a mathematical formulation for reactive transport that eliminates mineral concentrations we present a concise and general mathematical formulation for reactive transport in groundwater for general applications by means of linear algebraic manipulations of the stoichiometric coefficients of the chemical reactions we are able to reduce the number of unknowns of the equations to be solved to the number of degrees of freedom according to thermodynamic rules we present six formulations that differ from each other by number and type of unknowns and discuss their advantages and disadvantages with respect to the two most important numerical solution methods the sequential iteration approach sia and the direct substitution approach dsa our conclusion is that the proposed reduction of the number of variables is of special interest for the dsa we have applied one of these formulations to an example of the flushing of saline water by fresh water

a global strategy for solving reactive transport equations reactive transport models are complex nonlinear partial differential algebraic equations pdae coupling the transport engine with the geochemical operator we propose an efficient and robust global numerical method based on a method of lines and differential algebraic equations dae solvers combined with a newton method using a powerful sparse linear solver numerical experiments show the performances of the method we also propose a unified framework to describe classical methods such as sequential non iterative approach sequential iterative approach direct substitution approach and compare them with our global method

the balanced linear programming problem abstract the balanced linear programming problem blpp arises in situations which require equitable distribution of a scarce resource the blpp can be transformed to the standard form of the linear programming problem by introducing 2 n 2 additional variables and 2 n additional constraints this transformation is not desirable from the computational point of view for larger values of n as it increases the problem size substantially it is also undesirable from a theoretical perspective as it might affect the special structure of the constraint matrix in this paper we develop an algorithm for the blpp which does not require problem enlargement the algorithm is based on the relationship between the blpp and the minimax linear programming problem and solving the latter problem parametrically our algorithm in essence performs steps that are similar to those performed in the parametric simplex method with parametric right hand side we then adapt our algorithm for the network flow problem and this specialized algorithm can be applied on the network directly without maintaining the simplex tableau

bounded knapsack sharing a bounded knapsack sharing problem is a maximin or minimax mathematical programming problem with one or more linear inequality constraints an objective function composed of single variable continuous functions called tradeoff functions and lower and upper bounds on the variables a single constraint problem which can have negative or positive constraint coefficients and any type of continuous tradeoff functions including multi modal multiple valued and staircase functions is considered first limiting conditions where the optimal value of a variable may be plus or minus infinity are explicitly considered a preprocessor procedure to transform any single constraint problem to a finite form problem an optimal feasible solution exists with finite variable values is developed optimality conditions and three algorithms are then developed for the finite form problem for piecewise linear tradeoff functions the preprocessor and algorithms are polynomially bounded the preprocessor is then modified to handle bounded knapsack sharing problems with multiple constraints an optimality condition and algorithm is developed for the multiple constraint finite form problem for multiple constraints the time needed for the multiple constraint finite form algorithm is the time needed to solve a single constraint finite form problem multiplied by the number of constraints some multiple constraint problems cannot be transformed to multiple constraint finite form problems

some exact algorithms for the knapsack sharing problem abstract the knapsack sharing problem ksp is formulated as an extension to the ordinary knapsack problem the ksp is n p hard we present a branch and bound algorithm and a binary search algorithm to solve this problem to optimality these algorithms are implemented and computational experiments are carried out to analyse the behavior of the developed algorithms as a result we find that the binary search algorithm solves ksps with up to 20 000 variables in less than a minute in our computing environment

a min max sum resource allocation problem and its applications in this paper we consider a class of discrete resource allocation problems with a min max sum objective function we first provide several examples of practical applications of this problem we then develop a branch and bound procedure for solving the general case of this computationally intractable problem the proposed solution procedure employs a surrogate relaxation technique to obtain lower and upper bounds on the optimal objective function value of the problem to obtain the multipliers of the surrogate relaxation two alternative approaches are discussed we also discuss a simple approximation algorithm with a tight bound our computational results support the effectiveness of the branch and bound procedure for fairly large size problems

a graphical method to solve a family of allocation problems abstract this paper discusses the classical resource allocation problem by very elementary arguments on lagrangian duality it is shown that this problem can be reduced to a single one dimensional maximization of a differentiable concave function moreover a simple graphical method is developed and applied to a family of well known problems from the literature

technical note integer allocation problems of min max type with quasiconvex separable functions the paper treats the problem of integer resource allocations using the min max criterion the objective function is assumed to be strictly quasiconvex in the integer sense and separable the optimality conditions are used to obtain a solution algorithm which may be simplified in the case of strict monotonicity

