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References
For some relevant discussion see J. Marschak in Haire,op. cit.; Blau and Scott,op. cit., pp. 121–128; March and Simon,op. cit., pp. 201–210; C. B. McGuire, “Some Team Models of a Sales Organization,”Management Science, vol. 7 no. 2, January 1961, pp. 101–130; Roy Radnor, “The Application of Linear Programming to Team Decision Problems,”Management Science, vol. 5 no. 2, January 1959, pp. 143–150.
This point is to be qualified to the extent that information flows from lower-order nodes to higher-order nodes, and from one node along one branch to another node of the same order along a different branch via a lower-order node.
See Marschak,op. cit.
For a good but very general concept and definition of social organization, refer to E. W. Bakke, “Concept of Social Organization,” in Haire, ed.,op. cit.
In actual physical space, there would tend to be one regional office close by or at the location of the central office, and one local office close by or at the location of each regional office. Too, the members of each set of subsidiary nodes will be at different physical distances from the lower-order, mother node.
We shall not inquire at this point how these two functions may have been derived by an organization, and with what assumptions they might be inconsistent. We simply posit that they are given as a result of some reasonable synthesis of both information and customary practices of the organization.
Observe that the expected rate is taken to be a single figure; consideration of a frequency distribution of expected rates is precluded.
Strictly speaking, the decision maker at the first-order node is able under conditions of full information to make superior estimates of a local rate of growth than the local decision maker since the former has information on all local economies. This factor which may contribute to overview advantage in the real world is ignored in our simplified example.
Formally speaking, for a decision maker at a second order node the decision rule is: Invest in new capacity if 2r r +r l ≥15; otherwise invest in service improvement.
His decison rule is: Invest in new capacity when 3r l ≥15; otherwise invest in service improvement.
Similarly for the node at (h), a decision maker at the second-order node (β) would assume that the sum of expected rates is 15 and would invest in new capacity. This would be a wrong decision, since the sum of expected rates based on full information is 13. The cost (foregone returns) would be %6,666. For the node at (j), a decision maker at node (γ) would assume that the sum of expected rates is 15, and would invest in new capacity, a wrong decision. The cost (foregone returns) would be $3,333. Finally, for the node at (k), a decision maker at (k) would assume that the sum of expected rates is 12, and would invest in service improvement, a wrong decision. Since the sum of expected rates based on full information is 15, and since at this point both new capacity and service improvement yield the same return, the cost of this wrong decision would be zero.
When the individual or authority at the first-order node is viewed as reaching a decision on the basis of discussion in a group of representatives from higher-order nodes, the citations in and the findings of E. J. Hall, J. S. Mouton, and R. R. Blake, “Group Problem Solving Effectiveness under Conditions of Pooling vs. Interaction,”Journal of Social Psychology, vol. 59 no. 1, February 1963, pp. 147–157 are relevant. In a test situation,which however was not related to any organization structure, these analysts found that “grouping of individual judgements improves the chances of success statistically due to the simple cancellation of individual errors, but the addition of interaction apparently further improves the success trend due to the objectiveevaluation of individual judgments which it fosters. The decision which results from group interacion may be consideredemergent since it represents more than either a simple conbination of member contributions or a reflection of the best member effort” (p. 155). Of course it may be contended that in the problem with which we are concerned, the same improved judgment may be achieved from interaction and group discussion at each higher-order node as at the first-order node. It may be questioned, however, whether the same average quality of discussion and ability for judgment would be present at each higher-order node, if a decision were to be reached at each, than at a first-order node at which representatives from each higher-order node might assemble for group discussion. It is also to be noted that here, as elsewhere, we ignore the effects of random elements. Moreover, by our highly simplified, non-dynamic case, we ignore time dependence and structure of decisions, and the different extents to which errors at one order of node may lead to poor decisions at other order nodes, etc.
For example, a decision-maker at (β) would assume that the sum of expected rates is 20 with respect to investment at the third-order node (g) when the sum is 18. He would make the wrong decision to invest in new capacity; the cost would be $4263. (The equation of curves relating to new capacity and service improvement are, respectively:y=4,215 x 95 y=45,000+1,600 x 95)
For example, a decision maker at third-order node (p) would assume that the sum of expected rates is 21 when the sum is 17. He would make the wrong decision to invest in new capacity; foregone revenue would be $6414.
