separating k separated ence graph languages an ence graph grammar is k separated k 1 if the distance between any two nonterminal nodes in any of its sentential forms is at least k let sepk denote the class of graph languages generated by k separated grammars then sep1 sep2 is the class of ence boundary ence graph languages and so sep2 sep1 recently engelfriet 1991 showed that sep3 sep2 and conjectured that in fact sepk 1 sepk for each k 1 we prove this conjecture affirmatively

the lagrangian relaxation method for solving integer programming problems this article originally appeared in management science january 1981 volume 27 number 1 pp 1 18 published by the institute of management sciences one of the most computationally useful ideas of the 1970s is the observation that many hard integer programming problems can be viewed as easy problems complicated by a relatively small set of side constraints dualizing the side constraints produces a lagrangian problem that is easy to solve and whose optimal value is a lower bound for minimization problems on the optimal value of the original problem the lagrangian problem can thus be used in place of a linear programming relaxation to provide bounds in a branch and bound algorithm this approach has led to dramatically improved algorithms for a number of important problems in the areas of routing location scheduling assignment and set covering this paper is a review of lagrangian relaxation based on what has been learned in the last decade

graph grammars with neighbourhood controlled embedding abstract a central feature that distinguishes graph grammars we consider grammars generating sets of node labelled undirected graphs only from string grammars is that in the former one has to provide a mechanism by which a daughter graph the right hand side of a production can be embedded in the rest of the mother graph while in the latter this embedding is provided automatically by the structure that all strings possess left to right orientation in this paper we consider a possible classification of embedding mechanisms for node rewriting graph grammars this classification originates from the basic ideas of 9 on the one hand it allows one to fit a number of existing notions of a graph grammar into a common framework and on the other hand it points out new natural possibilities for defining the embedding mechanism in a graph grammar the relationship between the graph language generating power of graph grammars using various embedding mechanisms is established

nicholson s blowflies revisited a fuzzy modeling approach we apply fuzzy modeling to derive a mathematical model for a biological phenomenon the regulation of population size in the australian sheep blowfly lucilia cuprina this behavior was described by several ethologists and fuzzy modeling allows us to transform their verbal descriptions into a well defined mathematical model the behavior of the resulting mathematical model as studied using both simulations and rigorous analysis is congruent with the behavior actually observed in nature we believe that the fuzzy modeling approach demonstrated here may supply a suitable framework for biomimicry that is the design of artificial systems based on mimicking natural behavior

solving nonlinear single facility network location problems we present a general approach to solving nonlinear single facility network location problems we assume that cost is any convex function of distances and solve this class of problem by solving convex subproblems on treelike segments into which the network is decomposed we show that only a fraction of treelike segments generally need be examined and that our method results in a reasonably efficient general purpose algorithm the algorithm is particularly effective on real world as opposed to random networks and when the cost function is nondecreasing and semiseparable as are many popular cost functions finally we describe theoretical complexity bounds and computational experience

location on tree networks p centre and n dispersion problems we consider two problems of locating facilities on trees in the first we wish to determine the location of n points so as to maximize the minimum distance between any pair in the second we wish to locate p centers of a single type of facility so as to minimize the maximum distance between any point and the center nearest to it we provide polynomial algorithms for both problems of o n 2 log n log n for the first problem and of o n 2 log p for the second where n is the number of nodes in the tree

optimal locations for a class of nonlinear single facility location problems on a network this paper investigates a class of single facility location problems on an arbitrary network necessary and sufficient conditions are obtained for characterizing locally optimal locations with respect to a certain nonlinear objective function this approach produces a number of new results for locating a facility on an arbitrary network and in addition it unifies several known results for the special case of tree networks it also suggests algorithmic procedures for obtaining such optimal locations

a branch and bound algorithm for determining locations of long term care facilities this paper focuses on the problem of determining locations for long term care facilities with the objective of balancing the numbers of patients assigned to the facilities we present a branch and bound algorithm by developing dominance properties a lower bounding scheme and a heuristic algorithm for obtaining an upper bound for the problem for evaluation of the suggested branch and bound algorithm computational experiments are performed on a number of test problems results of the experiments show that the suggested algorithm gives optimal solutions of problems of practical sizes in a reasonable amount of computation time

heuristics for the fixed cost median problem we describe in this paper polynomial heuristics for three important hard problems the discrete fixed cost median problem the plant location problem the continuous fixed cost median problem in a euclidean space and the network fixed cost median problem with convex costs the heuristics for all the three problems guarantee error ratios no worse than the logarithm of the number of customer points the derivation of the heuristics is based on the presentation of all types of median problems discussed as a set covering problem