algorithms for separable nonlinear resource allocation problems we consider a simple resource allocation problem with a single resource constraint the objective function is composed of separable convex performance functions one for each activity likewise the constraint has separable convex resource usage functions one for each activity the objective is to minimize the sum of the performance functions subject to satisfying the resource constraint and nonnegativity constraints this problem extends the well studied problem in which the resource constraint is linear we present several algorithms to solve the problem these algorithms extend approaches developed for the linearly constrained problem they can readily solve large problems and find the optimal solution in a number of iterations that does not exceed the number of variables we provide several examples for illustration purposes present computational results and highlight the similarities and differences among the algorithms

representation of general and polyhedral subsemilattices and sublattices of product spaces abstract it is shown that each element of the lattice of meet resp join sublattices of a product s of n chains has a representation as the intersection of n subsets of s the i th of which is decreasing resp increasing for each fixed value of the i th coordinate for each i this result is applied to show that an arbitrary element of the lattice of sublattices of s has a representation as the intersection of n 2 subsets the ij th of which is decreasing for each fixed value of the i th and increasing for each fixed value of the j th coordinate for each i j irreducible representations are given in each case providing an alternative proof of an instance of hashimoto s 1952 representation of sublattices of a distributive lattice moreover irreducible representations are given for the polyhedral members of the lattice of closed convex subsets of n dimensional euclidean space that are at once subsemilattices or sublattices it is alsoshown that the polyhedral subsemilattices and sublattices can be represented as duals respectively of pre leontief substitution systems and generalized network flow problems finally the problems of checking whether a polyhedral set is a subsemilattice or sublattice are reduced to that of solving a system of linear inequalities thereby showing that these recognition problems can be solved in polynomial time

on equitable resource allocation problems a lexicographic minimax approach in this expository paper we review a variety of resource allocation problems in which it is desirable to allocate limited resources equitably among competing activities applications for such problems are found in diverse areas including distribution planning production planning and scheduling and emergency services location each activity is associated with a performance function representing for example the weighted shortfall of the selected activity level from a specified target a resource allocation solution is called equitable if no performance function value can be improved without either violating a constraint or degrading an already equal or worse off i e larger performance function value that is associated with a different activity a lexicographic minimax solution determines this equitable solution that is it determines the lexicographically smallest vector whose elements the performance function values are sorted in nonincreasing order the problems reviewed include large scale allocation problems with multiple knapsack resource constraints multiperiod allocation problems for storable resources and problems with substitutable resources the solution of large scale problems necessitates the design of efficient algorithms that take advantage of special mathematical structures indeed efficient algorithms for many models will be described we expect that this paper will help practitioners to formulate and solve diverse resource allocation problems and motivate researchers to explore new models and algorithmic approaches

fluctuations of casimir forces on finite objects i spheres and hemispheres the mean square forces that result from the zero point fluctuations of quantized fields are calculated when acting on spheres and hemispheres of variable sizes for the maxwell field the boundary conditions of a perfectly conducting surface are imposed the scalar field is investigated for neumann and dirichlet boundary conditions the force is averaged over a finite time t small and large objects are distinguished on the scale of ct the results for the sphere and the hemisphere are compared with those for a piston that is embedded in an infinite plane a small hemisphere and a small piston are found to have fluctuations of the same order of magnitude while on a small sphere the fluctuations are by two orders of magnitude smaller because of correlations of fluctuations on the two sides of the sphere large spheres are shown to fit into the picture of large objects being composed of many patches each with the fluctuations impinging as on a large piston

solving knapsack sharing problems with general tradeoff functions a knapsack sharing problem is a maximin or minimax mathematical programming problem with one or more knapsack constraints an inequality constraint with all non negative coefficients all knapsack sharing algorithms to date have assumed that the objective function is composed of single variable functions called tradeoff functions which are strictly increasing continuous functions this paper develops optimality conditions and algorithms for knapsack sharing problems with any type of continuous tradeoff function including multiple valued and staircase functions which can be increasing decreasing unimodal bimodal or even multi modal to do this optimality conditions are developed for a special type of multiple valued nondecreasing tradeoff function called an ascending function the optimal solution to any knapsack sharing problem can then be found by solving an equivalent problem where all the tradeoff functions have been transformed to ascending functions polynomial algorithms are developed for piecewise linear tradeoff functions with a fixed number of breakpoints the techniques needed to construct efficient algorithms for any type of tradeoff function are discussed

