I. INVENTORY BEHAVIORThomas M. Stanback, Jr.
II. INVENTORY CONTROL THEORYT. M. Whitin
Inventories account for a relatively small portion of a nation’s wealth and long term capital formation: they constituted only 8 per cent of U.S. tangible assets in 1958 and 6 per cent of tangible asset accumulation from 1946 to 1958. Yet fluctuations in nonfarm business inventories, which make up roughly three-fourths of total inventories, are an important source of cyclical instability.
The explanation of this paradox (that nonfarm inventories which are relatively unimportant as a part of national wealth and long term wealth- accumulation are nevertheless of strategic importance during business cycles) lies in the fact that firms tend in the course of the business cycle to alter sharply their short term rates of inventory accumulation. Accumulation (investment) is a source of demand for the factors of production, and variations in the rate of accumulation or shifts from accumulation to reduction (disinvestment) are a source of variation in the demand for the factors of production. It is for this reason that attention often focuses on movements in inventory investment rather than on movements in inventories themselves. In the course of the business cycle rates of accumulation change rapidly and cyclically, typically moving upward to a peak of investment in late expansion and downward to a trough of disinvestment in late contraction.
Functions performed by inventories
Understanding of the nature of the forces which influence inventory investment must begin with a consideration of the reasons why firms hold stocks. An elaborate literature has dealt with this subject [seeInventories, article onInventory Control Theory], Mack (1966) has suggested that the functions performed by stocks may be described in a general way by two statements: (1)Stocks support the time required for processes (economic transformation) to be performed. (2) Stocks “buy efficiency” by substituting the lesser cost of carrying stocks for a greater cost of coping with a particular management problem in some other way. With regard to the first statement, not only are certain goods-in-process necessary if production is to take place, but some minimum of purchased materials are needed to cover routine, time-consuming operations related to receipt and warehousing, and some finished stocks must support warehousing and shipping activities. Similar reasons exist for holding quantities of distributors’ stocks in trade. All such stocks may be regarded as “sales linked,” and management will attempt to vary them with, though not necessarily in proportion to, the level of activity of the firm.
On the other hand, stocks can buy efficiency by making possible economies resulting from larger production or purchase lots, by providing insurance against being “caught short” as a result of unpredictable fluctuations in demand, by smoothing production in the face of predictable fluctuations in sales, by taking advantage of anticipated changes in purchasing conditions, and simply by providing freedom of action under conditions of uncertainty.
At the same time, holding stocks involves costs of storage, insurance, and financing, as well as the risk of obsolescence. The management of inventories is therefore a process of balancing gains from holding additional stocks against their marginal cost.
Such observations indicate that behavior of aggregate stocks will reflect a complex of somewhat dis-similar forces. To the extent that stocks are linked to sales or output they will tend to rise and fall with activity; to the extent that they are held against fluctuations they may move in an inverted fashion relative to sales or output; to the extent that inventory objectives are affected by other factors, such as purchasing conditions, still other patterns may occur. Finally, it should be noted that anticipations may be incorrect and that actual inventory behavior may reflect errors of estimation as well.
Explanation of observed cyclical patterns of inventory behavior must involve, therefore, explanations of why in the light of such a variety of influences there are more or less systematic movements in various types of stocks and in their rates of change.
Explanations of inventory behavior
Inventory behavior has long been the concern of business cycle theorists. Prominent among those who dealt with the topic in an earlier day are Hawtrey, Mitchell, Keynes, J. M. Clark, and Kuznets. Clark’s work (1917) is of special interest since he first made explicit the implications of any tendency for the stock of inventories to be linked to the volume of sales or output (and inventory investment to the rate of change in the volume of sales or output) and noted how this link would tend to increase the amplitude of business fluctuations and contribute to reversals (i.e., the acceleration principle).
More recent research has tended to be of three general types. The first is largely theoretical and is represented principally by the work of Metzler (1941). In the second, which includes the studies of Abramovitz (1950), Mack (1966), and Stanback (1962), the approach relies heavily upon the analysis of time series representing inventories, sales orders, output, and related activities, but does not impose upon the investigation the constraints inherent in a formal model. The third approach emphasizes the use of econometric models to explore the relationship between inventory movements and various hypothesized causal forces. Among the large number of economists who have done work along these lines are Darling (1961), Holt (see Holt & Modigliani 1961), Klein (see Klein & Popkin 1961), Lovell (see 1961; 1964), Mills (see 1954; 1957), Modigliani (see Modigliani & Sauerlender 1955), and Terleckyj (1960). Some builders of macro-econometric models have included equations designed to forecast levels of inventory investment.
Metzler, drawing upon earlier work of Lundberg (1937), traced out, under a number of assumptions, the results that would occur when businessmen attempt to bring inventories into some desired relationships with sales and thereby set off secondary changes in demand that preclude the desired equilibrium levels of stocks and that result in still further effects on inventory objectives and demand. In his models, desired levels of stocks are related to expected sales (the acceleration principle), and there is income feedback via the consumption function. Consumption expenditures are not lagged but production is lagged (i.e., is based upon sales of the previous period plus planned inventory investment, the amount necessary to bring inventories to desired levels). Actual inventory investment in any period is the sum of planned inventory investment plus the unplanned change that is due to actual sales turning out differently from anticipated sales.
A major contribution of the second type of research was to determine the typical patterns of timing, to show the relative importance of movements in manufacturers’ inventories during interwar business cycles, and to demonstrate how and why it is that inventory investment plays a more important role in short business cycle phases than in long business cycle phases (Abramovitz 1950).
Work done with postwar data (Stanback 1962) has disclosed a decline in the lag of stocks to sales and a reduction of tendencies toward inverted behavior. In addition, attention has been called to the role of market conditions and unfilled-orders positions in influencing inventory objectives for purchased materials. Recent work (Mack 1966) features still further the role of unfilled orders and finds it important to consider the backlog of orders placed by business enterprises in the same frame of reference as their materials stocks, i.e., to regard stocks on hand and on order as the primary variable to be explained. Variations in the functions that stocks serve are apparent in the different behavior of two important inventory time series: department store stocks and durable-goods purchased-materials stocks.
However, most investigations since the war have taken the form of econometric studies. Some have treated nonfarm inventory investment in the aggregate, others have investigated manufacturers’ total inventories or inventories held at different stages of fabrication.
A common property of the models tested in these studies has been a reliance upon the working of the acceleration principle in some form. In some instances a lagged relationship between changes in inventories and in output is assumed; in others the assumption is that the firm attempts only a partial adjustment toward some desired (equilibrium) level of stocks in a given period. In endeavoring to esti-mate the volume of stocks that firms desire to hold, a variety of influences have been examined, including credit restraint and price anticipations. In general, credit restraint and interest rates do not appear to have played a significant role, although findings have been mixed. Efforts to determine the influence of price anticipations have been inconclusive. The most useful variable by far has been unfilled orders; this variable has been found to be significant in every study in which it has been included. In dealing with the problem of determining firms’ planned sales, some investigators have attempted to use estimates based on actual business sales anticipations, although without much success. Until recently, however, such estimates have demonstrated a high degree of inaccuracy (Lovell 1966).