the stochastic location model with risk pooling abstract in this paper we present a stochastic version of the location model with risk pooling lmrp that optimizes location inventory and allocation decisions under random parameters described by discrete scenarios the goal of our model called the stochastic lmrp or slmrp is to find solutions that minimize the expected total cost including location transportation and inventory costs of the system across all scenarios the location model explicitly handles the economies of scale and risk pooling effects that result from consolidating inventory sites the slmrp framework can also be used to solve multi commodity and multi period problems we present a lagrangian relaxation based exact algorithm for the slmrp the lagrangian subproblem is a non linear integer program but it can be solved by a low order polynomial algorithm we discuss simple variable fixing routines that can drastically reduce the size of the problem we present quantitative and qualitative computational results on problems with up to 150 nodes and 9 scenarios describing both algorithm performance and solution behavior as key parameters change

finite graph automata for linear and boundary graph languages graph grammars can be regarded as a generalization of context free grammars from strings to graphs over the past 30 years a rich theory of graph grammars and their languages has been developed however there are no graph automata there is no duality between generative and recognizing devices as it is known for the chomsky hierarchy of formal languages here we introduce graph automata as devices for the recognition of sets of undirected node labelled graphs a graph automaton consists of a finite state control a finite set of instructions and a collection of heads or guards it reads an input graph in a systematic way and performs a graph search directed by the instructions as our main results we show that finite graph automata recognize exactly the set of graph languages generated by linear nce graph grammars and that alternating finite graph automata recognize exactly the languages of boundary graph grammars finally we generalize some automata theoretic properties from string to graph automata integrate the connectivity of graphs into graph automata and explain why graph automata cannot be generalized to deal with dynamic edge relabellings and ence graph languages

fuzzy optimization for supply chain planning under supply demand and process uncertainties in today s global marketplace individual firms do not compete as independent entities rather as an integral part of a supply chain this paper proposes a fuzzy mathematical programming model for supply chain planning which considers supply demand and process uncertainties the model has been formulated as a fuzzy mixed integer linear programming model where data are ill known and modelled by triangular fuzzy numbers the fuzzy model provides the decision maker with alternative decision plans for different degrees of satisfaction this proposal is tested by using data from a real automobile supply chain

on the coordination of product and by product flows in two level distribution networks model formulations and solution procedures abstract we study the problem of coordinating product and by product flows in a two level distribution network in this problem a single product is produced at multiple plants in order to fulfill customer demands furthermore in the production process a by product is produced that must be transported to and processed at a post processing unit the problem objective is to determine suitable locations for plants and post processing units from a predetermined set of feasible locations such that total costs are minimal here total costs consist of fixed costs associated with opening plants and post processing units and variable costs associated with transport of product and by product we discuss alternative mathematical model formulations for this problem and derive lower and upper bounding procedures the results from computational experiments in which we analyse the numerical behaviour of these procedures are also reported

an analysis of network location problems with distance constraints this paper concerns a class of network location problems with minimum or maximum separation requirements between uncapacitated facilities or between demand points and the facilities or both its purpose is three fold first it is to recognize distance constraints as increasing real life restrictions through various motivating illustrations using a new classification scheme the paper introduces a variety of distance constrained problems defined in a unified manner these include a number of new problems second it is to survey existing solution techniques available only for a few of such constrained problems finally it is to shed some light on yet unstudied problems by exploring possible extensions of some of the known solution techniques or discussing varying degrees of difficulties involved in particular the paper presents integer programming formulations of several new problems along with the results of applying linear programming relaxation methods although the computational experience is somewhat disappointing for some of these problems the results provide greater insight into the problems with the stated purpose it is hoped that this paper will stimulate future research in this important problem area

hamiltonian location problems abstract exact algorithms for a series of simultaneous location and routing problems are developed problems are formulated as integer programs which are solved by a constraint relaxation procedure numerical results are reported

on a general network location production allocation problem abstract in this paper we consider a network location production allocation problem in which demands are related to prices at markets profit maximization is achieved through the simultaneous determinations of plant locations and shipments between plants and markets we show that even subproblems of some special cases of this general problem are np hard for the np hard plant allocation problem both a dynamic programming formulation and two heuristic algorithms are proposed empirical results reveal that both heuristic algorithms are attractive in practice with one of them performing exceptionally well we also show that the problem has a class of interesting special cases which can be solved in polynomial time