vector fields on a disk with mixed boundary conditions vector fields on a disk satisfying two types of boundary conditions are studied these boundary conditions are selected by brst invariance in electrodynamics they also appear in the de rham complex the construction of the harmonic expansion is presented the eigenfunctions of the vector laplace operator are expressed in terms of fields satisfying pure dirichlet or robin boundary conditions for the case of four dimensional disk several first coefficients of the heat kernel expansion are computed an error in the analytical expression by branson and gilkey is corrected

fixed charge continuous knapsack problems and pseudogreedy solutions we investigate nonlinear continuous knapsack problems which can be classified as fixed charge problems with one equality constraint and explicit bounds on the variables the objective function of the general problem considered here has the form x x x constitutes a specific generalization of a linear function still allowing a greedy sorting of the variables x includes the fixed cost functions of many types of fixed charge problems as special cases e g sequence dependent fixed costs and the fixed cost function of the interactive fixed charge problem of benson and erenguc is an isotonic function but not sub modular in general we prove the existence of simple structured optimal solutions they show a partial greedy structure and at most one variable does not attain its upper or lower bound called pseudogreedy solutions moreover we state an algorithm for solving the problem and we give results concerning the sensitivity of the greedy solution and the pseudogreedy structure of optimal solutions

operator splitting for chemical reaction systems with fast chemistry abstract splitting methods are frequently used for large scale chemical reaction systems the main reason is the reduced computational cost for solving the subproblems in comparison to the time integration of the full problem however a splitting error is introduced the most popular splitting schemes are the first order lie trotter splitting and the second order strang splitting however in case of stiff differential equations the strang splitting suffers from order reduction and both schemes have order one for stiff differential equations therefore the step size restrictions due to the low order can result in a prohibitive small step size hence splitting schemes with order larger than one are necessary for stiff differential equations the richardson extrapolation of the lie trotter splitting is a second order scheme in this paper we examine differential equations with a fast chemical source term and a slow transport term thus all stiffness of the system is related to the chemical source term we show that the richardson extrapolation does not suffer from order reduction in this case furthermore we perform a stability analysis of the extrapolated splitting scheme for a linear test problem thereby the operators of the test problem do not commute

a survey on the continuous nonlinear resource allocation problem our problem of interest consists of minimizing a separable convex and differentiable function over a convex set defined by bounds on the variables and an explicit constraint described by a separable convex function applications are abundant and vary from equilibrium problems in the engineering and economic sciences through resource allocation and balancing problems in manufacturing statistics military operations research and production and financial economics to subproblems in algorithms for a variety of more complex optimization models this paper surveys the history and applications of the problem as well as algorithmic approaches to its solution the most common techniques are based on finding the optimal value of the lagrange multiplier for the explicit constraint most often through the use of a type of line search procedure we analyze the most relevant references especially regarding their originality and numerical findings summarizing with remarks on possible extensions and future research 2006 elsevier b v all rights reserved

technical note on min max integer allocation problems this note treats a bottleneck integer allocation problem the results obtained supercede those in this journal due to zeitlin zeitlin z 1981 integer allocation problems of min max type with quasiconvex separable functions opns res 29 207 211 who has considered a similar allocation problem with a strictly quasiconvex objective function

a minimax resource allocation problem with variable resources abstract the problem of optimally allocating the resources to competing activities where the amounts of the resources are not only previosly given but are also to be determined subject to certain linear constraints is considered the objective is to find such activity levels such that their weighted deviation from a prespecified target is as small as possible a primal decomposition approach for the problem and derive an explicit formula for the piecewise affine linear convex objective function of the upper level problem are suggested the lower level problem is a parametric optimization problem with a bottleneck objective function if the constraints on the amounts of the resources are all of knapsack type or if there is only one such constraint then the upper level problem is equivalent to the lower level problem with fixed right hand sides in the general case the problem can efficiently be solved by means of the level method

