Report: The Second Triennial 'Where to Stick It Conference'Author(s): Nigel WatersSource: Area, Vol. 14, No. 2 (1982), pp. 170-172Published by: The Royal Geographical Society (with the Institute of British Geographers)Stable URL: http://www.jstor.org/stable/20001806 .

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170 What is time distance?

maps because time-distance is a much more important determinant of most decisions to travel than physical distance. If the variability about the average time-distance between places for particular modes of travel is added to the difficulties of drawing average time-distance maps, it becomes impossibly complicated to represent the variation in accessibility among places in two dimensions. This perhaps explains why the problem is so frequently ignored. But it is this variability, especially for short distance travel, that places the public transport user at a disadvantage relative to the car-owner. Thus, cartographic difficulties have a tendency to bias the representation of travel possibilities in a way that understates the difficulties of the user of public transport. Consideration needs to be given therefore to mapping the effects on time distance of both the differential accessibility of various groups of the population to private, 'random access ', transport (e.g. in relation to car ownership, income and family size) and the time variability of access between places on different modes of

public transport.

Note 1. Bromma airport is used as Stockholm's airport for most domestic air services.

References Erlandsson, U. (1978) ' Kontakt- och resem6jligheter i Europa ', Rapporter och Notiser 48, Dept. of Soc. and

Econ. Geog., Univ. of Lund

Forer, P. C. (1974) 'Relative space and regional imbalance: domestic airlines in New Zealand's geometro

dynamics ', Proc. IGURegional Conf: and eighth New Zealand Geog. Conf:, 53-62, N.Z. Geog. Soc.

Haggett, P. (1979) Geography: a modern synthesis, Third edn. (Harper Rowe)

The second triennial ' Where to stick it conference '

Report of the International Symposium on Locational Decisions held at Skodsborg, Copenhagen, Denmark, 15-19June 1981.

The first International Symposium on Locational Decisions was held in Banff, Alberta, Canada, in 1978 and this conference set the tone for the one in Skodsborg. The Skodsborg Conference also employed a five day residential format with just over 50 participants and 44 papers. Most participants were from North America but this time they were a smaller majority and altogether 11 countries were represented. Despite renewed interest by British geographers in the use of operations research methods (see Gatrell, A. C. (1980), Area 12, 31-2) not one British geographer attended the Skodsborg Conference and the general attendance by geographers was down to about half the number who had attended the Banff Conference. Participants at Skodsborg were invited to submit their papers for subsequent publication.

The conference was opened by 0. Madsen (Technical University, Denmark), the local organiser, and by J. Halpern (Calgary), who began the Conference with the sad news of the death of Leon Cooper, for over two decades a leading light in the application of operational research techniques to spatial problems. It is tragic to record that Jonathan Halpern, himself, died following a heart attack immediately after the Skodsborg Conference.

The first papers presented were by L. Hakimi (Northwestern) on locating facilities in a competitive environment, Pruzan (Copenhagen) on the relationship between the minisum and minimax problems (a topic Halpern pioneered in his seminal paper on the cent-dian) and by J. Krarup (Copenhagen) on the assessment of approximate algorithms. Krarup analysed ' worst case ' or ' pathological ' situations and as D. Erlenkotter (California, Los Angeles) pointed out, if

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Where to stick it 171

such highly contrived examples rarely occur in the real world then it may not be useful to design algorithms for such unlikely cases. This point has, of course, been made in relation to the virtues of Khachian's new linear programming algorithms vis-a-vis the simplex procedure (Bland, R. G. (1981) Scientific American 244, 126-44). Monday morning concluded with a paper by C.

Lardinois (Ecole des Hautes Etudes) which discussed the use of a heuristic based on statistical optimisation for solving Quadratic Assignment Problems (QAP) and Optimal Network Problems (ONP) too large to be solved exactly.

Monday afternoon began with a paper by R. D. Galvao (Rio de Janeiro) on the generalised p-median problem. Galvao showed that where the fixed cost of a point varies with location then the solution is ' Hakimi optimal ' (i.e. at the vertices) if no point on an arc has lower fixed costs than its surrounding vertices. This was followed by a paper from A. Tamir (Tel-Aviv) in which the costs of establishing centres are allocated among the users. The problem was addressed using the game theory concept of a core allocation. Halpern's paper used a variety of objective functions including the median (representing efficiency), the centre (representing effectiveness), the variance (representing dispersion) and Lorenz (representing equity) to locate facilities.

Determining the appropriate objective function is interesting since it is largely a policy matter. Monday's sessions concluded with papers by S. Jacobsen (Technical University, Denmark) on heuristics for the capacitated plant location problem and by S. J. Ratick (Boston) and C. Revelle Uohns Hopkins) who explored the relationships between game theory and location problems in a paper which was theoretically similar to Tamir's paper.

Tuesday began with a paper by G. Laporte (Ecole des Hautes Etudes) in which an exact algorithm for the modified m-travelling salesman problem was given. J. Tind's (Aarhus) paper which followed discussed the location of bus depots in Aarhus, Denmark. The Tuesday morning session ended with papers by J. Morris (Wisconsin-Madison) in which a bounded algorithm was used to locate linear features such as bus lines, and by Madsen, who addressed the problem of locating depots from which customers are served by tours.