boundary nlc graph grammars basic definitions normal forms and complexity node label controlled nlc grammars are graph grammars operating on node labeled undirected graphs which rewrite single nodes only and establish connections between the embedded graph and the neighbors of the rewritten node on the basis of the labels of the involved nodes only they define possibly infinite languages of undirected node labeled graphs or if we just omit the labels languages of unlabeled graphs here we consider a restriction of nlc grammars so called boundary nlc bnlc grammars distinguished by the property that whenever in a graph already generated two nodes may be rewritten then these nodes are not adjacent the graph languages generated by this type of grammars are called bnlc languages although we show that this restriction leads to a smaller class of languages still enough generative power remains to define interesting graph languages for example trees complete bipartite graphs maximal outerplanar graphs k trees graphs of bandwidth k graphs of cyclic bandwidth k graphs of binary tree bandwidth k graphs of cutwidth k always for a fixed positive integer k turn out all to be bnlc languages we prove a number of normal forms for bnlc grammars and then we indicate their usefulness by various applications in particular we show that for connected graphs of bounded degree the membership problem for bnlc languages is solvable in deterministic polynomial time

the weighted euclidean 1 center problem we present an o n log n 3 log log n 2 algorithm for the problem of finding a point x y in the plane that minimizes the maximal weighted distance to a point in a set of n given points the algorithm can be extended to higher dimensional spaces for any fixed dimension our bound is o n1 for any 0

some properties of location problems with block and round norms the point objective problem and the weber problem are two well known formulations for locating a new facility with respect to a set of fixed facilities when locations are represented as points on a plane the point objective problem is a multiple objective formulation of minimizing the distance from a variable point to each of the fixed points similarly the weber problem is a single objective formulation of minimizing the sum of transportation costs between the variable point and the fixed points where transportation cost is a function of distance generalizing solution properties for these problems from distance measures given by the euclidean rectilinear ip and one infinity norms this paper develops solution properties under the broad classes of distance measures given by block and round norms for the point objective problem we show that i the efficient set for all round norms is the convex hull of the set of fixed points and ii the efficient set under a block norm tends to the convex hull for a sequence of block norms approaching a round norm for the weber problem we prove that i an optimal location for any block norm may be found in a finite set of intersection points belonging to the convex hull and ii this set tends to the convex hull for a sequence of block norms approaching a round norm finally we use these results to propose a synthesis of some of the main properties in continuous and network location theory

a new formulation and benders decomposition for the multi period maximal covering facility location problem with server uncertainty abstract facility location problems reported in the literature generally assume the problem parameter values like cost budget etc to be known with complete certainty even if they change over time as in multi period versions however in reality there may be some uncertainty about the exact values of these parameters specifically in the context of locating primary health centers phcs in developing countries there is generally a high level of uncertainty in the availability of servers doctors joining the facilities in different time periods for transparency and efficient assignment of the doctors to phcs it is desirable to decide the facility opening sequence assigning doctors to unmanned phcs at the start of the planning horizon we present a new formulation for a multi period maximal covering location problem with server uncertainty we further demonstrate the superiority of our proposed formulation over the only other formulation reported in the literature for instances of practical size we provide a benders decomposition based solution method along with several refinements for instances that the cplex mip solver could solve within a time limit of 20 hours our proposed solution method turns out to be of the order of 150 250 times faster for the problems with complete coverage and around 1000 times faster for gradual coverage

the heterogeneous p median problem for categorization based clustering the p median offers an alternative to centroid based clustering algorithms for identifying unobserved categories however existing p median formulations typically require data aggregation into a single proximity matrix resulting in masked respondent heterogeneity a proposed three way formulation of the p median problem explicitly considers heterogeneity by identifying groups of individual respondents that perceive similar category structures three proposed heuristics for the heterogeneous p median hpm are developed and then illustrated in a consumer psychology context using a sample of undergraduate students who performed a sorting task of major u s retailers as well as a through monte carlo analysis

a decomposition algorithm for a discrete location allocation problem this paper considers a discrete location allocation problem for simultaneously determining the location of a given number of capacitated facilities on certain predesignated sites and the allocation of their products among a fixed number of customers the objective is to determine the location and subsequent allocation that minimizes the total cost of construction or location production and transportation the formulation of this model is a specially structured generally nonconvex problem however we specify certain sufficient conditions for the solution to two network structured linear programs to provide an optimal solution to this problem for other situations we present an implicit enumeration algorithm within the framework of benders decomposition method which fully exploits the structure of the problem this method is an improvement over traditional lagrangian approaches computational experience is provided to demonstrate the practicality of this algorithm for reasonable size problems as well as its superiority over alternative implicit enumeration schemes this paper also sheds light on the general implementation of benders decomposition technique

backup 2 center on interval graphs a graph g is called an interval graph if there exists a set of intervals corresponding to the vertex set of g and two vertices are adjacent to each other if and only if the two corresponding intervals are intersecting with each other in this paper we apply the reliability based backup 2 center modal proposed by wang wu and chao in which each server may fail with a given probability to interval graphs and present an o n time algorithm