a multi product loading problem a model and solution method abstract an important operational problem arises during the transportation and delivery of several products which cannot be mixed in the same vehicle at regular intervals the vehicle has compartments to keep the products separately therefore a scheme of allocation of compartments which we call vehicle loading problem to maximize the efficiency of the system while the demands for the products at the destination s are satisfied a mixed binary model is developed for this multi product loading problem the solution method is based on simultaneously exploring the primal and dual structures derived from the lagrangian relaxation subset sum problems are obtained as subproblems to the partial lagrangian an algorithm is developed and its convergence is proved the efficiency of the method is demonstrated by running randomly chosen test problems an initial solution finding method is also developed

the line segmentation problem this paper describes a line segmentation problem in a multistage multimachine production system the production facility can concurrently produce several types of circuit boards because each production stage consists of multiple machines the items produced are categorized into families and items belonging to the same family share the common major setup while switching over from one family to another requires a major setup the line segmentation problem determines an allocation of machines at each production stage to families so as to minimize the time to complete all jobs as a result of segmenting the line several minilines are formed which are dedicated to the production of items in each family forming dedicated minilines and producing the items in a family on the same line captures the benefits of group technology and focused factory we first formalize the line segmentation problem as a quadratic integer programming problem and establish its np completeness since the problem is np complete we

a graphical method to solve a maximin allocation problem abstract this note extends a simple graphical method of a solving resource allocation problem the objective function being the sum of returns developed by vidal to the case where the objective function is of a maximin type

new two dimensional slope limiters for discontinuous galerkin methods on arbitrary meshes summary in this paper we introduce an extension of van leer s slope limiter for two dimensional discontinuous galerkin dg methods on arbitrary unstructured quadrangular or triangular grids the aim is to construct a non oscillatory shock capturing dg method for the approximation of hyperbolic conservative laws without adding excessive numerical dispersion unlike some splitting techniques that are limited to linear approximations on rectangular grids in this work the solution is approximated by means of piecewise quadratic functions the main idea of this new reconstructing and limiting technique follows a well known approach where local maximum principle regions are defined by enforcing some constraints on the reconstruction of the solution numerical comparisons with some existing slope limiters on structured as well as on unstructured meshes show a superior accuracy of our proposed slope limiters copyright 2004 john wiley sons ltd

a comparison of two reference point methods in multiple objective mathematical programming abstract when making decisions with multiple criteria a decision maker often thinks in terms of an aspiration point or levels of achievement for the criteria in multiple objective mathematical programming solution methods based on aspiration points can generate nondominated solutions using a variety of scalarizing functions these reference point solution methods commonly use a scalarizing function that reaches down from the ideal solution in a direction specified by the aspiration point conversely a similar scalarizing function can push out from the nadir point toward a specified aspiration point these scalarizing functions are similar in structure but diametrically opposed in their reference points in this paper we examine how these approaches behave from a technical point of view and conduct an experiment to understand better the human behaviour of users of these approaches insights we gain on the evenness of dispersion are relevant when attempting to construct a representation of the nondominated set further the technical characteristics of the two formulations solutions combined with behavioural tendencies allow us to comment on the implications for their use in interactive multiple objective methods

a max min allocation problem its solutions and applications this paper describes a max min allocation problem that has m constraints and n nonnegative integer variables by exploring the structure of the optimal solution to this max min allocation problem we develop a nonsimplex based algorithm that finds an optimal solution within omn2 operations in addition we show that a space allocation problem for a flexible component insertion machine can be formulated as a special case of this max min allocation problem with one constraint furthermore we present some manufacturing and production problems that can he formulated as max min allocation problems and hence can be solved efficiently

strategies for solving index one dae with non negative constraints liquid liquid extraction modeling leads to solve an index one dae system for the sake of robustness it is desirable to account for non negative constraints based on the dassl architecture a classical index one dae solver we propose and compare three different strategies to implement these bound constraints each of these strategies corresponds to a different newton modification clipping damping or interior point method the comparisons are made on two test cases the robertson ode problem and an example from liquid liquid extraction modeling

minimax resource allocation problems optimization and parametric analysis abstract we consider a linear minimax resource allocation problem with single variable terms in the objective function and multiple knapsack type resource constraints all variables are continuous and nonnegative efficient algorithms for such large scale problems have been developed by luss and smith and by tang this paper describes an enhanced algorithm that provides a more efficient search for the optimal solution further we develop post optimization schemes and parametric analysis that are employed once an optimal solution for the original minimax problem is obtained post optimization provides a perturbed optimal solution under a specified change in the data whereas parametric analysis provides a continuum of optimal solutions when some data elements are changed over a given interval

