aggregation and mixed integer rounding to solve mips in this paper we discuss the use of mixed integer rounding mir inequalities to solve mixed integer programs mir inequalities are essentially gomory mixed integer cuts however as we wish to use problem structure we insist that mir inequalities be generated from constraints or simple aggregations of constraints of the original problem this idea is motivated by the observation that several strong valid inequalities based on specific problem structure can be derived as mir inequalities here we present and test a separation routine for such mir inequalities that includes a heuristic row aggregation procedure to generate a single knapsack plus continuous variables constraint complementation of variables and finally the generation of an mir inequality inserted in a branch and cut system the results suggest that such a routine is a useful additional tool for tackling a variety of mixed integer programming problems

immersing almost geodesic surfaces in a closed hyperbolic three manifold let m 3 be a closed hyperbolic three manifold we construct closed surfaces that map by immersions into m 3 so that for each one the corresponding mapping on the universal covering spaces is an embedding or in other words the corresponding induced mapping on fundamental groups is an injection

random groups contain surface subgroups 1 introductiongromov famously asked the following surface subgroup question let g be a one ended hyperbolic group does gcontain a subgroup isomorphic to the fundamental group of a closed surface with 0 beyond its intrinsic appeal and its obvious connections to the virtual hakenconjecture in 3 manifold topology now a theorem of agol 1 one reason gromovwas interested in this question was the hope that such surface subgroups could beused as essential structural components of hyperbolic groups 9 our interest inthis question is stimulated by a belief that surface groups not necessarily closed can act as a sort of bridge between hyperbolic geometry and symplectic geometry through their connection to causal structures quasimorphisms stable commutatorlength etc despite receiving considerable attention the surface subgroup question is wideopen in general although in the speci c case of hyperbolic 3 manifold groups it waspositively resolved by kahn markovic 10 the main results of our paper may besummarized by saying that we show that gromov s question has a positive answerfor most hyperbolic groups in fact the executive summary says that 1 most groups contain many surface subgroups 2 these surface subgroups are quasiconvex i e their intrinsic and extrinsicgeometry is uniformly comparable on large scales and 3 these surface subgroups can be constructed and their properties certi edquickly and easily here most groups is a proxy for random groups in gromov s few relators ordensity models to be de ned presently in 8 9 also see 14 gromov introduced the notion of a random group infact he introduced two such models the few relators model and the density model in either model one rst xes a free group f

a multi item production planning model with setup times algorithms reformulations and polyhedral characterizations for a special case we study a special case of a structured mixed integer programming model that arises in production planning for the most general case of the model called pi we have earlier identified families of facet defining valid inequalities l s inequalities introduced for the uncapacitated lot sizing problem by barany van roy and wolsey cover inequalities and reverse cover inequalities pi is hard in this paper we focus on a special case called pic we describe a polynomial algorithm for pic and we use this algorithm to derive an extended formulation of polynomial size for pic projecting from this extended formulation onto the original space of variables we show that l s inequalities cover inequalities and reverse cover inequalities suffice to solve the special case pic by linear programming we also describe fast combinatorial separation algorithms for cover and reverse cover inequalities for pic finally we discuss the relationship between our results for pic and a model studied previously by goemans

capacitated facility location separation algorithms and computational experience we consider the polyhedral approach to solving the capacitated facility location problem the valid inequalities considered are the knapsack cover flow cover effective capacity single depot and combinatorial inequalities the flow cover effective capacity and single depot inequalities form subfamilies of the general family of submodular inequalities the separation problem based on the family of submodular inequalities is np hard in general for the well known subclass of flow cover inequalities however we show that if the client set is fixed and if all capacities are equal then the separation problem can be solved in polynomial time for the flow cover inequalities based on an arbitrary client set and general capacities and for the effective capacity and single depot inequalities we develop separation heuristics an important part of these heuristics is based on the result that two specific conditions are necessary for the effective cover inequalities to be facet defining the way these results are stated indicates precisely how structures that violate the two conditions can be modified to produce stronger inequalities the family of combinatorial inequalities was originally developed for the uncapacitated facility location problem but is also valid for the capacitated problem no computational experience using the combinatorial inequalities has been reported so far here we suggest how partial output from the heuristic identifying violated submodular inequalities can be used as input to a heuristic identifying violated combinatorial inequalities we report on computational results from solving 60 medium size problems