These studies have left many questions unanswered. Criticism has been voiced both in terms of deficiencies of underlying theory and ambiguity of the measured coefficients of relationship. One investigator (Lovell 1964) has stated that “part of the difficulty may arise from certain weaknesses in the accelerator principle. The model assumes that the impact of erroneous anticipations falls either upon output or inventory; making no allowance for the possibility that adjustments in either price or advertising expenditures may shoulder part of the burden.” Further, the assumption of profit maximization permits a wide range of choice of hypotheses about modes of behavior. As for ambiguity of findings, it has been suggested (Mack 1964) that investigations based on accelerator-type models do not support the notion that the volume of sales is the primary determinant of inventory investment, since the importance of this variable is rivaled by unfilled orders. Moreover, a variety of coefficients linking inventories to sales have been found, and reaction coefficients indicated by solutions to the estimating equations have been unrealistically long.
Importance in business cycles
During post-World War II U.S. business cycles, changes in non-farm inventory investment (measured as the difference between the amount of accumulation in nonfarm inventories in the calendar quarter of the business cycle peak and that of the trough) have accounted for as much as 176 per cent of total decline in gross national product and never less than 52 per cent of the decline during any recession. These movements have been the single most important source of weakness during recessions.
Changes in inventory investment have played a lesser role during U.S. business cycle expansions, accounting for between 11 and 19 per cent of the increase in gross national product during expansions. Early in an expansion, however, their influence is strong. During the first year of every expansion since 1949 increases in nonfarm inventory investment have accounted for at least 26 per cent of the increase in gross national product.
It is difficult to determine whether or not there is a long term tendency for inventories to play a more important role in business cycles. The data available, which are annual for the prewar years and which go back no earlier than 1919, indicate that changes in inventory investment played a major role in the mild recessions of the 1920s and in the brief but sharp recession of 1937–1938, just as they did in the recent mild recessions. During the prolonged 1929–1932 contraction, when many factors contributed to weakness, their role was relatively small.
Inventory investment changes have been less important during postwar than prewar expansions, but this appears to be due largely to the greater length of expansion phases (Abramovitz 1950, p. 484) coupled with the fact that peaks in inventory investment have occurred earlier in expansion, with the result that change in investment levels when measured from business cycle trough to peak understates the full extent of cyclical rise.
There are factors making for both relatively less and relatively more cyclical sensitivity of inventory investment in recent years. Inventories are smaller today relative to output or sales. During the period 1947-1954 manufacturers’ inventory-to-output ratios were about three-fourths of average 1920–1929 levels, and there is evidence of at least comparable declines in distributors’ stock-to-sales ratios. Since 1954 declines in stocks to sales or output ratios have continued, although in more recent years such declines have occurred principally in manufacturing. This reduction in size of stocks appears to be the result of adoption of improved management techniques made possible in part by the increased availability of electronic data processing. More effective control may be expected to reduce cyclical sensitivity of total inventory changes unless offset by tendencies for movements in investment in the various types of stocks to move together more closely and in greater conformity to cyclical fluctuations in aggregate demand.
There have been some such tendencies. The proportion of stocks held within the cyclically sensitive, durable manufactures sector is higher than prewar (see below), and there has been a decline in the tendency for manufacturers’ stocks, especially finished goods, to move in an inverted pattern following business cycle turns. Moreover, there has been a decline in the share of less cyclically sensitive finished goods and an increase in the share of the more volatile goods in process. These shifts have tended to offset the effect of the reduction in the relative size of inventories.
Composition and behavior patterns. The composition of U.S. nonfarm business inventories at the end of 1964 was as follows: manufacturing, 54 per cent; wholesale trade, 15 per cent; retail trade, 24 per cent; other nonfarm, 7 per cent.
The proportion accounted for by manufacturing in the postwar period (average 55 per cent) has been somewhat larger than during the prewar period, when it averaged about 50 per cent. More important, movements in manufacturers’ inventory investment have played a larger role than would be expected on the basis of their share of total non-farm stocks and have tended to dominate movements in nonfarm inventory investment. Changes in manufacturers’ inventory investment constituted 56 per cent of total cyclical change in nonfarm inventory investment from 1919 to 1938 and 83 per cent from 1946 to 1960.
To a large extent, explanation of this relatively high degree of cyclical sensitivity lies in the high proportion of durable goods inventories that are held by manufacturers. At the end of 1964 durables constituted 55 per cent of manufacturers’ stocks, 41 per cent of wholesale stocks, and 37 per cent of retail stocks. Investment in durable stocks is typically more sensitive mainly because durable goods output and sales are more volatile, which, in turn, is due to the fact that replacement is relatively postponable during recessions. Moreover, inventory investment in the various durable-goods-producing industries moves together in closer conformity to cyclical forces than is true for nondurables. As a result, movements in manufacturers’ durable inventory investment have tended to dominate the movements of manufacturers’ total inventory investment
Manufacturing inventories are held at different stages of fabrication (1962 composition was: purchased materials, 36 per cent; goods in process, 30 per cent; finished goods, 34 per cent). Purchased-material stocks in the postwar period have turned roughly coincident with business cycle peaks and lagged from 4 to 8 months at business cycle troughs. Finished goods have lagged 6 to 8 months at cycle peaks and 1 to 11 months at troughs. Goods in process inventory can be analyzed with less confidence because of special problems of adjustment for price variation, but typical timing appears to be a lead or coincident turn at cycle peaks and a coincident turn or short lag at troughs. Taken as a whole, manufacturers’ stocks have lagged business cycle peaks by 2 to 4 months; troughs by 1 to 8 months.
Purchased-materials investment shows a high degree of sensitivity to business cycles, particularly for durable goods manufacturing. Leads occur at all cycle turns. The amplitude of investment movements appears to be associated with the level of unfilled orders. When orders are rising at a faster pace than shipments so that the backlog of unfilled orders is growing rapidly, or when the backlog is very large and not significantly diminishing, heavier investment in purchased materials takes place. Consistent with this is the observation that purchased-materials investment movements tend to parallel movements in purchasing agents association data for suppliers reported to be making slower deliveries.
Finished goods investment reaches its peak or trough roughly coincident with the business cycle peak or trough. Even certain types of finished stocks known to be held as buffers against seasonal or irregular fluctuations show very little tendency to move significantly against the business cycle.
Investment in goods in process is cyclically sensitive. Although timing is somewhat irregular, investment turns typically occur at about the same time as turns in purchased materials and ahead of turns in finished goods.
Differences in the behavior of investment in these three types of stocks are not great enough to mute significantly the cyclical sensitivity of manufacturers’ inventory investment. Taken as a whole, manufacturers’ inventory investment shows decidedly cyclical patterns of movement.
As already noted, wholesale and retail inventory investment play a secondary role in changes of total nonfarm inventory investment. Inventory investment in retailing has moved irregularly, although major movements have agreed roughly in timing with those of manufacturers’ inventory investment. Wholesaling inventory investment shows more fully developed cyclical behavior, with timing similar to that noted for manufacturing.
Although gaps remain in our knowledge of the exact nature of the forces influencing inventory investment, research has produced a significant advance in understanding of the nature and importance of inventory movements. Whereas it was previously a matter of controversy whether inventories contributed to business cycles or caused them to be less severe (Whitin 1953, chapter 5), no such doubt exists today. The significance of changes in inventory investment, as distinct from movement in stocks proper, is widely appreciated. Government and trade association data on inventory investment and related variables are closely studied by analysts of business conditions.
Accurate forecasting has proven difficult, partly because it is always difficult to predict a widely fluctuating economic series with the same degree of accuracy as a more stable series. Thus, all other factors being the same, it is more difficult to predict inventory change than the level of consumer spending. Nevertheless, the forecasts that have actually been made in the post-World War n period have typically been significantly more accurate than mere extrapolations (National Bureau … 1964). Knowledge of current and prospective levels of inventory demand makes possible a more accurate evaluation by management of the extent to which the current level of sales is a reflection of final demand rather than inventory accumulation. Such knowledge permits more intelligent planning of operations both for the short run and on a longer range basis. Such forecasts have also been of major importance to government in the development of general economic policy.
