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This paper considers the dynamic inventory model with a discrete demand. There is a constant lead time, backlogging of excess demand, a fixed set-up cost, and holding and shortage costs whose negatives are unimodal. The criterion is the long-run average cost. A value iteration method with discount factor approaching to 1 is studied. This value iteration method supplies policies of the (s,S) type and convergent upper and lower bounds on the minimal average cost. Further, the average cost of the (s n ,S n ) policy found at then-th iteration lies between the corresponding upper and lower bound. Also, for alln sufficiently large the (s n ,S n ) policy is average cost optimal. Computational considerations are given for the special case of linear holding and shortage costs.

The design and construction of nuclear power plants has always involved much effort in the electrical area relative to that required in many other industries. This is a result of the relatively large quantities of components that are centrally controlled and plant variables that are centrally monitored, together with separation criteria imposed on safety - related circuits. The Floating Nuclear Plant has basically these same considerations in electrical design and construction as a land-based plant, but in addition has a much shorter plant manufacturing lead time as a design objective. Thus, the electrical installation -- which is typically on the critical path at peak effort near the end of the plant construction schedule -- could be a bottleneck if conventional electrical installation methods were used. This paper discusses a design for reducing electrical installation lead time by reducing termination time and maximizing simultaneous installation effort through use of a prefabricated control module.

Robert G. Brown's Statistical Forecasting for Inventory Control sketched out a dynamic inventory-control system with random demand and random lead time. For some reason, the system has had neither wide use nor further scrutiny. To rectify the situation, this paper puts both a more mathematical and a more meaningful basis under the system, and then discusses its actual operation and some possible extensions.

There are frequent occasions where the coordination of replenishment orders for selected groups of items can lead to significant savings in the costs of replenishment. This paper is concerned with a practical procedure for selecting the order-up-to-levels, can-order points and must-order points of a particular coordinated control system. Demand is Foisson and a fixed non-zero replenishment lead time is assumed. Cost comparisons with the best independent control strategy indicate that substantial savings (averaging 18-8% over some 104 examples) are possible through coordination.

It has been well established that for optimum operation of a re-order level policy, re-order levels and replenishment order quantities should be jointly calculated. There exist many solutions to this stock control problem. A number of these involve approximations which simplify the mathematics of the problem but yield non-optimal solutions, while others raise the question of whether the additional computational effort required, due to mathematical complexity, is economically justified. This paper describes that if the lead time demand can be considered as normally distributed and lead time is constant, then it is possible to arrive at optimal values of safety stocks-consequently re-order levels-and order quantities, with minimum computational effort, through a nomogram which accomplishes a major part of the necessary computations. The flow chart of a program that can make the calculations is also presented.

In an introductory psychology class of size 200, a computer-based testing and scoring system was tried out. Individual test forms were generated by a random process from an item pool and were printed by computer; test-response data were scored by computer; and test-score records for each student were maintained by computer. Advantages included: (1) increased frequency of tests, (2) immediacy of feedback, (3) accessibility and currency of cumulative records, (4) decreased opportunities for cheating, (5) decrease in difliculties and extra work associated with retests and make-up examinations, (6) decreased need for typing and secretarial services, (7) shortened lead time between initial stages of test preparation and administration, and (8) autonomy of the process, as it required little high-level decision making once in progress. Cost analysis indicated that such a system would be feasible for adoption by an individual instructor, given the required facilities at the university computer installation.

Using an exponential smoothing procedure and an autoregressive-moving average process; forecasts for the monthly Palmer Drought Severity Index were calculated. The autocorrelation and partial autocorrelation functions of severity index values were used as a starting point for the autoregressive-moving average model selection process. Of the many possible autoregressive-moving average models, the one that was selected provided the best forecasts based on the mean square error. Monthly data for the period 1929–1969 were utilized in a nonlinear least-squares computer routine to arrive at estimated parameter values for the autoregressive-moving average model. Monthly forecasts with a lead time of one month were generated using the exponential smoothing and autoregressive-moving average procedures for the period 1970–1972. These forecasts were compared with the myopic (persistence) forecasts, Xt+1=Xt. The mean square errors of the forecasts were 0.63 for the autoregressive-moving average model, 0.65 f...