the teacher assignment problem a special case of the fixed charge transportation problem a basic model of the task of assigning classes to professors in such a way that the average number of distinct subjects assigned to each professor is minimized is formulated as a mixed integer program it turns out that the problem is a special case of the fixed charge transportation problem which in some cases corresponds to finding a basic solution of a transportation problem which is as degenerate as possible we present an equivalent alternative formulation of the problem which makes it easy to prove that it is np hard in the strong sense and an exact branch and bound algorithm for its solution based on this alternative formulation is outlined computational experiments with data from a concrete problem concludes the paper

subset coefficient reduction cuts for 0 1 mixed integer programming we describe a method for generating cuts for mixed integer 0 1 programs these cuts are designed to tighten an integer program prior to applying linear programming based branch and bound algorithms the method involves two basic ideas subset selection and coefficient reduction coefficient reduction is a process of reducing the coefficients of the 0 1 variables subset selection is combined with coefficient reduction by applying the coefficient reduction process to the coefficients of a subset of variables from the constraints in the problem formulation the paper exploits these two simple ideas to derive a broad class of cuts for integer programs with both 0 1 and continuous variables it also reports on the use of this methodology in solving a variety of fixed charge problems

the merchant subtour problem we consider the problem of a travelling merchant who makes money by buying commodities where they are cheap and selling them in other places where he can make a profit the merchant ships commodities of his own choice in a van of fixed capacity given the prices of all the commodities in all of the places and the cost of driving from one place to another the problem the merchant faces each day is to select a subset of the cities that he can visit in a day and to determine the order in which the cities are visited such that the total profit is maximised we call this problem the merchant subtour problem the msp models the pricing problem of a rather complex pickup and delivery problem that was given to us by the dutch logistics company van gend loos we show that a special case of the msp has a totally unimodular constraint matrix this knowledge enables us to develop a tabu search algorithm for finding good feasible solutions to the msp and a branch and price and cut algorithm for solving the msp to optimality the relaxations solved in each node of the branch and bound tree are strengthened by lifted knapsack inequalities lifted cycle inequalities and mod k cuts we present computational results on data sets derived from our main instance of the van gend loos pickup and delivery problem

generating cuts in integer programming with families of special ordered sets abstract this paper describes families of cuts which can be added to integer programming formulations incorporating special ordered sets ways in which the cuts can be used are discussed and some computational experience is presented

asymptotic expansions of the distributions of the estimates of coefficients in a simultaneous equation system abstract in this paper asymptotic expansions are derived for the density functions of the tsls and liml estimates of coefficients in a simultaneous equation system when the sample size increases and the effect of the exogenous variables increases along the sample size these approximations are used to compare the asymptotic moments of the tsls and liml estimates and the concentration of probability around the true value of the estimates

evaluation of the distribution function of the limited information maximum likelihood estimator the distributions of the limited information maximum likelihood estimator for the coefficient of one endogenous variable are evaluated numerically tables are given for enough values of the parameters to cover all cases of interests comparisons are made with the two stage least squares estimator

o n log n procedures for tightening cover inequalities abstract we present two procedures for tightening cover induced inequalities in 0 1 programs by using knapsack constraints plus some other information from the program the tightening is obtained by solving successive knapsack problems with all 0 1 objective function coefficients and using dominance criteria to avoid the explicit solving of some knapsack problems the new constraints are 0 1 equivalent to and lp tighter than the original ones both procedures have o n log n complexity where n is the number of variables with nonzero coefficients in the knapsack constraint however one of them can strongly reduce the computational effort some computational experience is reported