In the usual case, the state of the environment will affect these functions since it will affect, for example, one or more rules governing the volume and nature of information to be collected, research methods and so forth.
See Isard and Dacey,op. cit., “The Scope and Nature of Regional Science,”Papers and Proceedings of the Regional Science Association, vol. VI, 1960, p. 20, and literature cited therein.
Observe that in the example presented the effect of the attitude variable is not crystal clear. If we were to follow standard statistical decision theory and consider three possible states of the environment without specifying their characteristics, then one could say that the 100 percent optimist should select alternativeM. His choice is motivated by the +6000 in the third column. However, when the characteristics of the several states of environment are noted, it is seen that the third column corresponds to an extremely tense international situation. Some people would consider an expectation of an extremely tense situation as a pessimistic attitude. Hence, they would consider it a contradiction that the 100 percent optimist's choice be guided by the +6,000 figure in the third column. These same people might also reason that the 100 percent pessimist would tend to expect an extremely tense international situation and thus might choose alternativeM rather thanA. It is clear that in analyzing examples of this type one must separate: (a) any attitude with reference to the characteristics of specific states of environment from (b) any attitude with respect to the occurence of outcomes where the specific characteristics of the several states of the environment may be considered irrelevant.
In addition to those cited in the text, several other attitudes and the corresponding optimal choices may be set down. Where an organization is motivated to minimize regret and is highly pessimistic alternativeM is optimal. Where such an organization is highly optimistic, alternativeM might also be considered optimal. Where an organization is a satisficing one, and considers any outcome of +1000 or more as satisfactory (+1 value) and others unsatisfactory (zero value), then alternativeZ is optimal if the organization is motivated to maximize the probability that it will be satisficed. Other relevant attitudes may involve consideration of the variance of payoff (or regret) as well as the mean expected value of payoff, or the consideration of only the worst and the best possible payoff associated with any choice (the Hurwicz-type solution), or the consideration of only the most likely favorable payoff and the most likely unfavorable payoff, or some variations of one or more of the several considerations already mentioned. Discussions of these and others may be found in isard and Dacey,op. cit.,, “The Scope and Nature of Regional Science,”Papers and Proceedings of the Regional Science Association, vol. VI, 1960, p. 20. and literature cited therein.
As already indicated, there would be considerable difficulty in estimating an extrareturns curve on the basis of the different magnitudes of participation potential corresponding to the different spatial patterns of decision-making authority. Here, the extra-returns may reflect, for example, the extent to which superior engineering and other technical plans are developed for the new plant to be constructed or for the renovation of the old.
It should constantly be kept in mind that the locational cost differential is in part dependent on overview advantage, and that in turn the overview advantage is dependent on the type of decision rule adopted. Thus, for different decision rules there can be different locational cost differentials.
In traditional location literature, this type of relationship also crops up when there is a change in the total use of an input (say labor) with shift in location from one site to a second having a different input price. In effect, a substitution among inputs takes place when continously differentiable transformation functions are involved. Or, this type of relationship may be said to be present when there is a change in total requirement for an input (say land) with the simultaneous relocation at one site of several spatially separated plants; here one might speak of agglomeration economy, or diseconomy. (It is recognized, of course, that in practical location studies, only the most important factors leading to cost differentials are identified for analysis, the others being assmed to have negligible, if any, effect. In many studies, the number and mix of decisions may be in the latter category.)
In general, it may be contended by some that for each category the degree of spatial decentralization of decision-making authority cannot be greater than that of production or other activities, unless there is some form of voting procedure. If all production is carried on at the third-order nodes in Figure 12, decision-making authority may also reside wholly at these same nodes. However, if production is carried on at first- and second-order nodes only, then decision-making authority cannot largely reside at third-order nodes within a simple organization. (If the organization is a complex one so that it includes, for example, both those who produce and consume the product, then the degree of spatial decentralization of decision-making authority may be greater than that of production. However, in many cases it may be better to treat such a complex organization as two more simple organizations, each of whose operations are consistent with the above rule.)