Unsolved questions of major importance involve (1) the issue of whether or not reversals in investment movements cause business cycle turns (cf. Burns 1960, p. 14; Darling 1961, part 5; Fromm 1962, p. 88; Stanback 1962, chapter 8) and (2) the problem of what type of government policy, if any, is appropriate to modify inventory investment swings.
Thomas M. Stanback, Jr.
Abramovitz, Moses 1950 Inventories and Business Cycles, With Special Reference to Manufacturers’ Inventories. New York: National Bureau of Economic Research.
Allen, Julius W.; and Gentry, Richard H. 1961 Inventories, Inventory Investment, and Inventory Control: A Selected Bibliography. Pages 203–217 in U.S. Congress, Joint Economic Committee, Inventory Fluctuations and Economic Stabilization. Part 3: Income Fluctuations and Economic Instability. 87th Congress, 1st Session. Washington: Government Printing Office. → Contains the most complete bibliography available.
Burns, Arthur F. 1960 Progress Towards Economic Stability. American Economic Review 50:1–19.
Clark, John Maurice 1917 Business Acceleration and the Law of Demand: A Technical Factor in Economic Cycles. Journal of Political Economy 25:217–235.
Darling, Paul G. 1961 Inventory Fluctuations and Economic Instability: An Analysis Based on the Post-war Economy. Pages 1–68 in U.S. Congress, Joint Economic Committee, Inventory Fluctuations andEconomic Stabilization. Part 3: Income Fluctuations and Economic Instability. 87th Congress, 1st Session. Washington: Government Printing Office.
Fromm, Gary 1962 Inventories, Business Cycles, and Economic Stabilization. Pages 35-133 in U.S. Congress, Joint Economic Committee, Inventory Fluctuations and Economic Stabilization. Part 4: Supplementary Study Papers. 87th Congress, 2d Session. Washington: Government Printing Office.
Hawtrey, R. G. 1929Trade and Credit. London and New York: Longmans.
Holt, Charles C.; and Modigliani, Franco 1961 Firm Cost Structures and the Dynamic Responses of Inventories, Production, Work Force and Orders to Sales Fluctuations. Pages 1–55 in U.S. Congress, Joint Economic Committee, Inventory Fluctuations and Economic Stabilization. Part 2: Causative Factors in Movements of Business Inventories. 87th Congress, 1st Session. Washington: Government Printing Office.
Keynes, John Maynard 1936The General Theory of Employment, Interest and Money. London: Macmillan. → A paperback edition was published in 1965 by Harcourt.
Klein, Lawrence R.; and Popkin, Joel 1961 An Econometric Analysis of the Post War Relationship Between Inventory Fluctuations and Changes in Aggregate Economic Activity. Pages 71–89 in U.S. Congress, Joint Economic Committee, Inventory Fluctuations and Economic Stabilization. Part 3: Income Fluctuations and Economic Instability. 87th Congress, 1st Session. Washington: Government Printing Office.
Kuznets, Simon 1926 Cyclical Fluctuations: Retail and Wholesale Trade, United States, 1919–1925. New York: Adelphi.
Lovell, Michael C. 1961 Manufacturers’ Inventories, Sales Expectations and the Acceleration Principle. Econometrica 29:293–314.
Lovell, Michael C. 1964 Determinants of Inventory Investment. Pages 177–224 in Conference on Models of Income Determination, Chapel Hill, N.C., 1962, Models of Income Determination. Princeton Univ. Press. → Contains an excellent bibliography of recent work.
Lovell, Michael C. 1966 Sales Anticipations, Planned Inventory Investment, and Realizations. Unpublished manuscript. → Submitted to the Conference on Investment Behavior, sponsored by the Universities–National Bureau Committe for Economic Research.
Lundberg, Eric (1937) 1954Studies in the Theory of Economic Expansion. New York: Kelley.
McGouldrick, Paul F. 1961 The Impact of Credit Cost and Availability on Inventory Investment. Pages 89–157 in U.S. Congress, Joint Economic Committee, Inventory Fluctuations and Economic Stabilization. Part 2: Causative Factors in Movements of Business Inventories. Washington: Government Printing Office. MACK, RUTH P. 1964 Comments on Lovell, “Determinants of Inventory Investment.” Pages 224–231 in Conference on Models of Income Determination, Chapel Hill, N.C., 1962, Models of Income Determination. Princeton Univ. Press.
Mack, Ruth P. 1966 Information, Expectations and Inventory Fluctuations: A Study of Materials on Hand and on Order. Unpublished manuscript, National Bureau of Economic Research.
Metzler, Lloyd A. (1941) 1965 The Nature and Stability of Inventory Cycles. Pages 100-129 in American Economic Association, Readings in Business Cycles. Homewood, 111.: Irwin. → First published in Volume 23 of Review of Economic Statistics.
Mills, Edwin S. 1954 Expectations, Uncertainty and Inventory Fluctuations. Review of Economic Studies22 , no. 1:15–22.
Mills, Edwin S. 1957 Expectations and Undesired Inventory. Management Science 4:105–109.
Mitchell, Wesley C. 1913Business Cycles. Univ. of California Press. → Part 3 was reprinted by the University of California Press in 1959 as Business Cycles and Their Causes.
Modigliani, Franco; and Sauerlender, Owen H. 1955 Economic Expectations and Plans of Firms in Relation to Short-term Forecasting. Pages 261-361 in Conference on Research in Income and Wealth, Short-term Economic Forecasting. Studies in Income and Wealth, Vol. 17. Princeton Univ. Press.
National Bureau OF Economic Research, Annual Report, 44TH 1964The National Bureau Enters Its Forty-fifth Year. New York: The Bureau. → See the progress report on “General Economic Forecasts”; by Victor Zarnowitz.
Nurkse, Ragnar 1952 The Cyclical Pattern of Inventory Investment. Quarterly Journal of Economics66 : 385–408.
Stanback, Thomas M. JR. 1962Postwar Cycles in Manufacturers’ Inventories. New York: National Bureau of Economic Research.
Terleckyj, Nestor E. 1960Measures of Inventory Conditions. National Industrial Conference Board, Technical Paper No. 8. New York: The Board.
Whitin, T. M. 1953 The Theory of Inventory Management. Princeton Univ. Press.
Inventory control theory seeks to establish optimal inventory decision rules for individuals and business firms. Inventory decisions may arise in purchasing or in production. A retailer or wholesaler generally must hold stocks of goods to meet the demands of his customers, and he must therefore decide on the quantities of the goods he will purchase and hold and at what point he will place new orders for each good. A manufacturer generally must hold inventories of finished goods because it is not possible (or economical) to synchronize perfectly his sales and his production process. His inventory decisions are therefore closely related to decisions regarding the scheduling of production. A manufacturer must also hold .stocks of semi-finished goods and stocks of raw materials. Inventory decisions regarding semifinished goods are, again, closely related to the scheduling of production, while those regarding raw materials are related both to production scheduling and to purchasing.
The optimal decision rules established for various inventory problems are not only of prescriptive value; they may also provide useful insights into observed fluctuations of inventories at the microeconomic and macroeconomic levels.
In past decades there were occasional periods of intensive interest in inventory theory, sometimes as the aftermath of forced inventory liquidation. For the most part, the literature consisted of a few articles in business journals that had little impact on business behavior and no impact on economic theory. More recently there has been an upsurge of interest which has far surpassed any of its predecessors with respect to the quantity and quality of the work accomplished and with respect to its over-all effect on business behavior and economic theory. Statisticians and economists have become interested in industrial problems concomitantly with increased attention in business to the techniques of advanced management, including operations research and management science. The development of these latter areas has included much detailed attention to inventory theory. [SeeOperations Research.]