a lift and project cutting plane algorithm for mixed 0 1 programs we propose a cutting plane algorithm for mixed 0 1 programs based on a family of polyhedra which strengthen the usual lp relaxation we show how to generate a facet of a polyhedron in this family which is most violated by the current fractional point this cut is found through the solution of a linear program that has about twice the size of the usual lp relaxation a lifting step is used to reduce the size of the lp s needed to generate the cuts an additional strengthening step suggested by balas and jeroslow is then applied we report our computational experience with a preliminary version of the algorithm this approach is related to the work of balas on disjunctive programming the matrix cone relaxations of lovasz and schrijver and the hierarchy of relaxations of sherali and adams

using lagrangean techniques to solve hierarchical production planning problems this paper proposes and tests a procedure for decomposing a large scale production planning problem modeled as a mixed integer linear program we interpret this decomposition in the context of hax and meal s hierarchical framework for production planning the procedure decomposes the production planning problem into two subproblems which correspond to the aggregate planning subproblem and a disaggregation subproblem in the hax meal framework the linking mechanism for these two subproblems is an inventory consistency relationship which is priced out by a set of lagrange multipliers the best values for the multipliers are found by an iterative procedure which may be interpreted as a feedback mechanism in the hax meal framework at each iteration the procedure finds both a lower bound on the optimal value to the production planning problem and a feasible solution from which an upper bound is obtained our computational tests show that the best feasible solution found from this procedure is very close to o

mixed 0 1 programming by lift and project in a branch and cut framework we investigate the computational issues that need to be addressed when incorporating general cutting planes for mixed 0 1 programs into a branch and cut framework the cuts we use are of the lift and project variety some of the issues addressed have a theoretical answer but others are of an experimental nature and are settled by comparing alternatives on a set of test problems the resulting code is a robust solver for mixed 0 1 programs we compare it with several existing codes on a wide range of test problems it performs as well as or better than some of the best currently available mixed integer programming codes

valid linear inequalities for fixed charge problems many problems in the operations research management science literature can be formulated with both zero one and continuous variables however the exact optimization of such mixed zero one models remains a computational challenge in this paper we propose to study mixed problems from a mathematical point of view that is similar in spirit to recent research on purely combinatorial problems that has investigated systems of defining linear inequalities or facets of the underlying polytope at least two numerical studies have validated this line of research computationally and the advances in the problem solving capabilities are considerable we expect that similar gains are possible for the mixed zero one problem more precisely we consider the mixed integer programs whose feasible region x is composed of i a simple additive constraint in the continuous variables xj for j 1 2 n and ii constraints 0 xj mjyj defined by binary variables yj for j 1 2 n this type of feasible region arises in a variety of mixed integer problems and particularly in network problems with fixed charges on the arcs we derive two classes of facet defining linear inequalities of the convex hull of x and show that the second of these classes gives a complete description of the convex hull when mj m for all j we also develop methods to detect violated inequalities from these classes so that these facets can be used as cutting planes to strengthen the formulations of certain mixed integer problems

asymptotic expansions of the distributions of the structural variance estimators in a simultaneous equations system abstract asymptotic expansions of three alternative classes of structural variance estimators associated with the k class estimators of structural coefficients are derived for two parameter sequences a sequence in which the non centrality parameter increases while the sample size stays fixed called large or small disturbance sequence and that in which the number of observations increases the accuracy of approximations to small sample distributions are numerically examined with help of monte carlo studies properties of the sum of squared residuals of an estimated structural equation are also found from our study

agent preferences and the topology of networks in this paper a different framework to study weighed networks is introduced the idea behind this methodology is to consider that each node of the network is an agent that desires to satisfy his her preferences in an economic sense moreover the formation of a link between two agents depends on the benefits and costs associated with this link therefore an edge between two given nodes will arise only if the tradeoff between satisfaction and cost for building it is jointly positive using a computational framework i intend to show that depending on the agents combination of benefits and costs some very well known networks can naturally arise