minimax resource allocation problems with resource substitutions represented by graphs resource allocation problems focus on the allocation of limited resources among competing activities we examine such problems when certain substitutions among resources are possible the substitutional relations can be represented by a graph comprised of multiple components in each component the nodes correspond to resources and the arcs correspond to feasible substitutions the objective is of the minimax form where each term is a continuous strictly decreasing function of a single activity level the objective is to minimize the largest term subject to a limited supply of multiple resources potential applications to such problems are found for example in the manufacture of high tech products we develop an efficient algorithm to solve such problems at each iteration a relaxed minimax problem is solved a max flow algorithm is then applied to determine whether the solution of the relaxed problem is feasible for the original problem if the solution is infeasible a tighter relaxed problem is f

on the max min 0 1 knapsack problem with robust optimization applications given a set of items a set of scenarios and a knapsack of fixed capacity a nonnegative weight is associated with each item and a value is associated with each item under each scenario the max min knapsack mnk problem is defined as filling the knapsack with a selected set of items so that the minimum total value gained under all scenarios is maximized the mnk problem is a generalization of the conventional knapsack problem to situations with multiple scenarios this extension significantly enlarges its scope of applications especially in the application of recent robust optimization developments in this paper the mnk problem is shown to be strongly np hard for an unbounded number of scenarios and pseudopolynomially solvable for a bounded number of scenarios effective lower and upper bounds are generated by surrogate relaxation the ratio of these two bounds is shown to be bounded by a constant for situations where the data range is limited to be within a fixed percentage from its mean this result leads to an approximation algorithm for mnk in the special case a branch and bound algorithm has been implemented to efficiently solve the mnk problem to optimality extensive computational results are presented

a cooperative local search based algorithm for the multiple scenario max min knapsack problem the purpose of this article is to present a novel method to approximately solve the multiple scenario max min knapsack problem msm2kp this problem models many real world situations e g when for many scenarios noted pi in mathcal p 1 ldots p the aim is to identify the one offering a better alternative in term of maximizing the worst possible outcome herein is presented a cooperative approach based on two local search algorithms i a limited area local search applied in the elite neighborhood and which accepts the first solution with some deterioration threshold of the current solution ii a wide range local search is applied to perform a sequence of paths exchange to improve the current solution results have been analyzed by means state of the art methods and via problem instances obtained by a generator code taken from the literature the tests were executed in compeltely comparable scenarios to those of the literature the results are promising and the efficiency of the proposed approach is also shown

an exact algorithm for the knapsack sharing problem with common items we are concerned with a variation of the knapsack problem as well as of the knapsack sharing problem where we are given a set of n items and a knapsack of a fixed capacity as usual each item is associated with its profit and weight and the problem is to determine the subset of items to be packed into the knapsack however in the problem there are s players and the items are divided into s 1 disjoint groups nk k 0 1 s the player k is concerned only with the items in n0 nk where n0 is the set of common items while nk represents the set of his own items the problem is to maximize the minimum of the profits of all the players an algorithm is developed to solve this problem to optimality and through a series of computational experiments we evaluate the performance of the developed algorithm 2004 elsevier b v all rights reserved

a lexicographic minimax algorithm for multiperiod resource allocation resource allocation problems are typically formulated as mathematical programs with some special structure that facilitates the development of efficient algorithms we consider a multiperiod problem in which excess resources in one period can be used in subsequent periods the objective minimizes lexicographically the nonincreasingly sorted vector of weighted deviations of cumulative activity levels from cumulative demands to this end we first develop a new minimax algorithm that minimizes the largest weighted deviation among all cumulative activity levels the minimax algorithm handles resource constraints ordering constraints and lower and upper bounds at each iteration it fixes certain variables at their lower bounds and sets groups of other variables equal to each other as long as no lower bounds are violated the algorithm takes advantage of the problem s special structure e g each term in the objective is a linear decreasing function of only one variable this algorithm solves large problems very fast orders of magnitude faster than well known linear programming packages the latter are of course not designed to solve such minimax problems efficiently the lexicographic procedure repeatedly employs the minimax algorithm described above to solve problems each of the same format but with smaller dimension