network location problems with continuous link demands p medians on a chain and 2 medians on a tree abstract this paper is concerned with minisum location allocation problems on undirected networks in which demands can occur on links with uniform probability distributions two types of networks are considered the first type considered is simply a chain graph it is shown that except for the 1 median case the problem is generally non convex however for the p median case a discrete set of potential optimal facility locations may be identified and hence it is shown that all local and global minima to the problem may be discovered by solving a series of trivial linear programming problems this analysis is then extended to prescribe an algorithm for the 2 median location allocation problem on a tree network involving uniform continuous demands on links some localization theorems are presented in the spirit of the work done on discrete nodal demand problems

an exact algorithm for minimizing routing and operating costs in depot location abstract the problem of locating a single depot among n points is considered the objective is to minimize the sum of depot operating cost and routing cost the best depot location is found by means of an exact algorithm that determines simultaneously both the best depot location and the associated optimal delivery routes a global integer programming formulation of the problem is given the model is solved by relaxing most of its constraints and by introducing them only when they are violated

a faster scaling algorithm for minimizing submodular functions combinatorial strongly polynomial algorithms for minimizing submodular functions have been developed by iwata fleischer and fujishige iff and by schrijver the iff algorithm employs a scaling scheme for submodular functions whereas schrijver s algorithm achieves strongly polynomial bound with the aid of distance labeling subsequently fleischer and iwata have described a push relabel version of schrijver s algorithm to improve its time complexity this paper combines the scaling scheme with the push relabel framework to yield a faster combinatorial algorithm for submodular function minimization the resulting algorithm improves over the previously best known bound by essentially a linear factor in the size of the underlying ground set

lagrangian heuristics for the two echelon single source capacitated facility location problem facility location problems form an important class of integer programming problems with application in the distribution and transportation industries in this paper we are concerned with a particular type of facility location problem in which there exist two echelons of facilities each facility in the second echelon has limited capacity and can be supplied by only one facility or depot in the first echelon each customer is serviced by only one facility in the second echelon the number and location of facilities in both echelons together with the allocation of customers to the second echelon facilities are to be determined simultaneously we propose a mathematical model for this problem and consider six heuristics based on lagrangian relaxation for its solution to solve the dual problem we make use of a subgradient optimization procedure we present numerical results for a large suite of test problems these indicate that the lower bounds obtained from some relaxations have a duality gap which frequently is one third of the one obtained from traditional linear programming relaxation furthermore the overall solution time for the heuristics are less than the time to solve the lp relaxation

an exact method for the two echelon single source capacitated facility location problem facility location problems form an important class of integer programming problems with applications in the telecommunication distribution and transportation industries in this paper we are conc

an overview of representative problems in location research we present a survey of over 50 representative problems in location research our goal is not to review all variants of different location models or to describe solution results but rather to provide a broad overview of major location problems that have been studied indicating briefly how they are formulated and how they relate to one another we review standard problems such as median center and warehouse location problems as well as less traditional location problems which have emerged in recent years our primary focus is on problems for which operations research type models have been developed most of the problems we review have been formulated as optimization problems

a two echelon joint continuous discrete location model abstract the problem of locating up to a given number of facilities in continuous euclidean space that can serve as intermediate transshipment points between multiple stakeholders in a supply chain suppliers and customers who are distributed over the same space is considered the first contribution is in considering the multisource weber problem mwp in the presence of both source points and demand points rather than either alone the second contribution is that the selection of intermediate facilities for further discrete analysis is based on a quantitative determination rather than a subjective selection process which is typical of most popular commercial grade mathematical programming lp and ip based location models while the mathematical programming approach benefits from a degree of richness in features and a sense of computational optimization one limitation is that the candidate locations to be evaluated must be specified often without any computational basis for them computational experiments on randomly generated problem instances and real case studies indicate that significant gains can be achieved with relatively little effort by expanding the boundary of analysis to include multiple suppliers and multiple customers in the analysis and design of a supply chain network an alternating location allocation type heuristic method is developed that is easy to implement the third contribution is the development of two different lower bounding procedures that demonstrate the high quality of this obtained heuristic solution

node rewriting in graphs and hypergraphs a categorical framework vertex rewriting in graphs is a very powerful mechanism which has been studied for quite a long time in this paper we eventually provide a categorical theory of vertex rewriting and show how it can extend in a uniform way to node and pattern rewriting mechanisms in hypergraphs copyright 2001 elsevier science b v