a polyhedral study of the cardinality constrained knapsack problem a cardinality constrained knapsack problem is a continuous knapsack problem in which no more than a specified number of nonnegative variables are allowed to be positive this structure occurs for example in areas such as finance location and scheduling traditionally cardinality constraints are modeled by introducing auxiliary 0 1 variables and additional constraints that relate the continuous and the 0 1 variables we use an alternative approach in which we keep in the model only the continuous variables and we enforce the cardinality constraint through a specialized branching scheme and the use of strong inequalities valid for the convex hull of the feasible set in the space of the continuous variables to derive the valid inequalities we extend the concepts of cover and cover inequality commonly used in 0 1 programming to this class of problems and we show how cover inequalities can be lifted to derive facet defining inequalities we present three families of non trivial facet defining inequalities that are lifted cover inequalities finally we report computational results that demonstrate the effectiveness of lifted cover inequalities and the superiority of the approach of not introducing auxiliary 0 1 variables over the traditional mip approach for this class of problems

perturbative series and the moduli space of riemann surfaces on utilise des techniques de la theorie quantique des champs pour calculer des quantites reliees aux groupes de symetrie de paires f g ou f est une surface et g une epine de f

surface subgroups from linear programming we show that a random endomorphism of a free group gives rise to an hnn extension which contains a closed surface subgroup with probability one a special case is the hnn extension associated to the endomorphism of a rank 2 free group considered by sapir sending a to ab and b to ba we further show that a group obtained by doubling a free group along any collection of subgroups of arbitrary rank has the property that every rational 2 dimensional homology class is virtually represented by surface subgroups and the unit ball in the gromov norm is a finite sided rational polyhedron these results are obtained by a mixture of combinatorial geometric and linear programming techniques we obtain other related results of a more technical nature concerning stable commutator length in free groups especially concerning the structure of the space of so called counting quasimorphisms

scl in graphs of groups let g be a group acting on a tree with cyclic edge and vertex stabilizers then stable commutator length scl is rational in g furthermore scl varies predictably and converges to rational limits in so called surgery families this is a homological analog of the phenomenon of geometric convergence in hyperbolic dehn surgery

solving 0 1 integer programming problems arising from large scale planning models we present methods that are useful in solving some large scale hierarchical planning models involving 0 1 variables these 0 1 programming problems initially could not be solved with any standard techniques we employed several approaches to take advantage of the hierarchical structure of variables ordered by importance and other structures present in the models critical but not sufficient for success was a strong linear programming formulation we describe methods for strengthening the linear programs as well as other techniques necessary for a commercial branch and bound code to be successful in solving these problems

solving mixed integer programming problems using automatic reformulation in this paper we describe computational experience in solving mixed 0 1 programming problems using strong valid inequalities as cutting planes in particular we report on the solution to optimality of 18 medium to large size problems including production planning problems with setup costs and capacity constraints multilevel distribution planning problems drainage and heating system design problems and electricity generator scheduling problems the solution approach uses the theory of strong valid inequalities that we developed in a series of earlier papers here we report specifically on the implementation of an experimental system mpsarx which consists of the sciconic mathematical programming system and an automatic reformulation executor arx that use this theory and on the results obtained with this system

topology of finite graphs this paper derives from a course in group theory which i gave at berkeley in 1982 i wanted to prove the standard theorems on free groups and discovered that after a few preliminaries the notion of locally injective map or immersion of graphs was very useful this enables one to see in an effective easy algorithmic way just what happens with finitely generated free groups one can understand in this way 1 howson s theorem that if a and b are finitely generated subgroups of a free group then a b is finitely generated and 2 m hall s theorem that finitely generated subgroups of free groups are closed in the profinite topology during this course s m gersten came up with a simple proof of h neumann s inequality on the ranks in howson s theorem one of the ideas in gersten s proof was to use core graphs graphs with no trees hanging on subsequently i found that some consequences of a paper of greenberg s could be proved using core graphs and covering translations of immersions the most striking such result is that if a and b are finitely generated subgroups of a free group and if a c b is of finite index in both a and b then a b is of finite index in a v b the subgroup generated by a ub