The earliest attempts at developing inventory theory were primarily concerned with the problem of determining economical lot sizes in purchasing or production (discussed below). Raymond’s book (1931) is illustrative of these attempts. During World War II, a useful probabilistic model for controlling stocks was developed. Shortly thereafter a probabilistic version of economical lot-size analysis was developed by Whitin (1953), whose book was the first in English that dealt with probabilistic inventory systems in any detail. Several economists and mathematicians have provided rigorous mathematical analyses of inventory systems, the most noteworthy contributions being an article by Arrow, Harris, and Marschak (1951) and the rather abstract mathematical papers by Dvoretzky, Kiefer, and Wolfowitz (1952). The past few years have given rise to more than ten books on inventory theory, as well as chapters dealing with inventories in almost all of the many books on operations research. At the same time, business firms have been stressing the importance of stock control far more than ever before, as evidenced by the many new corporate vice-presidents in charge of inventory control. Several of the formal mathematical approaches to inventory analysis have been applied in practice by business firms.
From the standpoint of the national economy also, inventory theory has received a considerable amount of attention. One important development was Metzler’s formulation (1941) of a business cycle theory in which inventory behavior is the primary causal factor. A business cycle study of much empirical and theoretical interest was published by Abramovitz (1950), who showed that changes in inventory investment constituted a major component of the changes in national income in the five business cycles between the two world wars.
Approaches to inventory theory
There are a wide variety of mathematical analyses of inventory problems. A few different types will be presented here for the purpose of illustration. The mathematical analysis underlying each example will be avoided in order to make the material accessible to readers who are not mathematically oriented.
The newsboy problem
Suppose a newsboy is faced with the problem of determining how many papers to stock when his daily sales vary in a probabilistic manner. He buys papers at a unit cost C and sells them at a unit price P. He can be reimbursed an amount R for each paper not sold. How many papers should he stock to maximize his daily profit? This problem may be simply formulated in terms of the familiar marginal analysis. Let p(x) be the probability that customers will demand x or more papers. If the xth paper is sold, the newsboy makes a marginal profit of P — C on this paper. If it is not sold, the newsboy incurs a marginal loss of C —R. Weighting the marginal profit and the marginal loss by their probabilities, p(x) and I — p(x) respectively, one can readily ascertain that the xth paper should be stocked if
(1) p(x) (P — C) ≥ (1-p(x)) (C — R).
Simple computations show that condition (1) will be satisfied if p(x) > (C — R)/(P-R) . That is, the newsboy should continue to add papers to his stock as long as the probability of selling the marginal paper exceeds a known critical ratio. It can readily be seen that the newsboy should stock more papers the higher the profit margin (P — C) and the lower the loss on papers not sold (C —R). One of the principal lessons is that he should not, in general, stock the number of papers that corresponds to average sales. The existence of random demand changes the basic nature of the problem.
Economical lot-size problems
As mentioned before, the earliest inventory problems subjected to mathematical analysis were those involving the determination of economical purchase quantities of goods for inventories. Consider, for example, the case of a retailer who must hold stocks of the goods he sells. There are some inventory costs that decrease as the quantity of inventory goods he orders increases—for example, costs of procurement and costs of receiving. These costs are usually referred to as “ordering costs.” Other inventory costs increase with the size of the quantity ordered, for example, costs of holding inventories—interest, depreciation, obsolescence, etc. These costs are usually referred to as “carrying costs.” The problem for the retailer is, when faced with a known demand, to purchase a lot (a quantity of the inventory good) that fulfills demand and minimizes the sum of the ordering and carrying costs.
Let Y be the number of units the retailer sells per year (assumed to be sold at a constant rate during the year). At one extreme, he could purchase Y units at the beginning of the year; at the other extreme, he could purchase Y/365 units each day of the year. Obviously the first policy would entail very high carrying costs, and the second policy would entail very high ordering costs. If S is ordering costs per order and I is carrying costs per unit per year (both assumed to be constant), it can be shown that minimum costs will be incurred for lots of size Q* where
This equation indicates that the optimal lot size varies proportionately with the square root of expected sales and the square root of procurement expenses and varies inversely with the square root of unit inventory carrying costs.
The problem of determining economical lot sizes in manufacturing has been subjected to a similar analysis. In these cases, the lot is the amount to be produced rather than purchased, and S is defined as the cost per setup, i.e., the clerical and other costs of preparing the machines for a production run. The identical formula results. Although many restrictive assumptions are made in deriving them, economical lot-size formulas are perhaps the most widely applied mathematical technique of inventory analysis.
Probabilistic lot-size models
Probabilistic lot-size models deal with the problem of determining economical lot sizes when demand is not known with certainty but varies about a given mean in accordance with a known probability distribution. Because of the random variations in demand, it is possible to incur unintended stockouts or shortages. The optimal lot size is the one that minimizes an expected-cost expression which includes procurement costs, carrying costs, and stockout costs. The details of this analysis will not be presented here. The result specifies an optimal reorder-point quantity (a point at which orders will be initiated) as well as an optimal lot size to be ordered. The optimal reorder-point quantity varies directly with the demand level, demand variance, and shortage penalty, and varies inversely with the unit inventory carrying charges and setup costs. Typically, the optimal lot size is higher in the probabilistic case than in the case of certainty, since the fewer the number of orders placed, the smaller is the expected number of stockouts. Hence the introduction of stockout costs makes it worthwhile to buy in larger quantities.
The mathematical analysis underlying the probabilistic lot-size model is presented at widely different levels of generality and sophistication in the literature. The literature also contains solutions to the lot-size problem for cases of certain and probabilistic demands in which there are variations in average demand over time (Hadley & Whitin 1963).
Another technique used for analyzing inventory control problems is linear programming [seeProgramming]. Business sales often behave roughly in accordance with a known seasonal pattern. If the fluctuations in sales are met by corresponding fluctuations in production, overtime costs will be incurred. Alternatively, if production is kept relatively constant, the fluctuations in sales may be absorbed by inventory adjustments. Linear programming analysis of the problem makes it possible to determine the production schedule that will meet sales at the minimum combined overtime costs and inventory carrying charges. The approach can be trivially extended to handle other situations in which marginal costs increase as the level of output increases. However, the linear programming approach has not yet been extended to allow for random variations in demand or to include lot-size considerations.
Linear decision rules
The linear decision rule approach, developed at the Carnegie Institute of Technology (Holt et al. 1960), takes into account more types of cost factors than does the linear programming approach. Specifically, the approach minimizes a quadratic cost function including regular payroll costs, costs of overtime and idle time, costs of changing the level of the work force, and costs involved in having either too large or too small an inventory level. The quadratic approximation to costs plays a vital role in two ways. First, the derivatives of this function are linear, making it feasible to solve the equations resulting from setting the first derivatives of the function with respect to work force and production levels equal to zero. Second, when the cost function is quadratic, it is possible to consider only average sales, rather than the probability distribution of sales, for it has been demonstrated that the results are identical. The linear decision rules resulting from the solution of the derivative equations are simple linear expressions that can easily be handled in hand computations. The rules indicate the changes in the level of production and work force that are desirable. The derivative equations need only be solved again when cost conditions change.
