“Soviet Planning and Spatial Efficiency”
Three potential sources of short run spatial inefficiency in the cement industry may be distinguished:
1) Inefficient utilization of various modes of transport for given levels and regional patterns of cement production and consumption. This may arise from (a) selection of the wrong mode of transport or (b) imperfect shipping patterns—that is, incorrect linking of producers and users. In what follows we will refer to this problem as efficiency in distribution.
2) Inefficient allocation of production targets among plants, possibly resulting in lower industry average production costs, but also in higher average delivered costs than necessary.
3) A poor product mix, heavily weighted by low-strength cements, necessitating the shipment of greater tonnages to achieve given concrete strength requirements.
This chapter starts with an analysis of efficiency in distribution. First we study the modal composition of cement shipping patterns before 1935. Following that, we use a linear programming model to determine the optimal shipping patterns and see how it diverges from what was actually employed. To anticipate our results, the answer is that the deviation between actual and optimal patterns is not very serious.
We cannot say much about the second type of inefficiency. There is not enough information on individual plant cost curves to work out a minimum total delivered cost (minimum production plus transport cost) policy so that we cannot uncover any further gain that might have derived from an alternative plant production pattern. However, it does not seem likely that there were any great losses involved in the pattern of allocation of production targets among plants. Available information on the reasons for kiln shutdowns and on kiln operating rates suggests that industry policy required every plant to produce as much as was reasonably possible subject to normal maintenance and capital repair requirements and that fuel, materials, and labor shortages beyond the control of industry or plant managers were the main reasons that operating rates were sometimes depressed below capacity.1
The last section of this chapter examines the effect that upgrading of the product mix would have had on transport requirements. We shall see that it is in this area that a substantial saving might have originated if a more rational approach to output had prevailed.
In Chapter IV the transport requirement in the delivery of cement in the 1930’s was seen to be very large—the average haul was about three times as high as it had been in the prerevolutionary industry, and transport costs accounted for 50 percent of delivered cement costs. There we saw that substantial saving could have been achieved in total delivered costs through an alternative location pattern. In making this estimate the total physical transport expenditure actually incurred was assumed to be the best that could be achieved with given regional production levels. Is it possible that this was not the case and that a large part of the saving which we have attributed to the alternative location pattern could have been derived instead through rationalization of marketing patterns?
A priori there are many reasons to expect that shipping patterns at the time were inefficient. One reason lies in our general knowledge of the period, which we know to have been characterized by extreme pressures and shortages. We have come to expect a good deal of irrationality in the Soviet economy of the thirties, and we are not usually surprised to see additional evidence of it. A second reason is that, as we shall see, Russian observers themselves reiterated many times (and continue to do so today) that the cement industry was typified by inefficient shipping operations. Crosshauls are frequently adduced as evidence of this inefficiency, and a more rational scheme is often presented for the supply relations of a few origins and destinations. The modal composition of traffic is sometimes criticized as well. Also, as we have seen, the administration of the industry was not constrained to minimize transport costs. Hence, disorganized and inefficient marketing activities might be expected. Two other less direct reasons for expecting inefficient shipping operations are the cement pricing policy at this time and the railroad rate structure. A good many considerations, then, suggest that inefficiency in cement distribution in the 1930’s is to be expected, and we now confront these hypotheses with actual experience.
1. The Modal Composition of Cement Traffic
From time to time in Soviet periodicals greater use of river and of joint rail-river transport has been urged for the shipment of a great many commodities. Holland Hunter describes the often justified reluctance of shippers to use river shipment because of the limited navigable year of most rivers, the need to maintain larger inventories, and the damage to metals inflicted by river moisture. Hunter points to the greater real cost of joint shipments (because of reloading) as a major impediment to this kind of traffic.2 These or similar objections are also relevant, on many routes, to river shipment of cement. One objection peculiar to cement shipment is that water shipment would require bags or barrels to prevent hydration.
It is often argued that river and sea transport should be used more for cement,3 although this is a controversial issue.4 On one major cement supply arc (Vol’sk-Moscow) water shipment is sometimes a desirable mode of operation. On the other key water route (Novorossiisk-Leningrad) the mode of shipment is almost a matter of indifference. On still other, less important arcs, such as those involving Black Sea ports, water has manifest cost advantages, so that the question of water or rail need not even arise.
In the appendix to this chapter we discuss certain operations performed on an origin and destination table for 1936 (first half) first presented by Brodskii.5 The direct evidence of the table and our inferences from it show the following: water shipments originated in only three producing centers (Novorossiisk, Vol’sk, and Ukraine). Ukraine originations constituted only 3 percent of total water and water-rail shipments. Novorossiisk water shipments included many Black Sea shipments (for example, to Crimea and Odessa) for which rail would be patently unsuitable (much longer distances would be involved by rail, at a higher cost per kilometer).
The two major routes involving water for which the issue of rail versus water might have had substance—the Vol’sk-Moscow arc and Novorossiisk-Leningrad—may be deduced from Brodskii’s table to be 1800 and 2802 kilometers in length respectively. These distances are 80 percent and 23 percent greater than the minimum direct rail distances on these links.6
In the first half of 1936, 60,000 tons went by river or river-rail from Vol’sk to Moscow, while 79,000 tons went from Novorossiisk to Leningrad by river-rail (the total of 139,000 tons was about 5 percent of Soiuztsement production in the period). These shipments accounted for almost one half of the total shipped by routes involving water for which the question of rail substitutability might have been an issue.
A comparison of costs of alternative modes on the two main supply arcs involving water is shown in Table V-1. Cost of dust loss for rail shipments is taken into account, where necessary, by adding the costs of the extra cement needed and extra shipping costs (dust loss estimated at 8 percent on the Vol’sk-Moscow rail link and 15 percent on the Novorossiisk-Leningrad rail link). River-rail shipments are all assumed to go in bags. Not enough is known of the river-rail haul to Leningrad to estimate the cost precisely; the cost in the table is based on the assumption that half the distance was by rail and half by water.