Tuesday afternoon began with a paper by D. Erlenkotter and G. Leonardi (IIASA) in which a non-linear branch and bound algorithm was used to locate facilities in a system where customers travelled according to a gravity model formula. This was one of the few papers which made any extensive reference to the work of British geographers. The work which was cited was carried out almost exclusively by geographers associated with the Leeds school, such as Beaumont, Coelho,

Williams, and Wilson. P. Mirchandani (Rensselaer) provided an exact algorithm for locating facilities where demand and cost (i.e. arc length) are represented by random vectors. Such a model would be ideal for locating urban emergency facilities where rush hour traffic alters travel times and therefore, in effect, arc length. 0. Berman (Calgary) and A. Odoni (MIT) also addressed the problem of arc length due to changes in traffic volume. Where relocation costs are concave the solution was shown to be ' Hakimi optimal '. Algorithms were also presented for more generalised situations. Berman and Larson (MIT) considered the problem of locating a server on a network which operated as an M/G/1 queue. A simple model in which demand is not satisfied if the server is busy is shown to be ' Hakimi optimal '. A more complex model in which such demand enters a queue is ' Hakimi optimal ' only when the mean arrival rate approaches its upper and lower limits. An exact algorithm for a tree network is given for the second model. It is interesting to note that if the server starts and ends at some facility such as a hospital the network can be broken down into a tree using Haggett's well known procedure. C. D. T. Watson-Gandy (Imperial) discussed the multifacility constrained Weber problem. The algorithm used a piece

wise linear cost function and ingeniously used a graph colouring algorithm to partition the network.

On Wednesday morning P. Hansen and J. Thisse (Catholique de Louvain), respectively, discussed the Weber problem. Following this B. Gavish (Rochester) presented a paper on the topological design of computer communication networks, a problem which is structurally similar to the warehouse location problem. Most of these problems were shown to be NP-hard but the use of redundant constraints in formulating the branch and bound algorithms was shown to provide tighter bounds than Lagrangean relaxation. H. Juel (Odense) and R. F. Love (McMaster) looked at hull properties in location problems. Chalmet (Florida) suggested that the algorithm presented was of order n2 to n3 whereas the problem discussed could be solved in

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172 Where to stick it

n log n. Finally, on Wednesday morning T. Ditumbule (Vrije Universiteit Brussels) also looked at generalisations of the Weber problem.

The conference continued Thursday morning with a paper by J. Hodgson (Alberta) on interaction based location-allocation models. The model suggested that facility location should be based on consumers' welfare, which was inversely related to facility size, and expected interaction based on distance. Little attention was given to determining the specific, empirical form of the welfare function. S. C. Wirasinghe and N. Waters (Calgary) presented a paper on the location of refuse transfer stations which is similar to the warehouse location problem. The hybrid model used continuum approximations to determine the number of facilities and the heuristic program, WARELOC, to determine their location. A. Kolen (Mathematical Centre, Amsterdam) presented a polynomial time algorithm for solving the set covering problem on a tree. Soland (George Washington) discussed multiactivity, multifacility, multicriteria systems.

An excellent overview of hierarchical location-allocation problems was presented by S. Narula (Rensselaer). This paper used a queuing theory type of notation to classify problems according to the number of facility types, the arc flow discipline and the node flow discipline. Thursday afternoon began when Christofides (Imperial) discussed an algorithm for maximal planar graphs and looked at its application to facility layout problems. This was followed by L. Chalmet's paper on the use of extended continuous logic in power plant location problems. Chalmet raised two points of interest to geographers. The first of these was the topic of measures of site attractive ness and the second was the use of pair-wise comparisons to determine the relative importance of attributes. Surprisingly no mention was made of the topic of multidimensional scaling or related literature in geography. This again stressed the need for meetings such as this to allow inter disciplinary interaction. J. Osleeb (Boston) and S. Ratick presented a formulation of one of the world's largest mixed integer, multi-objective programming models. The model, designed to analyse coal handling in New England ports, contained approximately 8,000 variables and 2,000 constraints and was to be solved using the ' Sesame ' package from MIT. The last two papers on Thursday were by L. Lundqvist (Royal Institute of Technology, Sweden) and by D. Griffiths (SUNY, Buffalo) and H. Jacobs (Ryerson). The former provided an exact model for the spatial allocation of housing in an urban region and used the model to project various scenarios. The latter discussed experimental, simulation and gaming approaches to the problem of spatial decision-making. The work by Openshaw and by Goodchild on spatial aggregation is obviously of relevance here.

Friday morning began with papers by R. Larson (MIT) and A. Odoni in which they discussed facility location using the L1 or Manhattan metric, in the presence of barriers to travel and, secondly, in the presence of high speed corridors. Z. Drezner (Michigan-Dearborn) presented a paper on sensitivity analysis in single facility location. The change in optimal location resulting from small changes in the parameters was used to formulate a pair of differential equations which could then be used to solve for the optimal location of the modified problem. The problem of locating obnoxious facilities was examined by G. Wesolowsky (McMaster). Pruzan in ensuing discussion pointed out the importance of the degree of obnoxiousness. R. Wendell's paper (Pittsburgh) outlined a method for obtaining a metric which gives the best estimate of distance.

The final session began with two papers by R. Francis (Florida) and T. Lowe (Purdue) and by T. Hodgson (Florida) and Lowe, respectively. The first paper examined the node covering problem on a tree under the constraint that related nodes would be covered by distinct centres. The second paper examined the production of lot sizes and the assignment of warehouse storage space as a single, optimisation problem. Juel discussed the generalised Weber problem under conditions of locational uncertainty and the symposium concluded with a presentation by D. K. Kulshresta (Flinders) on an approach to optimum location called k-elliptic optimisation. The method determines the optimum location of a point in two dimensional Euclidean space when the optimum belongs to a set of feasible points and the objective function is to minimise the sum of weighted, Euclidean distances.

The next International Symposium on Locational Decisions will be held in the summer of 1984 in the Boston-Cape Cod area of northeastern United States.

Nigel Waters University of Calgary

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