The problem of determining reorder quantities and reorder points that minimize the total costs of carrying inventory, placing orders, and penalties for back orders, in the face of uncertain demand, is considered in this paper. By making approximations to the total cost function and the safety factor versus service function relationship, an economic order quantity is derived that depends on the uncertainty in the foiecast of demand during the lead time, but is independent of the back order cost. Reorder points are then determined for the case in which the back order cost is explicitly stated, and for the case in which the back order cost is unknown and the desired customer service is used as the controlling parameter. Simulations indicate that, when compared with use of the Wilson economic order quantity, the use of the formulae derived in this paper will lead to approximately a 5-7-percent reduction in the total cost.

This paper outlines the impending U. S. change to the metric measurement system. Using the recent NBS metric study and current legislation to establish the inevitability of the metric transition, the paper identifies those areas in which computer resources will be affected. The recent NBS study failed to examine the impact of metric conversion on existing computer systems and resources even though many potential problems exist in the areas of data field sizes, file design, file conversion, precision and accuracy. The paper explores these problem areas and identifies those steps alert managers can take to avoid major problems. The author presents this challenge as an opportunity to the data processing industry; an opportunity to take the lead and show users that we can perform in a professional manner. Because of the long lead time in systems development this problem must be tackled in the immediate future if we are to keep on top of it. No other country has been so dependent on computers when they went through a metric conversion; thus, we are on our own and must plan now for the metric transition and its impact on computer resources.

Problems of inventory control for items with extremely low demand (say less than one unit per month average demand) have received relatively little attention in the literature. However, for military supply systems it is well known that an extremely large proportion of the total number of items fall into this category. The problem of designing a control system for these low demand items is therefore one of the most critical inventory management problems faced by the National Military Establishment. In the following, a single echelon, multidepot supply system is studied for low demand items having a stationary Poisson probability distribution for demand. Instantaneous information concerning inventory levels is assumed to be available. Procurement lead time is assumed to be constant as well as the time required for either of two available modes of redistribution. Items are ordered one at a time and decision rules are developed for allocation of new procurement, redistribution of stocks among the depots, and for determining system and depot stockage objectives in order to minimize the expected costs resulting from system and depot stockouts, cost of redistributing stocks among the depots, and costs of transportation from the source. The model is an extension of previous models in that redistribution costs and depot stockout costs are considered in the determination of the stockage objective for the system as a whole. When more than a single unit is on order, the allocation of a unit ready to be delivered is determined by the solution of a dynamic programming problem. When only a single unit is on order (and this is the one ready to be delivered), the optimal allocation procedure is reduced to allocating the unit to the depot which has the greatest probability of using it in a time period T + (1/λ) where T is the procurement lead time and λ the system demand rate for the item.

This paper is concerned with the optimum decision variables found using order quantity, reorder point (Q, R) inventory models. It examines whether the optimum variables (Q* and R*) are necessarily monotonic functions of the backorder cost parameter (or equivalently of the performance objective). For a general class of models it is proved that R* must increase as the performance objective is raised, and an inequality condition is derived which governs how Q* will change. Probability distributions of lead time demand are cited or found for which Q* increases, Q* decreases, and Q* is independent of increases in performance objectives or backorder cost parameter.

IN A FULL-EMPLOYMENT economy a firm's bankruptcy is prima facie evidence of resource misallocation. This is not to say, however, that the authorities should adopt every policy which minimizes bankruptcy. Fostering monopolies to reduce failures, for example, only increases the misallocation of resources. In one sense bankruptcy is desirable for it prevents further losses. But it is nevertheless true that a change of policy, voluntary liquidation, or any other method of eliminating losses at an early date would be preferable to bankruptcy from both a social and private viewpoint. Predicting failures, due to whatever cause, reduces the length of time losses are incurred and the misallocation of resources. The following section briefly discusses the causes of bankruptcies. Section II presents the empirical results. To screen potential failures from viable firms, we calculated regression equations in which the regressand is dichotomous and the regressors are the value and trend of selected balance sheet and income variables. The regressions differ in the number of independent variables and in the lead time of the data to failure. The regressions are significant though, as expected, their explanatory power is negatively related to the time period the data lead bankruptcies. Section III demonstrates the ability of these functions to classify solvent and closed firms and to predict the proper classification of a randomly selected holdout sample. We also illustrate how efficient regulatory policy should be formulated. While the techniques used in this paper could be applied to an analysis of bankrupt firms in any industry, our sample industry is banking.' The sample is particularly appropriate for two reasons. First, since defalcation explains a substantial proportion of bank failures in the post-World War II period, the banking industry provides an especially strict test of the predictive value of financial ratios, as will be explained more fully in Section I.2, 3 Second, federal

A key factor in establishing inventory policy for an item is the procurement lead time demand distribution (LTDD). Demand during lead time is a random variable if at least one of the components-length of lead time, order intensity, and order size-is a random variable. This paper discusses the problem of estimating the functional form of the LTDD for various combinations of the component random variables, using the method of generating functions. Since a normal approximation will often be used in practice, expressions are also given for the mean and variance of the LTDD for the various cases.