railroad blocking a network design application in this study we formulate the railroad blocking problems as a network design problem with maximum degree and flow constraints on the nodes and propose a heuristic lagrangian relaxation approach to solve the problem the newapproach decomposes the complicated mixed integer programming problem into two simple subproblems so that the storage requirement and computational effort are greatly reduced a set of inequalities are added to one subproblem to tighten the lower bounds and facilitate generating feasible solutions subgradient optimization is used to solve the lagrangian dual an advanced dual feasible solution is generated to speed up the convergence of the subgradient method the model is tested on blocking problems from a major railroad and the results show that the blocking plans generated have the potential to reduce the railroad s operating costs by millions of dollars annually

on the polyhedral structure of a multi item production planning model with setup times we present and study a mixed integer programming model that arises as a substructure in many industrial applications this model generalizes a number of structured mip models previously studied and it provides a relaxation of various capacitated production planning problems and other fixed charge network flow problems we analyze the polyhedral structure of the convex hull of this model as well as of a strengthened lp relaxation among other results we present valid inequalities that induce facets of the convex hull under certain conditions we also discuss how to strengthen these inequalities by using known results for lifting valid inequalities for 0 1 continuous knapsack problems

modeling and solving the two facility capacitated network loading problem this paper studies a topical and economically significant capacitated network design problem that arises in the telecommunications industry in this problem given point to point communication demand in a network must be met by installing loading capacitated facilities on the arcs loading a facility incurs an arc specific and facility dependent cost this paper develops modeling and solution approaches for loading facilities to satisfy the given demand at minimum cost we consider two approaches for solving the underlying mixed integer program a lagrangian relaxation strategy and a cutting plane approach that uses three classes of valid inequalities that we identify for the problem we show that a linear programming formulation that includes these inequalities always approximates the value of the mixed integer program at least as well as the lagrangian relaxation bound our computational results on a set of prototypical telecommunication data show that including these inequalities considerably improves the gap between the integer programming formulation and its linear programming relaxation from an average of 25 to an average of 8 these results show that strong cutting planes can be an effective modeling and algorithmic tool for solving problems of the size that arise in the telecommunications industry

using cutting planes in an interactive reference point approach for multiobjective integer linear programming problems we propose an interactive approach for multiple objective integer linear programming moilp problems that combines the use of the tchebycheff metric with cutting plane techniques at each interaction the method computes the nondominated solution for the moilp problem that is closest to a reference point according to the tchebycheff metric the information provided by the decision maker in each dialogue phase is used to adjust the next reference point through a sensitivity analysis stage cutting plane techniques enable the method to take advantage of computations performed at previous iterations to solve the next scalarizing integer program we address both theoretical issues and the computational implementation

different transformations for solving non convex trim loss problems by minlp in the present paper trim loss problems often named the cutting stock problem connected to the paper industry are considered the problem is to cut out a set of product paper rolls from raw paper rolls such that the cost function including the trim loss as well as the costs for the over production is minimized the problem is non convex due to certain bilinear constraints the problem can however be transformed into linear or convex form the resulting transformed problems can thereafter be solved as mixed integer linear programming problems or convex mixed integer non linear programming problems the linear and convex formulations are attractive from a formal point of view since global optimal solutions to the originally non convex problem can be obtained however as the examples considered will show the numerical efficiency of the solutions from the different transformed formulations varies considerably an example based on a trim optimization problem encountered daily at a finnish paper converting mill is finally presented in order to demonstrate differences in the numerical solutions

obtaining clique cover and coefficient reduction inequalities as chvatal gomory inequalities and gomory fractional cuts abstract we show how clique and cover induced inequalities implied from 0 1 knapsack constraints can be obtained as chvatal gomory inequalities lp tighter and 0 1 equivalent constraints to 0 1 knapsack constraints obtained by the big m reduction procedure can also be generated as chvatal gomory inequalities we also show how some extended coefficient reduction based lp tighter and 0 1 equivalent constraints can be generated as gomory fractional cuts