The “queuing” or waiting-line approach to the inventory problem has received a considerable amount of attention in recent years (Morse 1958). The level of inventory serves as the queue, which is depleted by customer demands and increased by production or procurement. Mathematical expressions (or “equations of detailed balance”) for the rate of change of the probabilities that the queue is at each of its possible levels or “states” are developed. Under long-run, steady-state conditions these state probabilities remain unchanged, i.e., the probability that there are exactly x items in the queue at a random instant of time remains constant. This implies that each of the equations of detailed balance can be set equal to zero, making it possible to solve for the (steady) state probabilities. These state probabilities, combined with the associated costs of each state, can be used to make simple evaluations of the costs of various inventory policies. The assumption required concerning the nature of demands and/or deliveries is typically quite restrictive, so that the approach cannot be applied to a wide range of problems. [SeeQueues.]
Inventory theory and the theory of the firm
Classical versions of the economic theory of the firm do not take inventories into account explicitly in any way [seeFirm, Theory Of The]. Since inventories are of considerable importance in the actual operation of almost all firms, the theory appears to have serious deficiencies on this score. Only in the case of stationary demand known with certainty and stationary cost conditions can inventories be included in the classical theory. It has been shown that inventory carrying charges and setup costs can be included in the traditional longrun cost curve of the firm, i.e., the envelope of the short-run cost curves, the short-run average cost curves being based on a fixed time between orders, i.e., a fixed lot size (Wagner & Whitin 1958). Some nonstationary inventory situations can be handled by price-discrimination techniques. However, there remain important fundamental differences between inventory theory and classical economic theory. For example, consider the costs included in the linear decision rule example above. Of the several types of costs discussed, only regular payroll costs are taken into consideration by the classical approach, for under stationary demand conditions there would be no overtime, no idle time, no changes in the work force, and no changes in the average inventory level. The very existence of this inventory approach is based on nonstationarity. No longrun equilibrium is ever achieved. A more realistic theory of the firm must allow for some of these nonstationary aspects.
Another aspect of inventory theory that has relevance for the theory of the firm is the existence of economies of scale in most inventory models. Lot-size analysis indicates that inventory costs vary less than proportionately with sales, and the analysis of reorder-point stocks also gives rise to economies of scale because, by the law of large numbers, stocks held as protection against random variations in demand vary less than proportionately with demand. Thus at least two causes of decreasing average costs are established. The arguments for increasing average costs, which are an essential ingredient of classical economic theory (both the theory of the firm and the theory of the economy), have not been convincing, typically being rather vague statements concerning diseconomies of large-scale management or control. Inventory analysis has much to contribute to problems of returns to scale, including problems of vertical and horizontal integration. Few attempts have thus far been made to complete such analyses. [SeeEconomies OF SCALE.]
One of the few attempts to incorporate inventory behavior into the theory of the firm was Boulding’s reconstruction of economic theory on the basis of balance sheet considerations (1950). “Preferred asset ratios” played a vital role in his analysis, but he spent little time explaining the basic determinants of these ratios.
Inventory theory and aggregate economics
At the level of aggregate economic analysis, inventory theory is of interest from several standpoints. Its relevance to business cycle theory was mentioned above. In addition, inventory theory can readily be related to Keynesian economics through the three Keynesian motives for holding cash (or goods)—the transactions motive, the precautionary motive, and the speculative motive. According to the transactions motive, it is necessary and desirable to hold some inventories of goods for the purpose of meeting demand. Lot-size analysis provides an approach to determining the quantities that should be held for this purpose in order to minimize the sum of setup costs and inventory carrying charges. The determination of reorder-point quantities involves the precautionary motive. Safety or “cushion” stocks are held to avoid stockouts arising from random sales variations. Finally, inventories may be held for speculative reasons, that is to say, in anticipation of changes in demand or supply conditions. Aggregate levels of stocks held for any of these reasons are of significance in aggregate models of the economy.
Stocks of money have also been subjected to probabilistic inventory analysis. (Here, brokerage fees play the role of setup costs.) For example, the precautionary motive for holding stocks of cash was discussed by Edgeworth in 1888 in connection with the determination of bank reserve ratios.
In a general sense, the behavior of economic aggregates depends upon the behavior of the detailed components of the aggregates, which, in turn, depend quite heavily on inventory considerations. Thus, a better understanding of inventory theory is needed for a more complete theory of aggregate economics.
T. M. Whitin
Abramovitz, Moses 1950 Inventories and Business Cycles, With Special Reference to Manufacturers’ Inventories. New York: National Bureau of Economic Research.
Arrow, Kenneth J.; Harris, Theodore; and Marschak, Jacob 1951 Optimal Inventory Policy. Econometrica 19:250–272.
Arrow, Kenneth J.; Karlin, Samuel; and Scarf, Her-bert 1958Studies in the Mathematical Theory of Inventory and Production. Stanford Mathematical Studies in the Social Sciences, No. 1. Stanford Univ. Press.
Boulding, Kenneth E. 1950 A Reconstruction of Economics. New York: Wiley.
Buchan, Joseph; and Koenigsberg, Ernest 1963 Scientific Inventory Management. Englewood Cliffs, N.J.: Prentice-Hall.
Dvoretzky, A.; Klefer, J.; and Wolfowitz, J. 1952 The Inventory Problem: I. Case of Known Distributions of Demand; II. Case of Unknown Distributions of Demand. Econometrica 20:187–222, 450–466.
Edgeworth, Francis Y. 1888 The Mathematical Theory of Banking. Journal of the Royal Statistical Society 51:113–127.
Fetter, Robert B.; and Dalleck, Winston C. 1961 Decision Models for Inventory Management. Home-wood, 111.: Irwin.
Hadley, George; and Whitin, T. M. 1963 Analysis of Inventory Systems. Englewood Cliffs, N.J.: Prentice-Hall.
Hanssmann, Fred 1962 Operations Research in Production and Inventory Control. New York: Wiley.
Holt, Charles C. et al. 1960 Planning Production, Inventories, and Work Force. Englewood Cliffs, N.J.: Prentice-Hall.
Metzler, Lloyd A. (1941) 1965 The Nature and Stability of Inventory Cycles. Pages 100–129 in American Economic Association, Readings in Business Cycles. Homewood, 111.: Irwin. → First published in Volume 23 of Review of Economic Statistics.
Mills, Edwin S. 1962 Price, Output, and Inventory Policy: A Study in the Economics of the Firm and Industry. New York: Wiley.
Morse, Philip M. 1958 Queues, Inventories and Maintenance: The Analysis of Operational Systems With Variable Demand and Supply. New York: Wiley.
Raymond, Fairfield E. 1931 Quantity and Economy in Manufacture. New York: McGraw-Hill.
Starr, Martin; and Millier, David W. 1962 Inventory Control: Theory and Practice. Englewood Cliffs, N.J.: Prentice-Hall.
Wagner, Harvey M. 1962 Statistical Management of Inventory Systems. New York: Wiley.
Wagner, Harvey M.; and Whitin, T. M. 1958 Dynamic Problems in the Theory of the Firm. Naval Research Logistics Quarterly 5:53–74.
Whitin, T. M. 1953 The Theory of Inventory Management. Princeton Univ. Press.
An inventory is the entirety of those things owned by a company and intended for resale or the raw materials and parts to be used in producing salable goods and products. Inventories are time-sensitive storage systems that can be divided into three categories. First are cycle stocks: the order quantity or lot size received from the plant or vendor. Second are in-transit stocks: inventory in shipment from the plant or vendor or between distribution centers. Third are safety stocks: the items in inventory that serve as a buffer against forecast error and lead time variability.