the generating power of boundary nlc graph grammars and cycle graphs it is known that a can be generated by a node label controlled nlc graph grammar sa cannot be generated by nlc graph grammars and a cannot be generated by boundary nlc bnlc graph grammars where a is the set of all graphs labeled by the single label a and sa is the set of all cycle graphs labeled by the single label a in this paper we consider the class lc of all graph languages including sa we show that the class lc and the class of bnlc graph languages are mutually disjoint furthermore we provide a new simple graph language that can be generated by an nlc graph grammar but cannot be generated by bnlc graph grammars using a method different from rozenberg and welzl

the p median problem a survey of metaheuristic approaches the p median problem is one of the basic models in discrete location theory as with most location problems it is classified as np hard and so heuristic methods are usually used to solve it metaheuristics are frameworks for building heuristics in this survey we examine the p median with the aim of providing an overview on advances in solving it using recent procedures based on metaheuristic rules

power properties of nlc graph grammars with a polynomial membership problem a research into syntax analysis of node label controlled nlc graph grammars introduced and investigated in janssens and rozenberg 1980 and janssens et al 1982 has resulted in defining their subclasses with a polynomial membership problem flasinski 1988 1989 1993 good complexity properties have been shown in the last referred paper by defining an efficient parsing algorithm o n2 for the so called etpl k subclass of nlc grammars in this paper we investigate power properties of this parsable subclass the paper contains also a short bibliographical survey and a discussion concerning a problem of constructing graph languages with a polynomial membership problem

solution of the multisource weber and conditional weberproblems by d c programming d c programming is a recent technique of global optimization that allows the solution of problems whose objective function and constraints can be expressed as differences of convex i e d c functions many such problems arise in continuous location theory the problem first considered is to locate a known number of source facilities to minimize the sum of weighted euclidean distances between a user s fixed location and the source facility closest to the location of each user we also apply d c programming to the solution of the conditional weber problem an extension of the multisource weber problem in which some facilities are assumed to be already established in addition we consider a generalization of weber s problem the facility location problem with limited distances where the effective service distance becomes a constant when the actual distance attains a given value computational results are reported for problems with up to 10 000 users and two new facilities 50 users and three new facilities 1 000 users 20 existing facilities and one new facility or 200 users 10 existing and two new facilities

on the structure of linear apex nlc graph grammars it is known that linear apex nlc lin a nlc grammars can generate np complete graph languages the present paper examines the source of this expressive power by analyzing complexity and decidability of the so called k connecting lin a nlc k lin a nlc grammars in which the right hand side of each production contains at most k nodes that can be connected to outside nodes the number of connecting nodes is indeed one source of the expressive power of graph grammars in that k lin a nlc k 1 lin a nlc for every k 0 there exists a 2 lin a nlc language which is np complete but every 1 lin a nlc language is in nlog the equivalence problem is undecidable for 1 lin a nlc languages but is decidable for 0 lin a nlc languages even when one of two input languages is an arbitrary b nlc language

graph grammars with path controlled embedding abstract in this paper we define graph grammars called the node replacement graph grammars with path controlled embedding npce grammars which use a sequence of edges instead of a single edge to embed a newly replaced graph into the host graph then we show that there exists a class of npce grammars generating a class of graph languages which is equal to the class of context free array languages under some stipulations it means that the path controlled embedding brings no significant contexts into the production rules then we characterize the above mentioned class of npce grammars by making use of the partial path group

fuzzy lyapunov based approach to the design of fuzzy controllers in this paper we extend the classical lyapunov synthesis method to the domain of computing with words this new approach is used to design fuzzy controllers assuming minimal knowledge about the plant to be controlled the proposed method enables us to systematically derive the fuzzy rules that constitute the rule base of the controller we demonstrate the approach by designing mamdani type and takagi sugeno kang type fuzzy controllers for two well known plants

state of the art location on networks a survey part ii exploiting tree network structure the discussion of the fundamental p center and p median problems in part i of this paper provides the basis for the work surveyed in part ii part ii deals with the minimax and minisum location problems with mutual communication location problems involving multiple objectives the distance constraints problem and problems involving the location of paths in addition convexity issues in network location problems are discussed virtually all of this work exploits network structure specifically it is based on the assumption that the network is a tree the conclusion section gives a brief discussion of the state of the art and of current trends in network location research

on the continuous fermat weber problem we give the firstexact algorithmic study of facility location problems that deal with finding a median for acontinuum of demand points in particular we consider versions of the continuousk median fermat weber problem where the goal is to select one or more center points that minimize the average distance to a set of points in a demandregion in such problems the average is computed as an integral over the relevant region versus the usual discrete sum of distances the resulting facility location problems are inherently geometric requiring analysis techniques of computational geometry we provide polynomial time algorithms for various versions of thel1 1 median fermat weber problem we also consider the multiple center version of thel1k median problem which we prove is np hard for largek