minimax resource allocation with tree structured substitutable resources we examine an allocation problem in which limited resources are allocated among competing activities certain substitutions among resources are possible the substitutional relations are formulated using tree structures where a node resource can substitute for all its descendants potential applications with such resources are found for example in the manufacturing of high technology products the objective is to minimize the maximum weighted relative deviation of the activity levels from given demands our formulation of this problem involves a large number of possible resource constraints we develop an efficient minimax algorithm that is based on an iterative solution of relaxed problems where each such problem considers at most one aggregated constraint from each tree the algorithm is extended to minimize lexicographically the nonincreasingly sorted vector of all terms in the objective each of which represents an activity s deviation computational results show that the algorithm solves large problems using relatively small computation time

a reduction scheme for coupled multicomponent transport reaction problems in porous media generalization to problems with heterogeneous equilibrium reactions 1 in this article a systematic approach for the efficient computation of the transport and reaction of a multispecies multireaction system is proposed the objective of this approach is to reformulate the given system of differential or differential algebraic equations in such a way that the couplings and the nonlinearities are concentrated in a reduced number of equations if compared to the original formulation while some linear equations decouple from the system the resulting system is handled in the spirit of a global implicit approach one step method avoiding operator splitting techniques the reduction of the problem size proposed in this article helps to limit the large computational costs of numerical simulations for such problems the reduction mechanism is a generalization of the method proposed in a previous paper now problems with mixed mobile immobile species homogeneous heterogeneous kinetic equilibrium reactions are considered while the previous publication was restricted to problems without heterogeneous equilibrium reactions such as equilibrium sorption an application of the reduction mechanism to an example problem is given in order to investigate the reduction of the number of coupled nonlinear equations and to compare it to other methods

a variant of sqp method for inequality constrained optimization and its global convergence in this paper a variant of sqp method for solving inequality constrained optimization is presented this method uses a modified qp subproblem to generate a descent direction as each iteration and can overcome the possible difficulties that the qp subproblem of the standard sqp method is inconsistency furthermore the method can start with an infeasible initial point under mild conditions we prove that the algorithm either terminates as kkt point within finite steps or generates an infinite sequence whose accumulation point is a kkt point or satisfies certain first order necessary condition finally preliminary numerical results are reported

continuous maximin knapsack problems with glb constraints this paper introduces the continuous minimax knapsack problem with generalized lower bound constraints and describes an algorithm that solves this problem in o n logn time we also discuss the related problem with generalized upper bound constraints

an algorithm for solving linearly constrained minimax problems abstract in this study we propose an algorithm for solving a minimax problem over a polyhedral set defined in terms of a system of linear inequalities at each iteration a direction is found by solving a quadratic programming problem and then a suitable step size along that direction is taken through an extension of armijo s approximate line search technique we show that each accumulation point is a kuhn tucker solution and give a condition that guarantees convergence of the whole sequence of iterations through the use of an exact penalty function the algorithm can be used for solving constrained nonlinear programming in this case our algorithm resembles that of han but differs from it both in the direction finding and the line search steps

relaxation based algorithms for minimax optimization problems with resource allocation applications we consider minimax optimization problems where each term in the objective function is a continuous strictly decreasing function of a single variable and the constraints are linear we develop relaxation based algorithms to solve such problems at each iteration a relaxed minimax problem is solved providing either an optimal solution or a better lower bound we develop a general methodology for such relaxation schemes for the minimax optimization problem the feasibility tests and formulation of subsequent relaxed problems can be done by using phase i of the simplex method and the farkas multipliers provided by the final simplex tableau when the corresponding problem is infeasible such relaxation based algorithms are particularly attractive when the minimax optimization problem exhibits additional structure we explore special structures for which the relaxed problem is formulated as a minimax problem with knapsack type constraints efficient algorithms exist to solve such problems the relaxation schemes are also adapted to solve certain resource allocation problems with substitutable resources there instead of phase i of the simplex method a max flow algorithm is used to test feasibility and formulate new relaxed problems

the functional integral for fields in a cavity the functional integral for a scalar field confined in a cavity and subjected to linear boundary conditions is discussed herein it is shown how the functional measure can be conveniently dealt with by modifying the classical action with boundary corrections the nonuniqueness of the boundary actions is described with a three parameter family of them giving identical boundary conditions in some cases the corresponding green s function will define a kind of generalized gaussian measure on function space the vacuum energy is discussed paying due attention to its anomalous scale dependence and the physical issues involved are considered

