy prevents tangles in the trajectory and collisions between the two tours results of tests indicate that the proposed approach is efficient and reliable for harvest sequence planning moreover the enhancements added to the pure self organizing map concept are of wider importance as proved by a traveling salesman problem version of the program simplified from the double version for comparison

lagrangian relaxation methods for solving the minimum fleet size multiple traveling salesman problem with time windows we consider the problem of finding the minimum number of vehicles required to visit once a set of nodes subject to time window constraints for a homogeneous fleet of vehicles located at a common depot this problem can be formulated as a network flow problem with additional time constraints the paper presents an optimal solution approach using the augmented lagrangian method two lagrangian relaxations are studied in the first one the time constraints are relaxed producing network subproblems which are easy to solve but the bound obtained is weak in the second relaxation constraints requiring that each node be visited are relaxed producing shortest path subproblems with time window constraints and integrality conditions the bound produced is always excellent numerical results for several actual school busing problems with up to 223 nodes are discussed comparisons with a set partitioning formulation solved by column generation are given

algorithms for the vehicle routing and scheduling problems with time window constraints this paper considers the design and analysis of algorithms for vehicle routing and scheduling problems with time window constraints given the intrinsic difficulty of this problem class approximation methods seem to offer the most promise for practical size problems after describing a variety of heuristics we conduct an extensive computational study of their performance the problem set includes routing and scheduling environments that differ in terms of the type of data used to generate the problems the percentage of customers with time windows their tightness and positioning and the scheduling horizon we found that several heuristics performed well in different problem environments in particular an insertion type heuristic consistently gave very good results

a race model for responses and response times in tests latent trait models for responses and response times in tests are often pure statistical models without a close connection to features of the assumed response process in the present paper a new model is presented that is more closely related to assumptions about the response process the model is based on two increasing stochastic processes each stochastic process represents the accumulation of knowledge with respect to one of two response options the correct and incorrect response both accumulators compete and the accumulator that first exceeds a critical level determines the response general assumptions about the accumulators result in a race between two response times that follow a bivariate birnbaum saunders distribution the model can be calibrated with marginal maximum likelihood estimation feasibility of the estimation approach is demonstrated in a simulation study additionally a test of model fit is proposed finally the model will be used for the analysis of an empirical data set

a branch first cut second approach for locomotive assignment the problem of assigning locomotives to trains consists of selecting the types and number of engines that minimize the fixed and operational locomotive costs resulting from providing sufficient power to pull trains on fixed schedules the force required to pull a train is often expressed in terms of horsepower and tonnage requirements rather than in terms of number of engines this complicates the solution process of the integer programming formulation and usually creates a large integrality gap furthermore the solution of the linearly relaxed problem is strongly fractional to obtain integer solutions we propose a novel branch and cut approach the core of the method consists of branching decisions that define on one branch the projection of the problem on a low dimensional subspace there the facets of the polyhedron describing a restricted constraint set can be easily derived we call this approach branch first cut second we first derive facets when at most two types of engines are used we then extend the branching rule to cases involving additional locomotive types we have conducted computational experiments using actual data from the canadian national railway company simulated test problems involving two or more locomotive types were solved over 1 2 and 3 day rolling horizons the cuts were successful in reducing the average integrality gap by 52 for the two type case and by 34 when more than 25 types were used furthermore the branch first cut second approach was instrumental in improving the best known solution for an almost 2 000 leg weekly problem involving 26 locomotive types it reduced the number of locomotives by 11 or 1 1 at an equivalent savings of 3 000 000 per unit additional tests on different weekly data produced almost identical results

vehicle routing problem with time windows and a limited number of vehicles abstract this paper introduces a variant of the vehicle routing problem with time windows where a limited number of vehicles is given m vrptw under this scenario a feasible solution is one that may contain either unserved customers and or relaxed time windows we provide a computable upper bound to the problem to solve the problem we propose a tabu search approach characterized by a holding list and a mechanism to force dense packing within a route we also allow time windows to be relaxed by introducing the notion of penalty for lateness in our approach customer jobs are inserted based on a hierarchical objective function that captures multiple objectives computational results on benchmark problems show that our approach yields solutions that are competitive to best published results on vrptw on m vrptw instances experiments show that our approach produces solutions that are very close to computed upper bounds moreover as the number of vehicles decreases the routes become more densely packed monotically this shows that our approach is good from both the optimality as well as stability point of view

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

multiple pickup and delivery traveling salesman problem with last in first out loading and distance constraints abstract we extend the traveling salesman problem with pickup and delivery and lifo loading tsppdl by considering two additional factors namely the use of multiple vehicles and a limitation on the total distance that a vehicle can travel both of these factors occur commonly in practice we call the resultant problem the multiple pickup and delivery traveling salesman problem with lifo loading and distance constraints mtsppd ld this paper presents a thorough preliminary investigation of the mtsppd ld we propose six new neighborhood operators for the problem that can be used in search heuristics or meta heuristics we also devise a two stage approach for solving the problem where the first stage focuses on minimizing the number of vehicles required and the second stage minimizes the total travel distance we consider two possible approaches for the first stage simulated annealing and ejection pool and two for the second stage variable neighborhood search and probabilistic tabu search our computational results serve as benchmarks for future researchers on the problem