Table V-1 shows that bulk rail shipment cost 30 percent less than water shipment on the Vol’sk-Moscow arc, and 20 percent less on shipments from Novorossiisk to Leningrad. Moreover, rail shipment was certainly faster than water, and this saving is not taken into account. When cement was to go in bags in any-event, and speed was not essential, water would have been an acceptable alternative on the Vol’sk-Moscow arc. Water shipment would also have lightened congestion which is not taken into account in our rail cost estimate. On the other hand, on the Novorossiisk-Leningrad route, rail would have been preferred even when cement was shipped in bags. These comparisons show that even on these two important arcs, which accounted for about half of the divertible traffic, rail had a clearcut advantage as far as overall social costs are concerned.
2. Crosshauls and Other Inefficiencies
The next possible source of inefficiency in transport operations concerns use patterns within specific modes of transport, especially the railroads: were needlessly long hauls used? Were there wasteful crosshauls? It often happens in this industry that too much concentration on the instances of failure blinds the observer to the overall success. Thus an observed crosshaul from Vol’sk to Moscow and Moscow to Gor’kii in 1935 or, more recently, the pattern of shipping from Novorossisk to Kuibyshev and Vol’sk to Stalingrad are two examples of generalizing from a few egregious shipping errors.7 Almost any article on cement shipping and location will contain at least a reference to crosshauls if not specific examples. That Soviet thinking on the subject in the decade imputed the excess transport input to marketing inefficiency is further confirmed by the changeover to zone-of-destination pricing which took place probably in 1941. In Chapter III we saw that such a system would be more conducive to efficient transport operations than were previous pricing policies. But notwithstanding the animadversions of Soviet writers on the subject of transportation operations in the cement industry, and in spite of the faulty inferences sometimes drawn from experience in the 1930’s, the truth is that the Soviet cement industry did a good job of getting the product to market.
Notes: The following information has been used in deriving the costs of the table:
a) Cost of bags (14 rubles per ton) from Spravochnik 1935, p. 26.
b) Cost of cement (for loss en route) from Table II-3.
c) Distances based on Brodskii’s table and on minimum rail distances as calculated in the Appendix. Water-rail movement to Leningrad includes 2000 kilometers by water and 802 by rail.
d) Cost per rail kilometer (1.2 kopeks) estimated in Chapter II (see n. 32).
e) Water rates (Volga, Dnepr, and Northwest Basin) from Spravochnik 1935, pp. 284–291. Rates there given include loading and unloading charges. The rates are extrapolated as necessary for the distances here required. In the absence of precise knowledge of the Leningrad route, an estimate based on the Dnepr and Northwest Basin rates is used. Railroad loading and unloading costs (37.4 rubles per carload in bags; 27.2 rubles per carload in bulk) are from Spravochnik 1936, p. 268.
To test the proposition that transport operations were conducted efficiently in the 1930’s, we have two checks. First, careful analysis of 1935, which had a short average haul and sometimes provided the basis for Soviet criticism of the excesses of other years, shows instead that when the industry did reduce its transport utilization, it was only because of appreciable changes in demand patterns. And a linear programming solution for 1936 showing a saving of only around 7 percent confirms the proposition that transport operations were rational, given the existing production and demand configurations.
An article by Smurov and Slivitskii in a 1936 issue of Tsement shares the view of many authors that the long average haul of the early 1930’s was due to poor marketing organization. These authors write:
Analysis of the activities of the cement industry in recent years shows that the incredible increases in cement hauls depend not only on the location of the industry but also, to a lesser extent, on the organizational and managerial factors within the industry and the marketing system.
The example of 1935, especially the second half, which really marks the start of the growth of the cement industry, proves this assertion completely. In the course of that year there were really no serious changes in the geography of the cement industry. Two new plants at Chernaia Rechka (Western Siberia) and Spassk raised their output by only 100,000 tons, increasing the share in these regions by 2 percent. At the same time the average length of haul fell by more than 50 percent, from 1684 kilometers in 1934 to 807 in the second half of 1935—that is, by 877 kilometers or 52 percent. The average length of haul for 1935 as a whole is calculated to be 900 kilometers. Lack of data for the first half hinders accurate determination.8
It is not difficult to show the errors in the Smurov-Slivitskii assertion that “organizational and managerial factors within the industry and in the marketing system” accounted for the long average haul before 1935. This claim depends explicitly on near constancy of the production pattern and implicitly on constancy of the consumption pattern. However, there were very great changes in the regional pattern of consumption between 1935 and preceding years. Table V-2 shows the absolute and relative consumption of Eastern Siberia and the Far East, and also the change in consumption. These regions’ share of national consumption rose by 140 percent between 1932 and 1934, and it is significant that the national average length of haul rose by 50 percent over this period, from 1200 kilometers to 1800. Next, the share of these regions declined between 1934 and 1935 by about two thirds, as the average length of haul fell, and then, significantly, it more than doubled as the average haul went back up to 1150 kilometers.
The impact of these fluctuations on the average length of haul must be calculated in two parts: first it is necessary to calculate the reduction caused by the substitution of local for “imported” cement, and then we must determine the reduction caused by the absolute decrease in cement consumption in this region.
We start with the substitution effect. The Spassk plant produced about 60,000 tons in 1935 (second half),9 which was about 2.7 percent of national output. This replaced cement that previously had an average haul of about 11,500 kilometers,10 and permitted a reduction of 300 kilometers in the national average length of haul between 1934 and 1935.
The other reason for the reduction in the national average haul is to be found in the reduction in cement consumption in these eastern regions. Table V-2 showed the reduction to be 6.7 percentage points between 1934 and 1935. In 1934 the average haul for cement to the Far East was, as noted, 11,666 kilometers. The average haul to Eastern Siberia in 1934 is not known, but in 1933 it was 4608 kilometers, and almost two thirds of cement to this region originated at points more than 5000 kilometers away.11 The source of the data in Table V-2 does not break consumption down between Eastern Siberia and the Far East. If it is assumed that the reduction in consumption, 6.7 percentage points, was evenly distributed between these regions, and if it is conservatively assumed that the consumption forgone in Eastern Siberia would have traveled 5000 kilometers (a modest estimate), the effect of this reduction in consumption can easily be calculated to have reduced the 1935 average length of haul by about 550 kilometers from what it otherwise would have been. Adding this to the 300-kilometer reduction secured through the introduction of Spassk production gives a total decrease of 850 kilometers from the national average haul that would have been observed if 1934 production and consumption patterns had continued unchanged in 1935. In this case the 1935 average would have been 1660 kilometers and as such would have represented no significant change from the 1750-kilometer average of 1934.