cutting planes for integer programs with general integer variables we investigate the use of cutting planes for integer programs with general integer variables we show how cutting planes arising from knapsack inequalities can be generated and lifted as in the case of 0 1 variables we also explore the use of gomory s mixed integer cuts we address both theoretical and computational issues and show how to embed these cutting planes in a branch and bound framework we compare results obtained by using our cut generation routines in two existing systems with a commercially available branch and bound code on a range of test problems arising from practical applications 1998 the mathematical programming society inc published by elsevier science b v

effective heuristics for multiproduct partial shipment models motivated by real applications we consider the problem of shipping products to multiple customers from limited inventory after formulating the optimization problems under different restrictions on partial shipments we find that commercially available packages applied directly are unsatisfactory as are simple greedy approaches we develop a scheme of heuristics that enables the user to select a good balance between computation time and effectiveness a detailed computational study of one and two period industrial sized problems indicates that these heuristics are computationally practical and generate solutions that are on average within 34 of the optimum

fixed charge transportation problem facets of the projection polyhedron in this paper we consider the well known fixed charge transportation problem to send any flow from source si to destination tj we incur a unit variable shipping cost of cij and a fixed cost fij here we study the structure of the projection polyhedron of this problem in the space of 0 1 variables associated with fixed charges and we develop several classes of valid inequalities and derive conditions under which they are facet defining in some cases if the conditions are not satisfied we show how they can be lifted to define facets several heuristics for generating and adding these facets are presented using these results we develop a computationally effective algorithm for solving the problem the computational results clearly indicate the usefulness of this approach

valid inequalities and projecting the multicommodity extended formulation for uncapacitated fixed charge network flow problems multicommodity extended formulations of single source uncapacitated fixed charge network flow problems have significantly sharper linear programming relaxations than the standard flow formulations however the tradeoff is the introduction of many new constraints and variables to accomodate a sink oriented flow disaggregation in this paper we introduce a new family of dicut collection inequalities and show that they completely describe the projection of the multicommodity formulation onto the original variables a simple subclass is seen to include a variety of known inequalities for particular models and combinatorial separation is examined for some special cases

a lagrangean relax and cut approach for the two stage capacitated facility location problem abstract the two stage capacitated facility location problem is to find the optimal locations of depots to serve customers with a given demand the optimal assignment of customers to depots and the optimal product flow from plants to depots in order to solve this problem a lagrangean heuristic is proposed which is based on the relaxation of the capacity constraints the resulting lagrangean subproblem is an uncapacitated facility location problem with an aggregate capacity constraint and can be solved efficiently by branch and bound methods the best bound available from this relaxation is computed by means of a weighted dantzig wolfe decomposition approach feasible solutions are constructed from those of the lagrangean subproblems by applying simple reassignment procedures furthermore the relaxation is strengthened by adding and dualizing valid inequalities which are violated by the fractional primal solution of the dual master program computational results and comparisons with some other bounds and heuristics for this problem are presented

progressive interval heuristics for multi item capacitated lot sizing problems we consider a family of n items that are produced in or obtained from the same production facility demands are deterministic for each item and each period within a given horizon of t periods if in a given period an order is placed setup costs are incurred the aggregate order size is constrained by a capacity limit the objective is to find a lot sizing strategy that satisfies the demands for all items over the entire horizon without backlogging and that minimizes the sum of inventory carrying costs fixed order costs and variable order costs all demands cost parameters and capacity limits may be time dependent in the basic joint setup cost js model the setup cost of an order does not depend on the composition of the order the joint and item dependent setup cost jis model allows for item dependent setup costs in addition to the joint setup costs we develop and analyze a class of so called progressive interval heuristics a progessive interval heuristic solves a js or jis problem over a progressively larger time interval always starting with period 1 but fixing the setup variables of a progressively larger number of periods at their optimal values in earlier iterations different variants in this class of heuristics allow for different degrees of flexibility in adjusting continuous variables determined in earlier iterations of the algorithm for the js model and the two basic implementations of the progressive interval heuristics we show under some mild parameter conditions that the heuristics can be designed to be e optimal for any desired value of e 0 with a running time that is polynomially bounded in the size of the problem they can also be designed to be simultaneously asymptotically optimal and polynomially bounded a numerical study covering both the js and jis models shows that a progressive interval heuristic generates close to optimal solutions with modest computational effort and that it can be effectively used to solve large scale problems