node replacement graph languages squeezed with chains trees and forests we present results on language theoretic properties such as closure membership and other decision properties of node replacement graph languages such as nlc b nlc and lin nlc languages squeezed with chains trees and forests

integer programming formulations of discrete hub location problems abstract hubs are facilities that serve as transshipment and switching points for transportation and telecommunication systems with many origins and destinations this paper present integer programming formulations for four types of discrete hub location problems the p hub median problem the uncapacitated hub location problem p hub center problems and hub covering problems hub median and uncapacitated hub location problems have received limited attention from researchers this paper introduces discrete hub center and hub covering problems basic formulations and formulations with flow thresholds for spokes are presented

dynamic facility location when the total number of facilities is uncertain a decision analysis approach models developed to analyze facility location decisions have typically optimized one or more objectives subject to physical structural and policy constraints in a static or deterministic setting because of the large capital outlays that are involved however facility location decisions are frequently long term in nature consequently there may be considerable uncertainty regarding the way in which relevant parameters in the location decision will change over time in this paper we propose two approaches for analyzing these types of dynamic location problems focussing on situations where the total number of facilities to be located in uncertain we term this type of location problem nofun number of facilities uncertain we analyze the nofun problem using two well established decision criteria the minimization of expected opportunity loss eol and the minimization of maximum regret in general these criteria assume that there are a finite number of decision options and a finite number of possible states of nature the minisum eol criterion assumes that one can assign probabilities for the occurrence of the various states of nature and therefore find the initial set of facility locations that minimize the sum of expected losses across all future states the minimax regret criteria finds the pattern of initial facility locations whose maximum loss is minimized over all possible future states

an efficient tabu search procedure for the p median problem abstract in this paper we present a new solution heuristic for the p median problem the algorithm is based on tabu search principles and uses short term and long term memory as well as strategic oscillation and random tabu list sizes our proposed procedure is compared with two other move heuristics a well known interchange heuristic and a recent hybrid heuristic in computational tests on networks ranging in size up to 500 nodes the new heuristic is found to be superior with respect to the quality of solutions produced

results on nlc grammars with one letter terminal alphabets abstract node label controlled graph grammars nlc grammars are a mechanism to generate sets of graphs called graph languages this paper examines the generating power of nlc grammars with a restricted connection relation and some closure properties of the class of nlc languages also a modified language generating mechanism for nlc grammars is introduced and the resulting class of graph languages is compared to the class of nlc languages all results are based on grammars with one letter terminal alphabets

a comparison of boundary graph grammars and context free hypergraph grammars context free hypergraph grammars and boundary graph grammars of bounded nonterminal degree have the same power both for generating sets of graphs and for generating sets of hypergraphs arbitrary boundary graph grammars have more graph generating power than context free hypergraph grammars but they have the same hypergraph generating power to obtain these results several normal forms for boundary graph grammars are given it is also shown that the class of boundary graph languages is closed under the operation of edge contraction where the label of the edge indicates whether or not the edge should be contracted

duality and distance constraints for the nonlinear p center problem and covering problem on a tree network the problem of locating a fixed number p of facilities centers on a network where there are constraints on the center locations and where the centers provide a service to customers demand points located at vertices of the network is addressed the cost or loss of servicing a given demand point is a nonlinear function of the distance between the demand point and the closest center we consider the case where the network has special structure a tree network i e there is a unique shortest path between any two points on the network we also provide and interpret a dual to this problem and give polynomially bounded procedures for solving both problems the primal location problem is solved with the aid of a related problem for which we also give a dual

a dual based procedure for stochastic facility location in this paper we study how the uncapacitated facility location problem is transformed into a two stage stochastic program with recourse when uncertainty on demand selling prices production and transportation costs are introduced we then present a dual based procedure and indicate how the dual descent and primal dual adjustment procedures proposed by d erlenkotter 1978 in the static case can be made monotonically improving in the stochastic case results of computer experiments are reported

a product positioning model with costs and prices abstract in this paper products are conceptualized as bundles of attributes so that consumers perceptions of existing products and their conceptions of ideal products can be represented as points in an attribute space preferences are assumed to be governed by these locations a new approach to the problem of finding an optimal position for a new product in the attribute space is presented the sales oriented objective function of existing models is replaced by a profit oriented function which explicitly observes price and positioning costs the approach generalizes the underlying behavioral hypothesis and reduces computing time

technical note bounds in the generalized weber problem under locational uncertainty an existing analysis of the bounds on the weber problem solution under uncertainty is incorrect for the generalized problem with arbitrary measures of distance we give easily computable ranges on the bounds and state the conditions under which the exact values of the bounds can be found with little computational effort numerical examples illustrate the analysis