Consumption of Hydraulic Cement in the Far East and Eastern Siberia, 1932–37
Source: All information from Brodskii 1938, pp. 8–9. The table reflects output only of Soiuztsement (and of Kuvasai plant in local industry), around 75–80 percent of national production.
Note: For 1935 and 1936, full-year tonnages are assumed to be twice as high as the half-year totals given in source.
In other words, the decline in average length of haul in 1935 represents almost exclusively the decline in eastern consumption and the substitution of locally produced cement for imported cement in eastern regions rather than improvement in marketing or shipping efficiency. Put another way, the great length of haul of 1933 and 1934 represents the much greater eastern consumption of those years and the presence of only small local production capacity rather than irrational transport operations.
Although our analysis does show great changes in the regional consumption patterns between earlier years and 1935, and although these changes are enough to account for the substantial reduction in average length of haul in 1935, the argument may still be valid that inefficiency and disorganization in marketing caused the average haul to be so long in all years. For example, were there crosshauls and inefficiencies west of the Urals, in Western Siberia, and in Central Asia which may have been common to earlier years as well? This question can be resolved by a linear program comparing the actual shipping pattern and the optimal pattern, given the existing structure of production and consumption.
Analysis of shipping operations for the first half of 1936 shows that use of an optimal shipping pattern for the given circumstances of production and consumption would have yielded a saving of about 7 percent over that actually used. Most of the details of this exercise are described in the appendix to this chapter. The present section considers some of the broader aspects of the analysis, their implications for interpretation, and the results of the investigation.
3. Choice of 1936
The year 1936, or rather the first half of 1936, was selected for several reasons. For it alone, of the three periods in the 1930’s for which good regional production and consumption information existed, can something be said about the modal composition of freight flows. The other origin-destination table in the 1930’s (Brodskii 1938) aggregates rail, river, and combined shipment, and for 1933 there exists only a destination table (all modes—Brodskii 1935a), while regional production is broken down elsewhere. An origin-destination table does exist for the late 1920’s (NKPS, Materialy 108), but this is too early for our needs. In 1936 the industry was producing at a high rate, so that any excess transport utilization that might be uncovered could not be attributed to frequent bottlenecks in production.
Strictly speaking, the origin-destination table is not needed. Such a table shows all the flows from the various origins to the many destinations. All that would be needed is shipments and receipts by region. The origin-destination table does have the advantage of permitting one to compare, after the program is solved, the flows in the optimal schedule and those actually employed. Knowledge of the actual flows also helps in determining where water routes were used.
Besides the 1936 origin-destination table, almost all the other information necessary to the analysis is either directly available or easily and confidently derived. A rail map, discussed in the appendix, makes possible the calculation of shortest routes existing in 1936 between production points and consumption points, obviating the need to rely on information for an earlier or later year which might differ because of construction of new routes. In 1936 the political-administrative divisions, shown in a map cited in the appendix, coincide with the regions of the production and consumption data given by Brodskii, so that we are spared the always uncertain task of making sure that geographical units of the same name are indeed the same at different points in time. Fortunately, these divisions are small enough to make more plausible than it would otherwise be the representation of consuming regions by point (see below).
4. Assumptions
Several assumptions are required for the calculation of an optimal program for cement distribution. None of them is very controversial, and where a bias is implied it worsens slightly the appearance of the actual shipping pattern. With this knowledge we can be sure that the improvement that the linear program solution elicits is an upper bound to the improvement that might have been secured if this method had actually been used to construct a shipping schedule in 1936.
a) The Optimand. Our linear program has as its objective function the minimization of ton-kilometers of railroad shipment of cement. Implicit in minimization of total ton-kilometers is the assumption that the cost per kilometer does not depend on area or distance. In view of (1) the exclusion of certain regions such as the Transcaucasus, where the cost might be expected to be higher than elsewhere, and (2) the approximate linearity of costs starting at relatively short distances (see note 32 to Chapter II), this assumption is justified.
b) Supply and Demand Constraints. In our problem, total supply (production) equals total demand (consumption). The standard simplex procedure can be used to solve this type of problem.
For the purpose of our optimization we have made minor adjustments in Brodskii’s table. Water and truck shipments and shipments to some regions (such as the Transcaucasus) were excluded and were subtracted from origin and destination totals. These are discussed in the appendix following this chapter.
c) Product Diversity. Without further information we must assume that all the hydraulic cement in the table is homogeneous. This assumption does seem to fit reality as seen through the eyes of the planners. For many purposes they apparently thought of cement as a homogeneous commodity, since they apparently planned neither the seasonal consumption pattern nor the consumption mix of the various regions. (See Chapter III, section C. 1.)
On the other hand, the seasonality of construction operations must at times have required shipping patterns that would appear to be crosshauls when data are aggregated over a period of one year. Conceivably, a northern region might ship cement south in winter only to have a southern region ship northward in the summer. In annual data these shipments might appear to be needlessly wasteful crosshauls. Our optimization does not take account of seasonal requirements of this sort, but such instances must have been very rare, since there was no extensive northern production. Also, since the data are aggregated into only a half year rather than a full year, the seasonal crosshauls must be minimal. To whatever extent that they occurred, however, the computed value of our target function should be lower than it would be if seasonal constraints were imposed, thus overstating the improvement attainable through the use of linear programming.