We consider a single product dynamic inventory problem in which the demands in each period are independent and identically distributed random variables. There is a constant lead time, a discount factor 0 ≦ α ≦ 1, a unit ordering cost c and an expected holding and penalty cost function L(·) for which −[c(l − α)y + L(y)] is unimodal, and total backlogging of unfilled demand. In addition each order for stock must be in some nonnegative integral multiple of Q, a fixed positive constant. It is shown that the (k, Q) policy is optimal for the finite and infinite period models. With the (k, Q) policy if the initial inventory on hand and on order in a period is less than k, an order is placed for the smallest multiple of Q that will bring the inventory on hand and on order to at least k; otherwise, no order is placed. The optimal value of k is easy to compute and is the same for the finite and infinite period models. The results are generalized to the case where the demand distributions and cost functions vary over time. The (k, Q) policy is not optimal in general for the case where there is also a fixed charge for placing an order.

A study is made of a dynamic inventory model with stochastic lead times. A probability model is developed for the arrival of outstanding orders in which it is assumed that orders do not cross in time and that the arrival probabilities are independent of the number and size of outstanding orders. With these assumptions, it is shown that the sequential multidimensional minimization problem normally associated with the random lead time model can be reduced to a sequence of one-dimensional minimizations. The minimizations are a function of a variable representing the sum of stock on hand plus all outstanding orders. Optimal ordering policies are characterized under the assumptions of convex expected holding and shortage costs, a linear ordering cost and a fixed setup cost (greater than or equal to zero) paid when the order is placed. These policies are shown to be quite similar to those obtained with deterministic lead times but some differences in the behavior of the single-period critical numbers (when the setup cost is zero) are noted.

Information systems serve in a variety of ways in military environments but have the common objectives of supporting decision processes. Systems engineers have had difficulty in developing automated systems for this purpose because of the amount of lead time required to analyze a problem situation, to procure hardware and to design and prepare computer programs, and because the problems and the problem situation are highly dynamic. Extrapolating requirements for some time in the future from current problems and methods of operation have tended to result in inadequate or incomplete systems designs when systems are developed and tested against the actual requirements in an operational environment. A variety of approaches to system development have been employed. These have ranged from the "job shop" approach at one extreme to the "turn-key" approach at the other. The job shop approach is typified by many independent, special-purpose programs, each written to perform a particular job with its own data base. The programs are executed under job controls established by machine operators. New capabilities are developed and operated in the same way. This approach is usually responsive to individual staff elements since each program is designed for the specific purpose of the particular group which will have considerable input to the design, a good knowledge of the logic employed, and confidence in the products obtained from it. It has growth potential limited only by total machine capacity. Operational capability is provided and can be evaluated with relatively short lead time.

With the advent of new miniaturized mercury (Hg) switches with reputed transition times of the order of 10 ps, interest has been rekindled in their use in high-peed pulse measurements. Since there is no pretrigger signal available from a Hg switch, normal sequential sampling techniques are not useable to measure the fast Hg switch transition time. For this reason, a new random sampling time base unit was designed to perform these measurements at the low repetition rate of Hg switches. The time base may be used with commercial sampling oscilloscope systems through suitable interconnection terminals or possible interface equipment. It features three selectable time windows of 1 jus, 100 ns, and 10 ns. Using its time magnifier, the fastest sweep rate is 10 ps/cm. A variable trigger lead time control is provided. The trigger sensitivity is 5 mV.

This paper presents the adjustments in current theory of inventory that were required in a specific case. The demand during lead time was found to be skewed to the extent that it could not be represented by a two-parameter distribution. This skewness was handled by an augmentation of the standard deviation of the lead time demand. The analysis involving runout costs was complicated by the fact that, when one warehouse was short, it was possible sometimes to induce a customer to accept the delay inherent in delivery from another warehouse.

This article shows that a formula commonly used for establishing safety stocks can lead to erroneous results, particularly when the magnitude of forecast errors over a replenishment lead time is large in comparison with the replenishment quantity. A correct procedure involving only slightly more computational effort is developed. Numerical results are provided for the case of normally distributed forecast errors.