how does the dendrocoleum lacteum orient to light a fuzzy modeling approach we apply fuzzy modeling to derive a mathematical model for a biological phenomena the orientation to light of the planarian dendrocoleum lacteum this behavior was described by several ethologists and fuzzy modeling allows us to transform their verbal descriptions into a mathematical model the behavior of the resulting mathematical model as studied using both simulations and rigorous analysis is congruent with the behavior actually observed in nature this seems to indicate that the verbal explanations suggested by the ethologists are indeed correct we believe that the fuzzy modeling approach demonstrated here may supply a suitable framework for biomimicry that is the design of artificial systems based on mimicking a natural behavior observed in nature

new perspectives in competitive location theory abstract this paper gives new perspectives in competitive location theory by considering new norms in two dimensional problems and by considering for the first time the competitive location problem on a graph the results in competitive location theory are generalized by exploiting an isomorphism to the literature in voting theory and by developing new results for competitive location problems on a graph

a combinatorial strongly polynomial algorithm for minimizing submodular functions this paper presents a combinatorial polynomial time algorithm for minimizing submodular functions answering an open question posed in 1981 by grotschel lovasz and schrijver the algorithm employs a scaling scheme that uses a flow in the complete directed graph on the underlying set with each arc capacity equal to the scaled parameter the resulting algorithm runs in time bounded by a polynomial in the size of the underlying set and the length of the largest absolute function value the paper also presents a strongly polynomial version in which the number of steps is bounded by a polynomial in the size of the underlying set independent of the function values

an approach to the optimal positioning of a new product this study examines the problem faced by a firm which wishes to position a new choice object in an existing product class it is assumed that both the consumer and the firm are involved in a two stage decision process the consumer first decides on his budget for the product class he then evaluates within the product class that subset of competing objects which have prices approximately equal to his budget constraint this evaluation is performed through a weighted multi attribute utility model the product classes considered here are ones for which the consumer has a finite ideal level on each attribute the consumer is hypothesized to choose without error that object which is closest to his ideal different individuals are assumed to be heterogeneous in both attribute weights and ideal levels the firm is assumed to first identify in the attribute space which contains ideal points and competing objects promising product positions which would attract a large number of consumers it then evaluates these positions in terms of costs and resulting profits the problem of identifying the promising positions given information on a sample of individuals is formulated as a mixed integer nonlinear program due to the inability of such a program to solve even small sample problems the spatial properties of the problem are examined an exact solution algorithm which is computationally feasible for small samples is developed it is based on an examination of intersections of indifference hyperellipsoids for larger sample problems an efficient heuristic which is an extension of the random point search used in nonlinear programming is provided it involves random line search procedures for our noncontinuous type problem the positioning approach and the heuristic are illustrated in a simulated positioning problem in the small car market

a distribution map for the one median location problem on a network in this paper we consider the weber one median location problem on a network the weights at the nodes are drawn from a multivariate normal distribution we find the probability that the optimal location is at each of the nodes this set of probabilities is the distribution map the methodology is illustrated on two networks of 20 nodes each

solving covering problems and the uncapacitated plant location problem on trees abstract given a tree network on n vertices a neighborhood subtree is defined as the set of all points on the tree within a certain radius of a given point called the center it is shown that for any two neighborhood subtrees containing the same endpoint of a longest path in the tree one is contained in the other this result is then used to obtain o n2 algorithms for the minimum cost covering problem and the minimum cost operating problem as well as an o n3 algorithm for the uncapacitated plant location problem on the tree

nonterminal bounded nlc graph grammars il est montre que ces grammaires ne peuvent pas etre simulees par une grammaire graphe lineaire

minisum location of a travelling salesman on simple networks abstract in this paper we study the travelling salesman location problem on simple networks the problem is to find the optimal home location of the salesman e g a repair unit that in each working day must visit all the customers that require service the number of customers as well as their location can change from day to day in simple networks each link belongs to at most one cycle the paper includes o n algorithms for several types of simple networks and thus avoids the calculation of 2n 1 probabilities for each possible tour that may occur customers are located at n nodesof the network

the p median problem under uncertainty abstract consider the need to currently locate p facilities but it is possible that up to q additional facilities will have to be located in the future there are known probabilities that 0 r q facilities will need to be located the p median problem under uncertainty is to find the location of p facilities such that the expected value of the objective function in the future is minimized the problem is formulated on a graph properties of it are proven an integer programming formulation is constructed and heuristic algorithms are suggested for its solution the heuristic algorithms are modified to reduce the run time by about two orders of magnitude with minimal effect on the quality of the solution optimal solutions for many problems are found effectively by cplex computational results using the heuristic algorithms are presented