There must also have been instances of apparent crosshauls due to need for special products. For while the consumption mix of the various regions was not planned separately, it may be assumed that some consumers did prevail on the cement marketing organization to deliver to them special grades or types not produced in their own region. It is impossible to guess the frequency of such crosshauls. Since Portland cement still accounted for about 75 per cent of production in 1936, it may be that the crosshauls due to need for different types were insignificant. In any case, to the extent that such crosshauls did occur, comparable constraints should also be built into our linear program. Not doing so means that again we may err in overstating the potential improvement.
d) Origins and Destinations Treated as Points. The production and consumption information given by Brodskii refers to regions of consumption. The originating regions are outlined in Figure V-1, which also shows the assumed points of origin and destination used in the program. (The selection of these points is discussed in the appendix.) Of the regions in Brodskii’s table we consider ten producers and 28 consumers. Most of the producing regions may unquestionably be treated as points, because they contain only single plants or plant complexes. Where this is not true, it is believed that a gravity center fairly represents the region. As concerns consumption, the regions of the table are, for the most part, so small that it is not inappropriate to treat them as points. For example, the Ukraine and the Crimea are divided into seven regions, as is the industrial center around Moscow. Where the regions are very large—Western Siberia, for example—consumption very probably did take place predominantly at single centers (the area around Novosibirsk in this case). Specific cases are discussed in the appendix, where a check on the reasonableness of the method is also discussed. This check involves the calculation of the Hypothetical Minimum Actual Average Length of Haul (HMA) of cement entering each region. This is the haul that would have resulted if the actual interregional flows had gone over the shortest route between the two terminal cities that are used to represent the regions. As is shown in the Appendix to this chapter, for almost all of the regions the deviations of the HMA from the actually observed length of haul are small. For the nation as a whole, the actual average length of haul is 2.1 percent longer than the HMA in the period in question, which indicates that the representation of regions by points is a reasonable approximation to the actual distribution of consumption and production within regions.
However, the deviation cited, 2 percent, is another source of overestimation of the possible gain to be achieved through linear programming. In other words, if we compare the optimal pattern, which makes use of the routes based on the point assumption, to the actual state of affairs in which points did not quite precisely represent the intraregional distribution of cement consumption, we will be unfairly attributing the difference wholly to the optimization procedure. Accordingly, the main comparison that should be made involves the ton-kilometer total implied by the actual interregional flows over the minimum rail distances, and the linear program solution based on those same distances and the optimal patterns of interregional flows. This, along with other measures, is shown in Table V-3.
Although consuming and producing regions are represented in our problem as points, in a region where both production and consumption occur, we do not necessarily represent both activities by the same point. For example, the distance for intraregional shipments in the Azov-Black Sea region is taken as 413 kilometers, the rail distance from Novorossiisk to Rostov-on-Don, the city used as the consumption point in this region.
Again, though Stalino is used as the point of origin for Ukrainian cement (it is about 40 kilometers from the large production complex at Amvrosievka) and also as the consuming point for the Donets oblast, it was thought proper to use a distance of 128 kilometers as the cost of getting Ukrainian cement to the Donets oblast, because of the rather even dispersion of industry in that oblast. This procedure is justified by the analysis of the HMA in the appendix.
5. The Algorithm
The standard simplex method was used to solve the linear program. Since the theory and application of the simplex method are discussed in numerous works, there is no need here to do more than set down the model used. This may be quickly done with the following notation.
| ai | = | the amount of cement produced in region i (i equals 1, 2 . . . . . . . . . . . . 10). |
| bj | = | the amount of cement consumed in region j (j equals 1, 2 . . . . . . . . . . . . 28). |
| xij | = | the amount of cement shipped from region i to region j. |
| Cij | = | the distance in kilometers over the shortest broad gauge rail route from region i to region j (point i to point j). |
The primal linear programming problem can be stated as:
There will be ten equations (1) and 28 equations (2). The negative sign in equation 1 indicates shipments from production at point i. The equations may be written out in more detail as follows:
6. The Results
Analysis of the savings generated through the linear program solution are summarized in Table V-3. (Other information, including comparisons of optimal and actual flow patterns, is presented in the appendix.) In the first part of the table are shown the actual, optimal, and HMA ton-mileage and the average hauls. Ten origins and 28 destinations were considered. The tonnage represented 88 percent of all rail shipments in Brodskii’s table. Through the linear program it was possible to reduce the expenditure of transport by 7.3 percent. This is the relative amount by which the value of the minimand falls short of the HMA ton-mileage, which, we saw above, was the appropriate sum to compare.
These savings relate only to the cement marketed by Soiuz-stromsbyt by the modes cited in the 28 regions. Several adjustments must be made to get an estimate for the industry as a whole. For example, shipments by local industry should be included. Also production in the Transcaucasus, which was a large consumer, and the output of Spassk in the Far East should be included. (Far East and Transcaucasus production was not programmed, since it was obvious that the optimal program would dictate its use in the producing regions, and some computational work could be saved by omitting it. Imports to the Far East were programmed, however.) These three adjustments can be made in the following way:
Local industry shipped 260,000 tons, and assuming an average length of haul of 75 kilometers, we have 19.5 million ton-kilometers. Far East production was 58,800 tons at Spassk, all of which is assumed to have gone to the Vladivostok area, about 200 kilometers away. It is unlikely that any of this output went to Khabarovsk, the other Far Eastern consuming center, since it is a point short of Spassk and its needs would have been fully satisfied by import. Transcaucasus output was 165,000 tons, and the actual average haul was 460 kilometers. This probably represented an efficient supply pattern, because of the lack of alternative shipping routes in the region.
After the foregoing adjustment, the optimal program reflects the disposition of 2,033,100 tons and yields a saving in transport cost of 6.8 percent. We do know that this total excludes several components of actual total output: (1) 161,000 tons marketed by Soiuzstromsbyt but not considered in the original data supplied by Brodskii; (2) the following amounts in the table: 44,400 tons, which quite correctly went to Odessa and Crimea from Novorossiisk by boat and 11,400 tons for the Kirgiz and Tadzhik SSR’s, which republics were excluded because of the confounding peculiarities of their shapes, 218,000 tons going by truck over relatively short distances; and (3) 235,300 tons which went by water or joint water-rail shipment in the actual plan. Our earlier analysis suggested that water shipment actually cost more than rail movement, unless it was absolutely essential to have bagged cement, in which case water shipment could provide a lower social cost on some routes, while not on others. The net overexpenditure on water shipments, therefore, was probably on the order of 8 percent. All these considerations suggest a total transportation overexpenditure of 7 percent.