A good example of such an organization might be a large iron and steel (or aluminum) corporation serving many local and regional markets from several production plants. According to location theory, the transport (or power and transport) cost differential should logically dominate all others in the determination of the spatial pattern of production. This pattern should logically be independent of the degree of spatial decentralization of decision-making authority. Thus, the question of whether decision-making authority should be concentrated at one central location (which implies one pattern of information collection, processing and flow) or distributed in some way among several nodes (which implies quite a different pattern of information collection, processing and flow) should have no effect on the locations at which iron and steel (or aluminum) is produced.
A good example of such an organization might be a government agency, such as the Federal Reserve system in the United States, or the Department of Interior or the Department of Agriculture. In the provision of basic services cost differentials among locations for such inputs as fuel, raw materials, labor, and even transport may be relatively minor whereas differences in participation potential, in cost of collecting and transmitting information and in overview advantage may lead to major decision-making cost differentials among different spatial patterns of decision making and other activities.
A good example of this third category would be an organization which requires for each node a large amount of information on local conditions and where (1) such information is to a large extent visible locally, or (2) the time-lag between receipt of information and the making of a decision must be short to avoid high inventory costs and poor production management, or both. Companies engaging in oil refining and distribution and research organizations operating for profit are two illustrations.
An example might be the manufacture of a toy, which beyond a relatively small output does not experience economies or diseconomies of scale, and where transport cost in the assembling of raw materials in the delivery of the finished product to the market is relatively minor.
For footloose organizations, however, the hexagonal arrangement does not have real significance. Footloose firms are not easily embraced by the Lösch conceptual framework.
conceptually, we may even search for hexagonal arrangements of different orders, impose political, legal, cultural or other restrictions upon the several sizes of hexagonal area, limit the number and pattern of major transportation and communication arteries, etc. and finally, allow for distortions in patterns because of the underlying spatial differences in population density and intensity of activities; see Isard,op. cit., “The Scope and Nature of Regional Science,”Papers and Proceedings of the Regional Science Association, vol. VI, 1960, p. 20. ch. 11.
See Isard et al,op. cit. “The Scope and Nature of Regional Science,”Papers and Proceedings of the Regional Science Association, vol. VI, 1960, p. 20. ch. 12.
It may claimed that constant interorganization coefficients are implicitly assumed as well as the constant interfirm, interindustry and interareal coefficients typical of national, regional and interregional input-output models.
The set of sectors and commodities will of course be extended to include government units (planning authorities, administrative agencies, etc.) and services, respectively.
It is beyond the scope of this paper to synthesize the balanced regional input-output model with a decison-making framework for analysis within the single large organization, short of a system of regions or society itself. If this were done, the various products, services and other items which the organization (say a large economic firm) might deliver to the outside world could be viewed as a final demand vector. All production activity might be considered as occurring at the highest-order (h th-order) nodes. (In Figure 12 these would be third-order nodes.) For simplicity's sake, each lower-order node capable of production could be taken to coincide locationally with a highest-order node. Any other lower-order node need not. Commodities which could be yielded at any of the producing nodes and shipped to all other producing nodes might correspond to national goods. Commodities which could be yielded at any given producing node but shipped only to producing nodes within that node's region might be considered regional goods. Commodities which could not be shipped from one producing node to another might be considered local goods. Given this scheme, the implication of a set of deliveries to the outside world for the level and mix of production at each producing node could be determined. Together with the activities by node associated with the spatial pattern of decision-making authority the production pattern by nodes would yield the total activity pattern by nodes.
Each organization of this sector would tend to have all its production concentrated at a single node, which need not be at the same geographic location for each organization.
Each organization which is regional would have all its production in a given region concentrated at a node of that region. However, this node need not be at the same geographic location for production (within a given region) of each regional organization.
By these definitions, 100 percent spatial decentralization of decision-making authority can exist within an organization only when all its production takes place and all its decision-making authority resides at the highest-order nodes of the conceptual system. When all production takes place and all decision-making authority resides at the nodes of another order (say the regional), 100 percent spatial decentralization does not exist, although it can be said thatrelative to the production pattern of the given organization 100 percent spatial decentralization does exist.