lifted flow cover inequalities for mixed 0 1 integer programs we investigate strong inequalities for mixed 0 1 integer programs derived from flow cover inequalities flow cover inequalities are usually not facet defining and need to be lifted to obtain stronger inequalities however because of the sequential nature of the standard lifting techniques and the complexity of the optimization problems that have to be solved to obtain lifting coefficients lifting of flow cover inequalities is computationally very demanding we present a computationally efficient way to lift flow cover inequalities based on sequence independent lifting techniques and give computational results that show the effectiveness of our lifting procedures

strong formulations for mixed integer programming a survey we attempt to motivate and survey recent research on the use of strong valid inequalities and reformulation to solve mixed integer programming problems

stable commutator length is rational in free groups for any group there is a natural pseudo norm on the vector space b h 1 of real homogenized group 1 boundaries called the stable commutator length norm this norm is closely related to and can be thought of as a relative version of the gromov pseudo norm on ordinary homology we show that for a free group the unit ball of this pseudo norm is a rational polyhedron it follows that the stable commutator length in free groups takes on only rational values moreover every element of the commutator subgroup of a free group rationally bounds an injective map of a surface group the proof of these facts yields an algorithm to compute the stable commutator length in free groups using this algorithm we answer a well known question of bavard in the negative constructing explicit examples of elements in free groups whose stable commutator length is not a half integer

a polyhedral approach to single machine scheduling problems we report new results for a time indexed formulation of nonpreemptive single machine scheduling problems we give complete characterizations of all facet inducing inequalities with integral coefficients and right hand side 1 or 2 for the convex hull of the set of feasible partial schedules i e schedules in which not all jobs have to be started furthermore we identify conditions under which these facet inducing inequalities are also facet inducing for the original polytope which is the convex hull of the set of feasible complete schedules i e schedules in which all jobs have to be started to obtain insight in the effectiveness of these classes of facet inducing inequalities we develop a branch and cut algorithm based on them we evaluate its performance on the strongly np hard single machine scheduling problem of minimizing the weighted sum of the job completion times subject to release dates

the numerical values of some key parameters in econometric models abstract in the case of two endogenous variables exogenous predetermined variables and normally distributed disturbances the distributions of the two stage least squares tsls and limited information maximum likelihood liml estimators can be compared on the basis of three key parameters the non centrality parameter a standardization of the structural coefficient and the number of excluded exogenous variables in this paper the values of these parameters are estimated in eleven structural equations from various actual econometric models the distribution functions of the normalized tsls and liml estimators are given for the first two key parameters set at approximately their trimmed means and the third at its median

on the 0 1 knapsack polytope this paper deals with the 0 1 knapsack polytope in particular we introduce the class ofweight inequalities this class of inequalities is needed to describe the knapsack polyhedron when the weights of the items lie in certain intervals a generalization of weight inequalities yields the so called weight reduction principle and the class of extended weight inequalities the latter class of inequalities includes minimal cover and l k configuration inequalities the properties of lifted minimal cover inequalities are extended to this general class of inequalities

local limit theorems for free groups in this paper we obtain a local limit theorem for elements of a free group g under the abelianization map cdot g to g g g this is obtained via an analysis involving subshifts of finite type where we obtain a result of independent interest the case of fundamental groups of compact surfaces of genus geq 2 is also discussed

capacitated facility location valid inequalities and facets we examine the polyhedral structure of the convex hull of feasible solutions of the capacitated facility location problem in particular we derive necessary and sufficient conditions for a family of effective capacity inequalities to be facet defining and further results on a more general family called submodular inequalities