Comparison of Optimal and Actual Rail Utilization in the First Half of 1936
Adjusting for these traffic components brings the total of cement shipments to nearly 2.7 million tons, which must be very close to the actual output for the first half of 1936.12 The savings in cost of transport which our optimal distribution pattern suggests were possible would therefore be 7 percent of the transport cost for the total output. This result, moreover, is very stable, as is shown in the appendix to this chapter.
This analysis suggests that the cement distribution pattern in the Soviet Union was not inefficient in any extreme sense. Part of the small gain apparently attainable was undoubtedly due to the need for special grades, a requirement to which we did not constrain our linear program solution. A very small part may have been due to seasonality of demand, also not a constraint in the linear program. If these constraints had been imposed, the saving would have been less, perhaps only 5 percent. This result is especially surprising when we recall such criticisms as that of Smurov and Slivitskii, who laid most of the blame for high transport costs on inefficient marketing. The subsequent change of pricing policy to the zone-of-destination basis also implies lack of confidence in marketing managers. Finally, when the result is compared with linear programming analyses in other countries, the Soviet performance compares very favorably. For example, in his linear programming study of efficiency in the American coal industry, James Henderson found that the total actual transport cost per ton ranged between 12.8 percent and 25.4 percent higher than the average cost under the optimal delivery pattern in 1947, 1949, and 1951. Henderson was minimizing total production and transport costs, and, since he found that actual production costs also exceeded those of the optimal solution by around 5 percent, we can see that if he had been optimizing on transport costs alone, the saving would have been still greater.13 A. Ghosh in studying the Indian cement industry concluded that linear programming would have produced a rail transport saving of 6–13 percent in a four-year period during the 1950’s.14
B. INEFFICIENCY DUE TO GRADE MULTIPLICITY
As we saw in the review of cement industry standards in Chapter III, there were 17 main grade/types of hydraulic cement after 1935. The multiplicity of grades in the industry never came under critical scrutiny in the prewar period, and even today it is never analyzed from the viewpoint of the resulting excess utilization of transportation. But the greatest potential saving existed precisely in this area.
The multiplicity of grades contrasts sharply with American practice, where all Portland cement must meet the same minimum grade (certain special-purpose cements have higher minima). As we noted, the American approach also characterized the cement industry in other nations, such as Brazil, even in the 1930’s. If this approach had been followed in the Soviet Union, savings would have resulted in both transportation and production.
For the 1930’s, there is little discussion in the Soviet press about the functional relation of grade and production cost. Some light can be shed on the matter by the conversion coefficients referred to earlier (see Chapter III) which have appeared since the war. If we convert Portland cement by the coefficients and compare the standardized strength ratios to the cost ratios, we find that strength increased faster than cost. For example, the three grades produced prior to 1936 were 0,00, and 000, with nominal strengths of 160, 275, and 420 kilograms per square centimeter. If we convert a ton of each into grade 400 by the appropriate conversion coefficient, we find them equivalent respectively to 0.5 ton, 0.78 ton, and 1.04 tons of grade 400. The standardized strength ratios relating strength of grade 0 to the higher two grades, therefore, are .64 and .48. The cost ratios, on the other hand, are .88 and .70.15 This means that lower-grade cements cost about 30 percent more than higher grades when their concrete-making strength is considered.
The same is true for the grades introduced in 1936. For example, the ratios of the standardized strength of grade 200 to that of grades 300, 400, and 500 are .76, .63, and .54, while the cost ratios are .78, .68, and .57. Again, therefore, the cost per unit of concrete strength declines as the cement grade rises, although the discrepancy is much less serious than before 1936. In both of these comparisons we are assuming that the relative prices for the different grades accurately reflect differentials in production costs for the different grades, so that permitting the industry to produce lower grades meant a real waste of resources. It will be recalled that the analysis of Chapter III strongly suggested that prices did reflect costs.
For the present period there is also good evidence of the production cost saving deriving from the production of higher grade cements. In a recent article, A. Evdokimenko of the building materials administration of the Moscow Sovnarkhoz gives coefficients showing that the production cost (sebestoimost’) of grade 700 is only about one sixth more than grade 400, though its effectiveness is almost 50 percent greater. For grade 500 the figures are 5 percent and 17 percent respectively.16 In view of this evidence for both the recent past and the prewar industry, it is safe to conclude that production costs per unit of concrete-making potential decrease relative to the index of effectiveness of cement as higher grades are produced. In this case, it would have been cheaper to produce a smaller tonnage of higher grade cement that would have done the same job. And since a smaller tonnage would have had to be shipped, a smaller transport cost also would have resulted.
The magnitudes of the savings attainable by adoption of the grade-400 specification may be easily calculated as 5.2 percent in production costs and 22.5 percent in transport costs. Since transport input accounted for half of total costs, the total implied cost reduction is 14 percent of delivered cement costs. These calculations imply overexpenditures of 5.5 percent, 28 percent, and 17 percent in terms of costs actually incurred.
The saving in cost of production would have been generated through production of grade 400 portland in place of all other cements. As Table V-4 shows, only 3,214,000 tons of this grade portland would have been required in place of the 3,958,000 tons actually produced, thus affording a cost saving of 4.1 percent. In addition, if we assume that the 1,445,300 tons of portland blends17 had the same nominal grade strength distribution as portland, this tonnage would have been equivalent to 978,000 tons of grade 400 portland, after we adjust for the weaker strength of these cements. This smaller tonnage would have permitted a 7.5 percent production cost saving, and the total reduction in production costs would have amounted to 5.2 percent.