new upper bounds and exact methods for the knapsack sharing problem a new upper bound is proposed for the knapsack sharing problem a new dichotomous search based exact algorithm is proposed the new algorithm outperforms a most recent exact algorithm of the literature and the cplex solver v 12 in this paper we study the knapsack sharing problem ksp which is a variant of the well known np hard knapsack problem we investigate the use of a dichotomous search based exact method for solving the ksp such a method is based on decomposing the original problem into a series of minimizing and maximizing knapsack problems where each of them is embedded into a dichotomous search bounded by both lower and upper bounds throughout the interval search we introduce new upper bounds and incremental valid lower bounds one of these upper bounds can be viewed as an extended of dantzig upper bound whereas a series of valid lower bounds are obtained when solving a subset of knapsack problems finally the proposed algorithm is evaluated on a set of problem instances of the literature and other new harder ones the provided results are compared to those reached by the cplex solver and a more recent exact algorithm of the literature the computational part shows the dominance of the new exact method

the linear sharing problem the linear sharing problem is defined as a linear programming problem with a maximin objective function comprised of nondecreasing continuous tradeoff functions this paper develops some properties including optimality conditions for this problem it also develops an efficient algorithm that alternately calculates a new global upper bound on the objective function and then determines if a feasible solution exists that meets the new objective function global upper bound the process continues until the algorithm finds a feasible and thus an optimal solution the algorithm also determines if the problem contains no feasible solution or if the objective function is unbounded a technique to handle problems with unbounded tradeoff variables is developed and computational experience is given

the flow circulation sharing problem the flow circulation sharing problem is defined as a network flow circulation problem with a maximin objective function the arcs in the network are partitioned into regular arcs and tradeoff arcs where each tradeoff arc has a non decreasing tradeoff function associated with it all arcs have lower and upper bounds on their flow while the value of the smallest tradeoff function is maximized the model is useful in equitable resource allocation problems over time which is illustrated in a coal strike example and a submarine assignment example some properties including optimality conditions are developed each cut in the network defines a knapsack sharing problem which leads to an optimality condition similar to the max flow min cut theorem an efficient algorithm for both the continuous and integer versions of the flow circulation sharing problem is developed and computational experience given in addition efficient algorithms are developed for problems where some of the arcs have infinite flow upper bounds

linear max min programming theoretical aspects of the programming problem of maximizing the minimum value of a set of linear functionals subject to linear constraints are explored solution strategies are discussed and an optimality condition is developed an algorithm is also presented

an o n algorithm for the multiple choice knapsack linear program an algorithm for solving the linear program associated with the multiple choice knapsack problem is described the algorithm is shown to work in time linear in the number of variables this improves the previously known best bound for this problem and is optimal to within a constant factor

modeling of chemically reactive groundwater transport a complete reactive groundwater transport model must account for both chemical and transport processes for the chemical processes one has to decide whether to formulate them kinetically or to assume a local chemical equilibrium state this decision in the chemical model part determines the mathematical structure of the overall model in a kinetic formulation the linear partial differential equations of the transport have to be coupled with a nonlinear system of ordinary differential equations describing the kinetic development whereas in an equilibrium formulation the equations of the transport are coupled to a nonlinear system of algebraic equations describing the equilibrium state basically two kinds of methods for solving reactive transport systems may be distinguished namely one step methods which simultaneously solve the transport and the chemical model parts and two step methods which solve these model parts separately we here present a sequential two step method for kinetic transport models and an iterative two step method for equilibrium transport models we conduct a timescale analysis to check whether the error of the sequential two step method is tolerable and whether a given kinetic transport system can be reduced to an equilibrium one the numerical methods and the timescale analysis are applied to two test cases zysset et al 1994 present a further application of the kinetic transport model to laboratory column experiments governed by biodegradation

a min max resource allocation problem with substitutions abstract in this paper a model for a resource allocation problem with substitution is presented the model extends a previous one proposed by luss and smith for resource allocation without substitutions in general two resources are substitutable if they can be used in place of one another in the allocation process if two resources are substitutable for the same set of activities then they can be combinaed into and treated as a single resource otherwise substitution needs to be dealt with explicitly one application of the resource allocation problem with substitutions arises from the assembly of electronic components onto circuit boards typically several components can be assembled in the same locations of a board they then become substitutes of one another the problem here is to determine how much to produce of the circuit boards and how to efficiently allocate the components so as to minimize the maximum weighted deviation from target demands of the boards it is explained how the proposed model can be solved by a parametric transportation algorithm present some computational results and discuss a nonlinear extension