linear graph grammars power and complexity abstract a graph grammar is linear if it generates graphs with at most one nonterminal node linear graph grammars can simulate nonterminal bounded graph grammars which generate graphs with a bounded number of nonterminal nodes and derivation bounded graph grammars if a linear graph language contains connected graphs of bounded degree only then it is in nspace log n these results are shown for graph grammars with neighbourhood controlled embedding and with dynamic edge relabeling ence grammars

the simple plant location problem survey and synthesis abstract with emphasis on the simple plant location problem splp we consider an important family of discrete deterministic single criterion np hard and widely applicable optimization problems the introductory discussion on problem formulation aspects is followed by the establishment of relationships between splp and set packing set covering and set partitioning problems which all are among those structures in integer programming having the most wide spread applications an extensive discourse on solution properties and computational techniques spanning from early heuristics to the presumably most novel exact methods is then provided other subjects of concern include a subfamily of splp s solvable in polynomial time analyses of approximate algorithms transformability of p center and p median to splp and structural properties of the splp polytope along the way we attempt to synthesize these findings and relate them to other areas of integer programming

restrictions on nlc graph grammars several models of graph grammars have been studied with the objective of generating graphs from graphs using a finite set of derivation rules in this way possibly infinite sets of graphs called graph languages can be finitely defined one aspect that must be addressed in any such model is the embedding problem that is when a production is applied how does the new subgraph get reconnected to the original graph node label controlled nlc grammars solve this problem in an elegant way that depends only on the labels of nodes in the new and original graphs this paper examines certain restrictions on nlc grammars similar to the chomsky or greibach normal forms for context free string grammars for example one restriction we consider requires each production to produce a terminal labeled node similar to greibach normal form we also consider restrictions on the form which the embedding mechanism can take our result is that each of the restrictions we examine causes a reduction in generating power for the grammars finally we discuss some directions for future research on nlc grammars

location coverage models with demand originating from nodes and paths application to cellular network design abstract location covering problems though well studied in the literature typically consider only nodal i e point demand coverage in contrast we assume that demand occurs from both nodes and paths we develop two separate models one that handles the situation explicitly and one which handles it implicitly the explicit model is formulated as a quadratic maximal covering location problem a greedy heuristic supported by simulated annealing sa that locates facilities in a paired fashion at each stage is developed for its solution the implicit model focuses on systems with network structure a heuristic algorithm based on geometrical concepts is developed a set of computational experiments analyzes the performance of the algorithms for both models we show through a case study for locating cellular base stations in erie county new york state usa how the model can be used for capturing demand from both stationary cell phone users as well as cell phone users who are in moving vehicles

a hierarchy of ence families of graph languages abstract even though ence and its subclasses have been studied intensively their inclusion relations are not completely known this paper proves some unknown relations among ence families of graph languages which yield together with other known relations a solid hierarchy of graph languages that completely determines equivalence proper inclusion and incomparability among nlc nce enlc ence and their boundary linear and apex subclasses the bottom level of this hierarchy i e lin a nlc contains an np complete graph language

nonterminal separation in graph grammars abstract the notion of nonterminal separation in ence graph grammars is introduced such a graph grammar is k separated with k 1 if the distance between any two nonterminal nodes in any of its sentential forms is at least k 2 separated ence grammars are known as boundary ence graph grammars there exists a 2 separated ence graph language that is not 3 separated apex ence graph grammars can be arbitrarily separated every apex ence graph language can be generated by a k separated apex ence grammar for every k

multidimensional extensions and a nested dual approach for the m median problem abstract a general framework for modeling median type locational decisions where i travel costs and demands may be stochastic ii multiple services or commodities need to be considered and or iii multiple median type objectives might exist is presented using the concept of multidimensional networks the classical m median problem the stochastic m median problem the multicommodity m median problem and and multiobjective m median problem are defined within this framework by an appropriate transformation of variables the multidimensional m median problem simplifies to the classical m median problem but with a k fold increase in the number of nodes where k is the number of dimensions of the network a nested dual approach to solve the resulting classical m median problem that uses erlenkotter s facility location scheme as a subroutine is presented computational results indicate that the procedure may perhaps be the best available one to solve the m median problem exactly

a pumping lemma and the structure of derivations in the boundary nlc graph languages abstract a pumping lemma is known in the nlc node label controlled graph languages 4 however the pumping lemma has an unnatural point at the first pumping that is zero time pumping is not allowed in the pumping lemma we consider the boundary nlc bnlc languages 10 then we obtain a pumping lemma without the unnatural point similar to one for the nlc graph languages using the church rosser property of the bnlc graph grammars we also construct the pumped graphs and provide a constructive proof for our pumping lemma as a result we provide the structure of derivations in the bnlc graph grammars and a role of the church rosser property in the nlc graph grammars