By having to transport only 4.2 million tons in place of 5.4 million, a transport cost reduction of 22.5 percent is implied if we assume that the lower tonnage would have had the same shipping patterns as were observed for the larger volume. In fact, however, the ton-mileage would have fallen disproportionately more because the quality improvement would have permitted the largest tonnage reductions on the longest hauls; portland-slag accounted for a large proportion of Ukrainian and Western Siberian production, and these were major supply regions to the Far East, with hauls of 10,000 and 5,600 kilometers respectively.
Average Strength of Portland Cement Produced in 1937
Source: Production based on total tonnage given in Promyshlennost’ 1964 and percentage distribution for 1937 given in E. S. Shatalov, “Zadachi tsementnoi promyshlennosti,” Ts (1938), No. 4, p. 12. The percentage for grade 200 is a residual.
In addition, with the more valuable grade 400, the use of bags on, perhaps, half of all shipments would have reduced dust loss sufficiently to justify their use and produce a further net gain. Besides this, a single grade would have greatly facilitated quality control and, by promoting builders’ confidence in the product, eliminated or minimized precautionary overinput of cement at construction sites.
Adoption of grade 500 as the standard would have yielded still greater savings. Applying the same kind of calculation as was just performed for grade 400 shows a production cost saving of 11 percent, a transport cost reduction of 31 percent, and a total cost reduction of 21 percent. Again, this understates the economy somewhat, since with this costlier cement the savings in dust loss which could have been secured through the use of bags would have produced a net saving on all shipments.
There is no technological reason why these higher grades could not have been produced. Higher strengths require finer grinding, longer roasting, and abstention from adulteration of portland (that is, the addition of 15 percent pozzolanic materials or 10 percent inert “micro-additives”). These conditions could have been brought about through imposition of a single strength standard to replace a standard that encouraged heterogeneity of output and through adoption of a policy that promoted quality instead of quantity.
This chapter has explored many possible sources of shortrun spatial inefficiency in the cement industry. Our conclusions run counter to what Soviet discussion might have led us to expect. In our judgment the interregional pattern of connecting suppliers and consumers appears to have departed only slightly from an optimum. Interregional rail movements were not characterized by crosshauls or similar wasteful practices despite frequent assertions to the contrary by Soviet authors. Nor were shipping operations irrational with regard to their modal composition. The total moving by water or water-rail routes involved many shipments for which water had unequivocal advantages over rail and others about which the cost relationship is less clear but which may have been justified in special conditions. But there is no reason to think that more extensive water shipment would have been economically justified.
The analysis shows that the primary source of excess transportation inputs in the short run was product heterogeneity. Our calculations showed that with a single higher-strength standard, production costs would have been about 5 per cent lower, and transport savings would have been much lower—22.5 per cent if Portland 400 specifications had been mandatory for the industry and much more if grade 500 had been set as the minimum. With higher grades it would also have been advantageous to do more packaging, which, through reduction of dust loss, would have permitted even further savings in transport costs.
LINEAR PROGRAM DATA AND SOLUTION
This appendix is concerned with procedures and principles underlying the linear program analysis of Chapter V. Three matters warrant attention: 1) the nature and coverage of product and flow statistics used; 2) the selection and calculation of routes; and 3) regional coverage.
1. The Nature and Coverage of Product and Flow Statistics
The basic data were first presented by Brodskii (1937a). The origin-destination table there shown includes information for the first half of 1936. He allocates to 33 regions a total of 2,265,000 tons of freight terminations out of a total of 2,427,400 tons originated—that is, detailed information on destination is given for over 93 percent of the total output of Soiuzstromsbyt, the main cement trust, and the local industry Kuvasai plant in Central Asia. Output of these organizations in turn comprised 90 percent of the national total. Only 7 percent of the Soiuzstromsbyt output and the local cement output of Leningrad, Moscow, and a few other places could not be taken into account in our cost minimization.
Table A-1 shows the basic data used for the linear program as well as characteristics of the solution. The main body of the table shows the optimal and actual flows between regions, total regional originations, and total terminations. Only rail shipments are included in the actual data-truck, water, or combined water-rail movements being assumed to be best shipped by the mode in question.
2. The Selection and Calculation of Routes
A 1937 communications map published by the NKPS (Skhema zheleznodorozhnykh i vodnykh putei soobshcheniia SSSR) served as the basis for calculating railroad distances between production points and consumption points shown in Table A-1. These distances are tabulated in Table A-2. In each case the minimum broad-gauge railroad distance was used. This was found as the sum of the distances given for intervals on the shortest route. The search for the minimum involved, for some links, the calculations of as many as four route lengths. All distances were checked and rechecked so that the distances used in the linear program are believed free of error. The map itself is almost free of error. Two errors that were found and corrected were the statement of 38 kilometers as the distance from Penza to Ruzaevka (adjusted to 108 kilometers in our cost-matrix calculation) and an extra 440 kilometers on the Semipalatinsk-Novosibirsk stretch (eliminated). There were surprisingly few other problems. The most serious was concerned with the question whether a railroad bridge had been built across the Volga at Gor’kii by 1936. The assumed absence (none shows on the map and no literary source could confirm the existence of a bridge) meant that certain minimum routes—for example, Krichev-Gor’kii—were about 100 kilometers longer than they would have been with a bridge or if ferry service had been introduced into the program. On the basis of internal evidence and analysis to be described shortly, it is safe to say that this did not affect the results.
Sources: Actual data from Brodskii, “Sokratit’ radius dostavki tsementa,” Ts (1937). No. 5–6. Optimal flows from linear program solution. Hypothetical Minimum Average hauls based on actual flows and minimum distances of Table A-2.