Historically, there have been two basic inventory systems: the continuous review system and the periodic review system. With continuous review systems, the level of a company's inventory is monitored at all times. Under these arrangements, businesses typically track inventory until it reaches a predetermined point of "low" holdings, whereupon the company makes an order (also of a generally predetermined level) to push its holdings back up to a desirable level. Since the same amount is ordered on each occasion, continuous review systems are sometimes also referred to as event-triggered systems, fixed order size systems (FOSS), or economic order quantity systems (EOQ). Periodic review systems, on the other hand, check inventory levels at fixed intervals rather than through continuous monitoring. These periodic reviews (weekly, biweekly, or monthly checks are common) are also known as time-triggered systems, fixed order interval systems (FOIS), or economic order interval systems (EOI).
INVENTORY AND THE GROWING COMPANY
Most successful small companies find that as their economic fortunes rise, so too do the complexities of their inventory system logistics. The resulting need for increased inventory management procedures is due primarily to two factors: 1) greater volume and variety of products, and 2) increased allocation of company resources (such as physical space and financial capital) to accommodate the growth in inventory. For a small company used to ordering parts and materials in an as-needed and informal basis, the transition to a formal and documented system of purchasing and inventory management can be a significant step. It requires the creation of new job functions to identify the costs (holding, shortage) associated with inventory and to implement and manage a formal inventory system. Formal inventory systems require extensive record keeping and on a periodic basis, they must be audited by someone. In addition, this transition to a formal inventory system requires substantial coordination between different functional areas of the company. Such a transition often leads into computerization of inventory management. This can be a challenging project, particularly for companies lacking employees with appropriate backgrounds in data management.
Just-In-Time Inventory Control
Just-in-time production is a straightforward idea that may be somewhat difficult to implement. The basic concept is that finished goods should be produced just in time for delivery, and raw materials should be delivered just in time for production. When this occurs, materials or goods never sit idle. This, in turn, means that a minimum amount of money is tied up in raw materials, semi finished goods, and finished goods. The result of a well-managed inventory system capable of supporting a just-in-time production system is sustained productivity and quality improvement with greater flexibility and delivery responsiveness. This production concept, which originated in Japan and became immensely popular in American industries in the early and mid-1990s, continues to be hailed by proponents as a viable alternative for businesses looking for a competitive edge.
SETTING AN INVENTORY STRATEGY
No single inventory strategy is effective for all businesses. When a company is faced with a need to establish or reevaluate its inventory control systems, a practice commonly known as "inventory segmenting" or "inventory partitioning" is a helpful tool. This practice is, in essence, a way of breaking down and reviewing total inventory so that a thorough assessment of each category may be made. The inventory may be broken down by product classifications, inventory stages (raw materials, intermediate inventories, finished products), sales and operations groupings, and excess inventories. Proponents of this method of study say that such categorical segmentations break the company's total inventory into much more manageable parts for analysis.
Inventory management is a key factor in the successful operation of any business for which inventories are an integral part. For both large and small companies, determining whether their inventory systems are successful can be done by answering one question: Does the inventory strategy insure that the company has adequate stock for production and goods shipments while at the same time minimizing inventory costs? If the answer is yes, then the company in question is far more likely to be successful. If, however, the answer is no, then the business is operating under twin burdens that can be of considerable consequence to its ability to survive, let alone flourish.
No factor is more important in ensuring successful inventory management than regular analysis of policies, practices, and results. A useful checklist of actions for those wishing to establish and maintain an effective inventory system includes:
- Regularly reviewing product offerings, including the breadth of the product line and the impact that peripheral products have on inventory.
- Ensuring that inventory strategies are in place for each product and that they are reviewed on a regular basis.
- Reviewing transportation alternatives and their impact on inventory/warehouse capacities.
- Undertaking periodic reviews to ensure that inventory is held at the level that best meets customer needs; this applies to all levels of business, including raw materials, intermediate assembly, and finished products.
- Regularly canvassing key employees for ideas and information that may inform future inventory control plans.
- Determining what level of service (lead time, etc.) is necessary to meet the demands of customers.
- Establishing a system for effectively identifying and managing excess or obsolete inventory, and determining why these goods reached such status.
- Devising a workable system wherein "safety" inventory stocks can be reached and distributed on a timely basis when the company sees an unexpected rise in product demand.
- Calculating the impact of seasonal inventory fluctuations and incorporating them into inventory management strategies.
- Reviewing the company's forecasting mechanisms and the volatility of the marketplace, both of which can (and do) have a big impact on inventory decisions.
- Instituting a "continuous improvement" philosophy in inventory management.
- Making inventory management decisions that reflect a recognition that inventory is deeply interrelated with other areas of business operation.
To summarize, inventory management systems should be regularly reviewed from top to bottom as an essential part of the annual strategic and business planning processes.
Indeed, even cursory examinations of inventory statistics can provide business owners with valuable insights into how things are going generally. Business consultants and managers alike note that if an individual business has an inventory turnover ratio that is low in relation to the average for the industry in which it operates, this may be a sign that the business is carrying a surplus of obsolete or otherwise unsalable inventory. Conversely, if a business is experiencing unusually high inventory turnover when compared with industry or business averages, then the company may be losing out on sales because of a lack of adequate stock on hand. Determining and tracking the turnover rate of all items in inventory helps in building up an inventory assessment.
The way in which a company accounts for its inventory can have a visible effect on its financial statements. Inventory is a current asset on the balance sheet. One may think that inventory valuation is relatively simple. For a retailer, inventory should be valued for what it cost to acquire that inventory. When an inventory item is sold, the inventory account should be reduced (credited) and cost of goods sold should be increased (debited) for the amount paid for each inventory item. This works if a company is operating under the Specific Identification Method. That is, a company knows the cost of every individual item that is sold. This method works well when the amount of inventory a company has is limited and each inventory item is unique. Examples would include car dealerships, jewelers, and art galleries.
The Specific Identification Method, however, is cumbersome in situations where a company owns a great deal of inventory and the items within that inventory are not easily distinguished one from another. As a result, other inventory valuation methods have been developed. The best known of these are the FIFO (first-in, first out) and LIFO (last-in, first-out) methods.
First-in, first-out is a method of inventory accounting in which the oldest stock items in a company's inventory are assumed to have been the first items sold. Therefore, the inventory that remains is from the most recent purchases. In a period of rising prices, this accounting method yields a higher ending inventory, a lower cost of goods sold, a higher gross profit, and a higher taxable income.
The FIFO method may come the closest to matching the actual physical flow of inventory. Since FIFO assumes that the oldest inventory is always sold first, the valuation of inventory still on hand is at the most recent price. Assuming inflation, this will mean that cost of goods sold will be at its lowest possible amount. Therefore, a major advantage of FIFO is that it has the effect of maximizing net income within an inflationary environment.
Last-in, first-out, on the other hand, is an accounting approach that assumes that the most recently acquired items are the first ones sold. Therefore, the inventory that remains is always the oldest inventory. During economic periods in which prices are rising, this inventory accounting method yields a lower ending inventory, a higher cost of goods sold, a lower gross profit, and a lower taxable income. The LIFO method is preferred by many companies because it has the effect of reducing a company's taxes, thus increasing cash flow. However, these attributes of LIFO are only present in an inflationary environment.
The other major advantage of LIFO is that it can have an income smoothing effect. Again, assuming inflation and a company that is doing well, one would expect inventory levels to expand. Therefore, a company is purchasing inventory, but under LIFO, the majority of the cost of these purchases will be on the income statement as part of cost of goods sold. Thus, the most recent and, assuming an inflationary period, most expensive purchases will be the first items sold. As they are sold, the cost of goods sold will rise and net income will be reduced. Net income is still high, but it does not reach the levels that it would if the company used the FIFO method.
