Thus some kinds of canning and preserving involve important weight and bulk loss as well as reduction of perishability. A further reason for the usual output orientation of modern by-product coke ovens is that the bulkiest output, gas, is in demand at the steel works where the coking is done. Coke produced by the earlier"beehive"process was generally made at coal mines, since weight loss more than offset fragility gain. (The gas went to waste.) Processing activities of course usually result in a product more valuable than the required amount of transferred inputs; and for a number of good reasons, transfer rates tend to be higher on more valuable commodities. Risk of damage or pilferage is greater there ic a greater interect cost an the working ranital tied nn in the enmmnditv in transit; and (as will be expl ained in the n nity to discriminate against high-value boring market orientation. 9 even when physical weight is zero or irrele energy, communications, and services g this information with the cost of an addit ransferable input or output is invol ved e categorizations of transfer-oriented activ S determination of locational preference that the unit we are considering is S the set of market locations and all that rema transferred input to that market more chea ts. The profitability of location at each FIGURE 2-2: Pairing of Sources and Markets he unit should locate source for a location at any the input more cheaply than for more than one market any of the market locations nging the ss and Ms. If the ich to locate. and then there nd of transferable input(for atterns and sand for molds) equired, say, x tons of one plex. In Figure 2-3, which may be at any one of those we can see immediately that formed by joining the input e points involved, as in Figure 2-3. If nan three sides the constraint will st ill e processing location, each attracting it towa ee pulls balance, so that a shift in any direc itive about which force will prevail. In t is, at least equal to the sum of all the other cases in which no single ideal weight gure: that is, the configuration of the M ion is such that the activity would be -or the market m. ll but with the same FIGURE 2-4: A Locational Triangle Conducive to iangle would be optimal, and we could Minimum Transfer Cost Location at the obtuse Corner We find, then, that it is not as easy as it first appeared to characterize by a simple rule the orientation of any given type of economic activity. If the activity uses more than one kind of transferable input(and/or if it produces more than one kind of transferable output ), we may well find that an optimum location can sometimes be at a market, sometimes at an input source. nd sometimes at an intermediate point. The steel industry is a good example of this. Some steel centers have been located at or near iron ore mines, others near coal deposits, others at major market concentrations, and still others at points not possessing ore or coal deposits or major markets but offering a strategic transfer location between sources and markets. Intermediate and varying orientations are most likely to be found in activities for which there are several transferable inputs and outputs of11 Thus some kinds of canning and preserving involve important weight and bulk loss as well as reduction of perishability. A further reason for the usual output orientation of modern by-product coke ovens is that the bulkiest output, gas, is in demand at the steelworks where the coking is done. Coke produced by the earlier "beehive" process was generally made at coal mines, since weight loss more than offset fragility gain. (The gas went to waste.) Processing activities of course usually result in a product more valuable than the required amount of transferred inputs; and for a number of good reasons, transfer rates tend to be higher on more valuable commodities. Risk of damage or pilferage is greater; there is a greater interest cost on the working capital tied up in the commodity in transit; and (as will be explained in the next chapter) transfer agencies commonly have both the incentive and the opportunity to discriminate against high-value goods in setting their tariffs. Value gain in processing is thus an activity characteristic favoring market orientation. 9 An important observation of ideal weights is that they are real and measurable even when physical weight is zero or irrelevant. We can directly evaluate the ideal weights of inputs or outputs such as electric energy, communications, and services by determining the costs of transferring them an additional mile and then comparing this information with the cost of an additional mile of transfer on the appropriate corresponding quantity of whatever other transferable input or output is involved in the process. As mentioned earlier, the comparison of ideal weights permits at least tentative categorizations of transfer-oriented activities as input-oriented or output-oriented and points the way toward more specific determination of locational preference for specific units and activities. Suppose for example that we have determined that the unit we are considering is output-oriented. Then the choice of possible locations is immediately narrowed down to the set of market locations, and all that remains is to select the most profitable of these. For each market location, there will be one best input source, which can supply the transferred input to that market more cheaply than can any other source. Figure 2-2 pictures this pairing of sources and markets. The profitability of location at each market can thus be calculated, and a comparison of these profitabilities indicates where the unit should locate. The situation shown in Figure 2-2 has some other features to be noted. First, the best input source for a location at any given market is not necessarily the nearest. A more remote low-cost source may be able to deliver the input more cheaply than the higher-cost source that is closer at hand. Second, any one input source may be the best source for more than one market location (but not conversely). Third, there may be some input sources that would not be used by any of the market locations. Finally, Figure 2-2 could be used to picture the ease of an input-oriented unit, by simply interchanging the Ss and Ms. If the unit is input-oriented to a single kind of input, all that is needed is to choose the best source at which to locate, and then there will be a best market to serve from that location. Next, let us complicate matters a little by considering an activity that uses more than one kind of transferable input (for example, a foundry that uses fuel and metals plus various less important inputs such as wood for patterns and sand for molds). Initially we shall assume that the various inputs are required in fixed proportion. We now have three or more ideal weights to compare. For each ton of output, there will be required, say, x tons of one transferable input plus y tons of another. The question of orientation is now somewhat more complex. In Figure 2-3, which pictures one market and one source for each of two kinds of input, the most profitable location may be at any one of those three points or at some intermediate point. Retaining our assumption of a uniform transfer surface, we can see immediately that the choice of intermediate locations is restricted to those inside or on the boundaries of the triangle formed by joining the input sources and market points. This constraint upon possible locations will always apply when there are just three points involved, as in Figure 2-3. If there are more market or source points, so that we have a locational polygon of more than three sides, the constraint will still apply if the polygon is "convex" (that is, if none of its corners points inward). Looking at Figure 2-3, we can envisage three ideal weights as forces influencing the processing location, each attracting it toward one of the corners of the triangle. The most profitable location is where the three pulls balance, so that a shift in any direction would increase total transfer costs.10 In the case of three or more factors of transfer orientation, we can no longer be positive about which force will prevail. In fact, we can really be sure only if one of the ideal weights involved is predominant: that is, at least equal to the sum of all the other weights. It does not follow, however, that an intermediate location will be optimal in all cases in which no single ideal weight predominates. The outcome in such a case depends on the shape of the locational figure: that is, the configuration of the various source and market points in space. For example, in Figure 2-4 the configuration is such that the activity would be input-oriented to source S2 even if the relative weights were 3 for S1, 2 for S2 and 4 for the market M. 11 But with the same weights and a figure shaped like that in Figure 2-3, an intermediate location within the triangle would be optimal, and we could not describe the activity as being either input-oriented or output-oriented. We find, then, that it is not as easy as it first appeared to characterize by a simple rule the orientation of any given type of economic activity. If the activity uses more than one kind of transferable input (and/or if it produces more than one kind of transferable output), we may well find that an optimum location can sometimes be at a market, sometimes at an input source, and sometimes at an intermediate point. The steel industry is a good example of this. Some steel centers have been located at or near iron ore mines, others near coal deposits, others at major market concentrations, and still others at points not possessing ore or coal deposits or major markets but offering a strategic transfer location between sources and markets. Intermediate and varying orientations are most likely to be found in activities for which there are several transferable inputs and outputs of