The minimum distances were calculated between the assumed points of production and consumption for each of the political-administrative areas used by Brodskii for his original table. It was usually not difficult to determine these points. Of the ten originating regions used in our calculations and listed in Tables A-1 through A-3, four regions actually had only one plant each, so that the point of origin was easily fixed (Briansk in Western oblast, Podgornoe in Voronezh, Krichev in Belorussian SSSR, and Kuvasai in Uzbek SSR). Two regions (Saratov oblast and Azov-Black Sea krai) had production at several plants concentrated at single points (Vol’sk, Novorossiisk). Plants in Moscow oblast were concentrated not at a single locale but within a relatively small triangle. Similarly, Ukrainian production had a very heavy concentration in the Amvrosievka area in the Donbass. To give expression to the smaller production units at Khar’kov, Kramatorsk, and Dnepropetrovsk, Stalino was used as the point of origin as an approximation to the center of gravity of these producing areas. In Western Siberia there were two plants, one about 20 kilometers south of Novosibirsk at Chernaia Rechka and the other at Iashkino, about 160 kilometers to the east-northeast. Novosibirsk itself was used as the terminal point in Western Siberia for shipments from outside regions.
Note that in addition to interregional distances, Table A-2 also shows estimated average lengths of haul for shipments between producers and consumers within regions. Most of these are between a plant at a known location and the center of consumption assumed for the region. But there are some special cases. Distances in Ukraine were traced from Stalino to each oblast, including Donets oblast, whose consumption point with respect to other regions was Stalino. To allow for the consumption of cement in cities other than Stalino, an intraregional distance of 128 kilometers was established for Donets oblast even though the production point and the consumption point used to relate this oblast to the rest of the nation were identical. In similar manner, 75 kilometers was used as the intraregional distance for the Moscow oblast even though Moscow was used as the point of origin and destination for this oblast for its relations with all other regions. This distance was predicated on the fact that the plants in this oblast were actually located outside Moscow and some of the consumption took place outside the city, and on the obvious assumption that shorter movements would have gone by truck. In estimating the intraregional distances, I was aided by the implications of intratabular consistency suggested in Brodskii’s original presentation.
The Ural region was a little more difficult because the three plants there were more dispersed than elsewhere. The three formed an isosceles triangle oriented southwest by northeast, with Katav-Ivanovsk, the southern vertex, about 350 kilometers from the other plants at Neviansk and Sukhoi Log. Sverdlovsk, 80 kilometers equidistant from Neviansk and Sukhoi Log, was used as the producing and consuming point for this region’s relations with the rest of the economy. However, an intraregional coefficient of 275 kilometers was used to reflect the great expanse of territory in Western Siberia and the widely dispersed population centers there (Omsk, Tomsk, Barnaul, Kemerovo, Novosibirsk). As in the case of Moscow and Donets oblasts, estimates of the intraregional distances were facilitated by evidence in Brodskii’s table.
A method was devised to check the reasonableness of our general point assumption as well as the specific selections. Table A-1 shows the amounts shipped by rail over links actually employed as well as the amounts in the optimal solution. In the right-hand section of Table A-1 is shown the actual average length of rail haul for each region of destination. Immediately to the right of this column is the Hypothetical Minimum Actual average length of haul (HMA). This is the average length of haul that would have resulted if the region had received the amounts that actually did come from the actual regions of origin but over the minimum rail distances calculated for the cost matrix. The ratio of HMA to the actual average length of haul is then an indication of the approximation of the minimum possible distance to the route actually used. It also is a reflection of the accuracy of the specific assumptions regarding particular points of production and consumption.
The ratios tend to be very close to 1.0; only one ratio falls below .902 (Leningrad with a ratio of .76), while the highest reached is 1.10 (the Kazakh SSSR). A ratio greater than unity tends to indicate that the assumption of point consumption is less justified than when it is unity. In Kazakh SSSR, for example, Chimkent is taken as the consuming point, almost at the southern apex of the Republic. This neglects the consumption of centers to the north such as Semipalatinsk or Aktiubinsk. But, unfortunately, terminations for Kazakh SSSR are given for the republic as a whole rather than for smaller regions, and there is no other way to handle them unless we wish to assume that import to the region terminated at the population center closest to the originating region. But this seems arbitrary.
The other large positive deviation of the ratio is in the Western oblast, where a ratio of 1.09 was observed, the actual average length of haul to this region being 272 kilometers. Smolensk was used as the consumption center here, but evidently consumption was more widespread, taking place closer to Briansk as well as elsewhere not reflected in the haul to Smolensk. The result is that the minimum trip to Smolensk overstates by about 9 percent the total tonkilometers involved in the distribution of cement in the Western oblast. The Gor’kii oblast deviation (5.6 percent) probably reflects our assumption of no bridge at Gor’kii and the resultant circuitous path thereto; but if a ferry service with transloading was used to achieve the lower actual average haul, this would compensate, at least in part, for the apparent lower cost of the actual as compared with the HMA. Most of the other deviations are small.
The negative deviations may also reflect less concentrated consumption, but it is more likely that they represent use of routes slightly less direct than the minima that we have calculated. In any event they are close enough to the minima to reassure us that errors were not made in our calculations either by oversight of typographical errors on the map or for other cause. The one extreme ratio—.76 of Leningrad oblast—is difficult to understand. Why should the average length of rail haul, calculated on the basis of the physical flows actually realized and the minimum distances calculated from the map, fall 24 percent below the actual? Since Brodskii’s table states “Leningrad oblast” quite clearly, and since elsewhere in his tables Brodskii refers to Archangel or Northern oblast and Karelian oblast, and since in 1936 Leningrad oblast was quite distinct from the aforementioned neighbors, there is little likelihood that the other regions were inadvertently combined with Leningrad oblast terminations. One possibility is that some cement destined for Murmansk was somehow confused in earlier stages of the statistical compilation so that the additional journey from Leningrad uzel to the Karelian border was reflected in the large actual average rail haul of 1977 kilometers.
In the calculation of the optimal program, the effect of the last-named factor was slight, however. The basis of the optimal solution is the same whether the distances used in the cost matrix are those of Table A-2 or are increased by enough to reflect the discrepancy between the actual average length of haul and HMA. If the problem is rerun, with all the distances to Leningrad set 475 kilometers longer than those shown in Table A-2 (so as to permit equality of HMA and the actual average haul), there is no change in the optimal solution, except that the value of the optimand would be increased by 475 × 42,900 ton-kilometers, the added distance multiplied by the amount shipped into Leningrad.