Given the important differences that exist between the various inventory accounting methods, it is important that the inventory footnote be read carefully in financial statements, for this part of the document will inform the reader of the method of inventory valuation chosen by a company. Assuming inflation, FIFO will result in higher net income during growth periods and a higher, and more realistic inventory balance. In periods of growth, LIFO will result in lower net income and lower income tax payments, thus enhancing a company's cash flow. During periods of contraction, LIFO will result in higher income levels, but it will also undervalue inventory over time.
Small business owners weighing a switch to a LIFO inventory valuation method should note that while making the change is a relatively simple process (the company files IRS Form 970 with its tax return), switching away from LIFO is not so easy. Once a company adopts the LIFO method, it can not switch to FIFO without securing IRS approval.
DONATING EXCESS INVENTORY
In recent years, many small (and large) businesses have gained valuable tax deductions by donating obsolete or excess inventory to charitable organizations, churches, and disaster relief efforts. The type of deduction that can be claimed depends on the business structure of the donating company. "If you're organized as an S corporation, a partnership, or a sole proprietorship and you donate inventory to a charity that uses the goods to assist the sick, the poor, or children, you're generally able to take a tax deduction for the cost of producing the inventory," stated Joan Szabo in Entrepreneur. C Corporations, meanwhile, can deduct the cost of the inventory plus half the difference between the production cost and the inventory's fair market value, provided the deduction does not exceed twice the cost of the donated goods.
A number of organizations have been established for the express purpose of distributing donated inventory. Gifts in Kind International (based in Alexandria, Virginia) distributes used computers, high-tech equipment, and other donated inventory to approximately 50,000 domestic and international charities. The Galesburg, Illinois-based National Association for the Exchange of Industrial Resources (NAEIR), meanwhile, distributes excess inventory to more than 5,000 schools, churches, homeless shelters, and other charitable organizations. Office supplies comprise much of the NAEIR goods, but clothing, janitorial supplies, and computer equipment are also distributed. The NAEIR estimates that it has distributed more than $1 billion in corporate inventory donations to American schools and nonprofit organizations since 1977.
see also Automated Storage and Retrieval Systems; Enterprise Resource Planning; Inventory Control Systems; Material Requirements Planning
Allen, Kelley L. "Lose that Inventory Baggage." Across the Board. January 2000.
Haaz, Mort. "How to Establish Inventory Levels." Gift and Decorative Accessories. April 1999.
Muller, Max. Essentials of Inventory Management. AMACOM Division of American Management Association, November 2002.
Szabo, Joan. "Spring Cleaning." Entrepreneur. April 1999.
Toomey, John W. Inventory Management. Springer, June 2000.
Hillstrom, Northern Lights
updated by Magee, ECDI
Inventories are sets of goods and materials held available to cover immediate or future needs. Inventories can be goods and materials for sale after some processing or as they are, or they can be goods (like fixtures, supplies, furniture, or equipment) that are not for sale but are nevertheless kept by organizations, manufacturers, and service providers.
In business, inventories are assets that are used in the productive process and transformed to realize sales of the final products the market demands. They may be classified in three major categories: raw materials, work in process, and finished goods.
Inventories of raw materials are the collections of items used to begin the production process of a firm. They could be materials from agricultural, forest, or mining operations, or they could be the finished goods of another company. For example, a computer microchip could be the final product of a firm that manufactures microchips and a raw material for a firm that manufactures personal computers. Work-in-process inventories exist and are created in all the stages of the production process from the moment raw materials are received to the stage just before the production of the final goods ready for sale. An inventory of final goods represents the last stage of the production process. It is a collection of items that are ready to be sold to customers, having been inspected for quality to meet certain standards.
Inventories are acquired based on a production schedule and a sales forecast to determine the target level of inventories in each category. If the inventory level is too high, the company faces an unnecessarily high cost of carrying inventories. If the level is too low, the firm might not have enough materials for its production process and risks losing sales and dissatisfying its clients by not meeting their demand. The management of a company must therefore determine how much inventory it should carry by evaluating the costs with the production requirements and customer demand.
The composition of a firm’s inventories depends on several factors. Raw-materials inventories depend on the plans and schedules of production, the seasonality of sales, the available technology, the level of confidence toward the various suppliers for the on-time delivery of the needed goods, and several other factors. The level of work-in-process inventories depends on the type of the finished goods to be made ready for sale and the complexity of the production process. The level of finished-goods inventories depends on external factors, such as the expectations of the consumers and other market forces.
Inventories in business have certain financial characteristics that can be divided into three categories. First, they are part of the current assets on a firm’s balance sheet and in most cases can be converted into cash during a period of one year. (There is an exception in some specialized industries in which the conversion might take longer.) Second, they are the least liquid of the current assets. This means that in companies with high variability in sales and production processes, it is more difficult to liquidate the company’s inventories when needed unless they are sold at a discount, or less than their true value. Third, during the various inventory stages beginning with the purchase of raw-materials inventories until the realized sales of finished-goods inventories, there exist certain time lags that can have a positive or a negative effect for the firm. These are:
Manufacturing lag: The inventories that are bought by the company from its suppliers are usually raw materials. The payment for these inventories is usually made on credit. The credit period usually is longer than one month, while other operating expenses of the firm, such as labor and wages, must be paid within a month. Furthermore, the firm can have the needed inventories available before it covers its obligations to its suppliers. Hence the firm has a type of financing for the goods it has obtained without any financial cost. This lag has a positive effect for the company.
Stockage lag: When the finished goods inventories are ready to be sold, in most cases they are not sold immediately and therefore do not create cash inflows. However, there are many cash outflows for the payment of labor, the payment of suppliers, and other expenses of the production process. This delay in selling the inventories and creating cash inflows to meet the realized cash outflows has a cost to the firm in reducing the firm’s liquidity.
Sales lag: Even when sales are realized for the finished-goods inventories, they could be on credit and not cash sales, creating accounts receivable for the firm that sells the inventory. These accounts receivable could take up to a year to be paid and generate cash inflows. This type of cost is called the cost of maintaining or creating accounts receivable.
A company keeps inventories for the reasons of transaction, safety, and arbitrage. For the purpose of transactions, a firm keeps inventories of all types to have raw materials to work with and to have finished goods to sell in order to minimize or eliminate the risk of stock outs, (the risk of not having enough inventories of a certain type needed in the production process, so production will not stop or be delayed) or total depletion of inventory and to make financial transactions. If it keeps large amounts of inventories, the cost of investing in inventories rises, but the likelihood of stock outs falls. For the purpose of safety in meeting product demand, a firm must keep a high enough level of inventories to meet the demand for its products. For the purpose of arbitrage, a firm might keep a high level of inventories to take advantage of situations where prices are expected to increase. A firm that has bought or produced inventories at a low cost may profit by selling them later at higher prices. Furthermore, by purchasing higher amounts of raw materials, a firm can take advantage of possible discounts offered by its suppliers due to the larger quantities ordered.
A company might consider four major categories of costs before making significant decisions regarding inventories. The first category is carrying, or holding, costs. This category relates to the keeping of inventories and can be distinguished into the following specific types of carrying costs:
Storage and handling costs: A firm needs to store its inventories in specific locations it owns or rents. This involves rental costs or the opportunity costs of using the storage areas rather than renting them to others along with the labor expenses of moving, storing, cleaning, distributing, reporting, securing, and generally handling the inventories.