Isard et al,op. cit. “The Scope and Nature of Regional Science,”Papers and Proceedings of the Regional Science Association, vol. VI, 1960, pp. 576–582.
W. Isard, “The Scope and Nature of Regional Science,”Papers and Proceedings of the Regional Science Association, vol. VI, 1960, p. 20.
Ideally, for a combination of sectors or parts of sectors, the possibility of scale, localization and urbanization (i. e. agglomeration) economies in collecting, processing, and transmitting information and in the use of executive time, etc., should be examined in an industrial complex framework. Such an examination would point up the fact that the classification of at least some sectors may be highly interdependent. In practice, this examination would be exceedingly difficult to undertake.
Other techniques such as factor analysis, scaling, and money flows analysis may also be employed. Refer to the discussion in Isard et al,op. cit. “The Scope and Nature of Regional Science,”Papers and Proceedings of the Regional Science Association, vol. VI, 1960, pp. 611–647, in connection with Figure 1, ch. 12.
Sectors comprising organizations which are footloose may also be classified as national, regional, or local, depending upon whether such organizations are footloose nationally, regionally or locally, respectively. The output of such sectors may be distributed among producing nodes on a probabilistic basis, or in accordance with the distribution of some base year, or in terms of some other reasonable criterion, or combination of criteria —subject of course to any constraints imposed by the scale-economy factor.
Recall that in a given region the demand for the output of a regional sector cannot. by definition, be met by producers (organizations) outside that region.
Recall that at a given third-order node the demand for the output of a local sector must, by definition, be met by producer (organizations) at that node.
For full discussion of these discrepancies, see Isard et al,op. cit. “The Scope and Nature of Regional Science,”Papers and Proceedings of the Regional Science Association, pp. 593–600, 650–651.
For some relevant discussion of the rerun procedure, see Isard et al,ibid. “The Scope and Nature of Regional Science,”Papers and Proceedings of the Regional Science Association, pp. 593–600, 650–651.
See Walter Isard,Location and Space-Economy, M. I. T. Press, Cambride, Mass. 1956; and L. N. Moses, “Location and Theory of Production,”Quarterly Journal of Economics, vol. 73 no. 2, May 1958, pp. 259–272.
Among others, we might list the following substitution points as generally significant: (1) transport outlays on each commodity (raw material or product) or meaningful group of commodities vs. outlays or revenues on each new category or meaningful group of categories listed in the text—for example, transport outlays on steel ingot vs. parltcipation returns when the choice is between location of a large steel fabricating establishment adjacent to an integrated steel works and location of fabricating in a number of small shops spatially dispersed, when the latter pattern would involve a higher degree of spatial decentralization of decision-making authority; (2) labor, power, or other processing outlay vs. outlays or revenues on each new category or meaningful group of categories listed in the text, when a cheap labor, or power, or other processing cost site exists and tends to deviate and agglomerate production at its location—for example, labor outlays vs. inforequire the collection of much information on local markets which would be visible if production were at the market; (3) production outlays in general vs. outlays or revenues on each new category or meaningful group of categories listed in the text, when scale economies tend to dictate concentration of production at one site—for example, production outlays vs. info-transmission outlays when important market information is of a qualitative nature easily visible but difficult to code and quantify. For all these substitutions, the possibility of changes in the number and mix of decisions would also have to be considered and adjusted for.
Isard and Tung,op. cit.
Additional information
with the Assistance of Tze Hsiung Tung
Part I of this paper has been published in the preceding volume (Vol. XI) of thePapers. The authors are indebted to the National Science Foundation and Resources for the Future, Inc., for financial support of their research.
The authors are associated with the Regional Science Research Institute and the Department of Regional Science, Wharton School, University of Pennsylvania, Philadelphia, U.S.A.
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Isard, W. Some concepts for the analysis of spatial organization: Part II. Papers of the Regional Science Association 12, 1–25 (1964). https://doi.org/10.1007/BF01941236
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DOI: https://doi.org/10.1007/BF01941236