The results of a sensitivity analysis, shown in Table A-3, indicate the general stability of the solution. The table shows the ranges within which the cost coefficients in the optimal basis of each of the problems may be varied.
The ranges for each basis vector show the minimum and maximum points within which the particular cost coefficient may be varied without change of basis. At the extreme points of the cost range, the vector in question may leave the basis or it may remain in the basis while another adjustment is made; the program printout designates the incoming vectors at the two extremes.
The cost ranges are very wide. Of the 74 possible cost range limits (two for each of the 37 basic vectors), only 17 differ by less than 5 percent from the assumed cost coefficient. Thus, even if most of our assumed consumption points and the associated distances which we have used as cost coefficients misstated the true distances by 5 percent or more, the solution basis would remain optimal. However, since some of the narrow cost ranges relate to major consuming regions, such as Moscow oblast or Donets oblast in Ukraine, one naturally wonders what would happen if the true cost did lie beyond the cost range within which our solution remains stable. The basic high-intensity activities which involve these regions and have narrow cost ranges are Donets-Moscow (251,750 tons) and Novorossiisk-Donets oblast (75,700 tons). What would happen to these two flows if the true cost coefficient lay beyond the limits shown in Table A-3? Although we have not here tabulated the details of the computer analysis which are necessary to determine the consequences of all such eventualities, it will be useful to consider these two particular examples. The discussion may be more easily followed with the help of Table A-1.
Cost Ranges for Linear Program Solution
Entries show minimum and maximum between which distances may be varied without requiring a change in basis from that of optimal solution. Figures in parentheses show these extremes as a percentage of the shipping distance in optimal solution. Dash indicates unbounded range.
To take first the Donets-Moscow activity; at the lower end of the cost range (1113 kilometers), Podgornoe-Voronezh enters the basis, and at the upper end (1120 kilometers) Novorossiisk-Gor’kii comes in. In the first case a small reduction in total transport cost can be secured by transferring 1400 tons of the Podgornoe-Moscow shipment to Voronezh and increasing the volume of the Donets-Moscow flow by 1400 tons. At the same time, the shipment from Novorossiisk to Voronezh would fall by 1400 tons, which Novorossiisk could now ship to Donets oblast. At the upper limit of the cost range an advantage can be secured by shipping 1400 tons from Novorossiisk to Gor’kii and relieving Podgornoe of the obligation to ship Gor’kii this amount. Podgornoe now has 1400 tons more at its disposal, which it can ship to Moscow, relieving Donets oblast of 1400 tons of its obligation to Moscow. Finally, the 1400 tons with which the cycle started when Novorossiisk was scheduled to ship to Gor’kii can be replaced by eliminating 1400 tons of the shipment from Novorossiisk to Donets oblast, the latter not now needing it because of the change in its own schedule to Moscow. The change in the solution value would be insignificant.
A similar phenomenon can be observed for the Novorossiisk-Donets flow. At the lower limit (632 kilometers), precisely the same thing happens that we observed at the lower limit of the Donets-Moscow activity; Podgornoe-Voronezh enters the basis. Again, not the whole of the amount formerly shipped from Novorossiisk to Voronezh is replaced by shipment from Podgornoe, but only 1400 tons. This is the amount formerly originating and terminating within the Donets oblast. Now Novorossiisk can increase its shipment to Donets oblast by 1400 tons. At the upper end of the Novorossiisk-Donets cost range (639 kilometers), Novorossiisk-Gor’kii enters the basis (just as it did at the upper end of the Donets-Moscow activity cost range). It is easy to see what will happen. Novorossiisk is rescheduled to ship to Gor’kii the 1400 tons that it formerly shipped to Donets oblast, and Podgornoe now ships this amount to Donets oblast, at the same time reducing its own shipment to Gor’kii by 1400 tons. Again we see that the important high-intensity activity does not become zero simply because the basis is changed—only its level changes, and that just slightly. In the two cases analyzed in detail the greatest change involved only 2 percent of tonnage shipped on the route in question. The other basis changes that would be required at the limits of the narrow cost ranges also are of minor importance, and the effects on the solution value would be minimal.
One other indication of the stability of the solution is measured by the values that would have to be assumed by the cost coefficients not in the basis in order for the corresponding flows to be brought into the solution. For the very great majority of activities these differences are large, indicating that a large drop in cost (distance) would have to be realized to bring these activities into the basis. This decrease would have to be greater than 100 kilometers for 209 of the 243 excluded activities.
3. Regional Coverage
Brodskii’s table included 33 destination regions and 12 origin regions. Our linear program included 28 and 10, respectively. The two excluded origins were the Transcaucasus and the Far East, where cement was produced at Spassk. The former was excluded because transport costs in a mountainous region like that are higher than those elsewhere, which means that its transport input, expressed in ton-kilometers, would not be directly comparable with ton-kilometers registered elsewhere. Moreover, all shipments originating in the Transcaucasus also terminate within the region and, since this region is a “vertex” geographically speaking, it was obvious that it would serve itself in the optimal solution. Far East originations were left out because this region was also geographically extreme, and its role as supplier exclusively to the Far East could easily be anticipated. Its output (58,800 tons in Brodskii’s table) was subtracted from total Far East terminations in Brodskii’s (133,800 tons) to arrive at the demand constraint (75,000 tons) for that region. Nothing at all is affected thereby.
The five destination regions excluded were omitted because of peculiar geographical characteristics. First of all, the Transcaucasus was omitted as a destination region, as already explained. The Odessa and Crimea oblasts were omitted because they receive all their supply from Novorossiisk by water, and this is efficient. The other two omitted regions were Kirgiz and Tadkzik SSR’s. It was thought best to exclude these republics because of their peculiar shapes, which caused a serious divergence between HMA and the actual average (ratios of 1,40 and 1.17 respectively). In each of these republics there were two or more major centers, one of which was supplied by Kuvasai and the other through import from the west. While these republics could easily have been partitioned and two extra constraints introduced for the consumption sector, nothing would have been gained by doing so, the computer solution simply restating what had been previously deduced.
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