Destruction or theft costs: Once a firm stores its inventories in specific locations, it needs to protect them from theft or destruction from those outside or inside the company.
Security costs: Both the inventories and their storage locations have to be secured from fires, floods, accidents, and other natural catastrophes, usually through a purchased security or insurance program.
Age costs: Certain categories of inventories, such as medicine, food, and computer products, have an expiration date beyond which they become obsolete and unfit for sale. The cost of keeping inventory beyond its expiration date is the age cost.
The second cost category is the ordering costs, which concern the placement of orders to the firm’s suppliers. Each order that is received by a supplier has costs for the invoice to be issued and paid, for the transportation of the goods, for their quality inspection once the goods arrive, and so on. If a firm reduces the number of orders it places (making fewer but larger orders instead), it also reduces the total ordering costs of its inventories and becomes more profitable.
The third category is the opportunity costs, which are related to the amount of funds invested in inventories. If a large amount of funds is tied up in inventories, the firm loses opportunities it might have had to invest its finances instead in more profitable opportunities. Furthermore, if inventories are financed by borrowed funds, this carries interest costs that the firm has to pay back, thereby reducing its profitability.
The fourth category is the stock out costs or the costs associated with keeping too low an inventory or depleting an inventory. This can cause breaks and delays in the production of the finished goods, with negative consequences for the firm. It will have dissatisfied clients and customers, it might lose sales, it might have to pay fees for delaying its products’ delivery, and it will damage its reputation. According to Geoff Relph and Peter Barrar (2003), there is also an opposite type of cost to stock out costs: that of having too much inventory, or overage. They suggest that firms should formally plan overage since an effective control of overage will enhance the company’s profitability by minimizing the investment in inventories.
Certain factors affect the level of inventories a firm should carry to be profitable and efficient. These include:
the required materials for each stage in the production process;
the sales forecast;
seasonal or cyclical factors that characterize the firm’s sales during a year; and
changes in technology that may render the finished-goods inventories obsolete.
Inventory-management techniques aim to reduce the total inventory costs by holding and ordering inventories in the most efficient ways. They are covered extensively in special courses of production management. Inventory management also has economic consequences for a business and affects the value of the firm, so it is also studied from a financial point of view. The most common inventory management techniques follow.
The ABC system separates inventories into the categories A, B, and C according to their importance and nature so the total cost of inventory control can be reduced. The most valuable inventories are in category A, while the least important ones are category C.
The economic ordering quantity (EOQ) system uses a simple mathematical model to determine the ideal quantity of each order of inventories that will reduce the total ordering and carrying costs.
The system of reorder point is based on the EOQ model and shows the quantity of inventories that should be on hand when an order is placed to keep the total inventory costs at a minimum.
The automated system of inventory control is used by firms that have many products and determines the optimal quantities to be ordered based on the EOQ. It is a dynamic system that is easily adjusted depending on a company’s needs.
The just-in-time inventory system is a system first introduced in Japan that minimizes the level of inventories a firm carries and the investment in them by achieving a perfect coordination between the ordering and receiving of necessary inventories at each stage of the production process. Hence no inventory stocks are created, and the inventory costs are kept at a minimum. The disadvantage of this system is that if the coordination is interrupted between the product suppliers and the customers’ orders, the costs can be high.
Inventories also play an important role in national accounts. Some short-term macroeconomic fluctuations are attributed to the inventory cycle. Goods held as inventories are considered an investment and are counted for the year produced, not the year sold. Although inventories are a small portion of the overall investment sector, all the inventories from all the businesses in one economy constitute a critical component of the gross domestic product (GDP).
If the economy is moving toward a recession period, an undesired accumulation of inventories is a negative signal. Leading up to a recession, consumers have less liquidity and reduce their purchases. This leads to fewer sales of goods and services, which causes inventories of finished goods to increase. As inventories pile up, businesses reduce their production of goods to keep costs low. Since there is less productive activity, fewer employees are needed, and firms lay off staff to further reduce costs. Unemployment rises, output falls, GDP growth falls, and the economy goes into a recession. The idea that a recession might be caused by low product demand was introduced as early as 1889 by Albert Frederick Mummery and J. A. Hobson in their book The Physiology of Industry and upset the neoclassical economists. However, the British economist John Maynard Keynes (1936) praised Mummery and Hobson for their “heresy,” as Keynes called their proposition. Mummery and Hobson further proposed that too much saving has a negative effect in the economy since it leads to underconsumption. Lower levels of consumption will mean less demand for goods and services, which will cause the piling up of inventories in the immediate future and eventually will lead to lower production output, more unemployment, and a decrease of the GDP.
Conversely, an undesired or unexpected decrease in business inventories means that the demand for goods is greater than the one predicted by the firms, and the existing inventories become depleted quickly. Businesses reorder more inventories, hire more employees, and increase production to meet the increased demand and realize higher sales. As this phenomenon occurs throughout the economy, the unemployment rate falls, and the economic output rises, resulting in an increase in economic growth as measured by the GNP.
In addition, with more jobs, less unemployment, and higher output, income also increases and contributes further to a rise in the demand for goods and services. Higher demand, though, leads to higher prices. The level of prices goes up, creating demand-pull inflation. As demand for more labor rises, wages increase, which will further increase the rate of inflation.
Inventories can thus be considered a leading indicator of business cycles. Changes in the variable of business inventories can lead to changes in the future condition of the economy and economic growth. Economic analysts therefore monitor the aggregate levels of business inventories for potential changes in future economic growth.
SEE ALSO Business Cycles, Real; Depression, Economic; Economic Crises; Expectations; National Income Accounts; Recession
Blinder, Alan S. 1981. Inventories and the Structure of Macro Models. American Economic Review 71 (2): 11–16.
Blinder, Alan S. 1982. Inventories and Sticky Prices: More on the Microfoundations of Macroeconomics. American Economic Review 72 (3): 334–348.
Blinder, Alan S., and Louis John Maccini. 1991. The Resurgence of Inventory Research: What Have We Learned? Journal of Economics Surveys 5 (4): 291–328.
Brigham, E. F. 1992. Fundamentals of Financial Management. 6th ed. Orlando, FL: Dryden.
Fisher, Jonas D. M., and Andreas Hornstein. 2000. Inventory Policies in General Equilibrium. Review of Economic Studies 67 (1): 117–145.
Irvine, F. Owen, Jr. 1981. Merchant Wholesaler Inventory Investment and the Cost of Capital. American Economic Review 71 (2): 23–29.
Keynes, John Maynard. 1936. General Theory of Employment, Interest, and Money. London: Macmillan.
Mummery, Albert Frederick, and J. A. Hobson. 1889. The Physiology of Industry: Being an Exposure of Certain Fallacies in Existing Theories of Economics. London: J. Murray.
Relph, Geoff, and Peter Barrar. 2003. Overage Inventory: How Does It Occur and Why Is It Important? International Journal of Production Economics 81–82 (1): 163–171.
in·ven·to·ry / ˈinvənˌtôrē/ • n. (pl. -ries) a complete list of items such as property, goods in stock, or the contents of a building. ∎ a quantity of goods held in stock: in our warehouse you'll find a large inventory of new and used bicycles. ∎ (in accounting) the entire stock of a business, including materials, components, work in progress, and finished products. • v. (-ries, -ried) [tr.] make a complete list of. ∎ enter in a list: about forty possible sites were inventoried.
A. S. Hargreaves
An itemized list of property that contains a description of each specific article.
Inventory of a company, for example, is the annual account of stock taken in the business, or the quantity of goods or materials in stock. The term is also used to describe a list made by the executor or administrator of the estate of a deceased individual.