In controlling stock it is necessary to make some estimate of future demand for each stock item. Exponential smoothing is a convenient and automatic means of making such an estimate and the optimal choice of the smoothing constant alpha will depend upon the order of smoothing employed, the relative magnitudes of the random and systematic variations in demand which may occur, the replenishment lead time and also the manner in which the rule used for generating replenishment orders is formulated. The dependence both of optimal alpha and of the necessary safety stock upon these factors has been investigated by means of a model which is believed to be of wide application in industry, and a method has been developed for setting up decision rules for both single and multi-stage systems.

The order cycle system of stock control can be formulated as follows: demands for stock occur according to some pattern which we call the demand process and specify in detail later in this section. At fixed intervals of time orders are placed to replenish stock. Let orders for stock be placed at the instants jN, j = 1,2, …; the interval [(j — 1)(N, jN) which we suppose closed at its lower end-point and open at its upper end-point, is called the j-th order cycle and N the length of this interval is called the order cycle period. We suppose that an order placed at time jN is delivered into stock at time jN + li where {li} is a sequence of non-negative random variables independent of the demand process and the order cycle period, we suppose also that the li are mutually independent and identically distributed with common distribution function L(x) with L(0 +) = 0 and finite expectation . The quantity li is called the lead time of the j-th order, that is of the order placed at jN and is supposed independent of the amount ordered. That portion of a demand, if any, which cannot be satisfied immediately is satisfied from future deliveries, thus every demand is satisfied eventually and a negative inventory or back orders can be held. We shall suppose that all order cycle periods under consideration are multiples of some fixed time interval of length τ which we shall take as our unit of time. For example, the interval of length τ could be one day and we would consider order cycle periods which were integral multiples of days. For convenience we take τ = 1 and suppose that the order cycle peiod N is an integer. In this paper we shall consider the following two demand processes.

Summary The infinite period stationary inventory model is considered. There is a constant lead time, a nonnegative set-up cost, a linear purchase cost, a holding and shortage cost function, a fixed discount factor β, 0 < β < 1, and total backlogging of unfilled demand. Both the total discounted cost (β < 1) and the average cost (β= 1) criteria are considered. Under the assumption that the negatives of the one period holding and shortage costs are unimodal, a unified proof of the existence of an optimal (s.S) policy is given. As a by-product of the proof upper and lower bounds on the optimal values of s and S are found. New results simplify the algorithm of Veinott and Wagner for finding an optimal (s, S) policy for the case β< 1. Further it is shown that the conditions imposed on the one period holding and shortage costs can be weakened slightly.

Design of a groundwater data collection system requires the recognition of several important concepts. (1) Groundwater is not an isolated resource; precipitation and surface water are important boundary conditions and water quality is an essential parameter. (2) Most groundwater data are not transferable; thus the network must be based on unique programs for each basin. (3) Data needs must relate to the anticipated stress on the basin, and stress should be related to time, both lag time in the response to hydrologic stress, and lead time needed by management. (4) Cost of data is related to data density and accuracy so program design must consider levels of funds. (5) The relatively small time variability and pronounced spatial variability of the environmental factors necessitates major emphasis on the appraisal of areal units. (6) The parametric data needed for completing areal investigations at several levels of study are based on physical, hydrologic, and chemical heterogeneity coefficients derived for each basin. (7) Ultimately the complexity of the water use and the resulting changes of the system, in relation to the undeveloped state, will be such that first generation models of the groundwater basin can no longer supply answers to the intricate and complex questions needing answers. A management model of each heavily stressed basin will be needed to ensure that data collection programs fulfill the requirements imposed by the economic, political, legal, social, and hydrologic constraints.

Two periodic review inventory models, (R, T) and (nQ, r, T), are analyzed for the situation where demands are characterized by either a Poisson or stuttering Poisson process. In each model, backorders are allowed and the procurement lead time is considered to be a constant. Average annual cost equations are developed for each model and solution techniques presented, so that minimum average annual costs can be determined. A numerical example is also presented. It is shown for large times between reviews that the (R, T) and (nQ, r, T) models are essentially equivalent.

PLANNING LAW COVERS ALL THOSE METHODS OF IMPLEMENTING PLANNING DECISIONS WHICH INVOLVE THE USE OF LEGAL DEVICES. THIS REVIEW INCLUDES THE MORE IMPORTANT COURT CASES REPORTED DURING 1965. BECAUSE OF THE LEAD TIME INVOLVED BETWEEN THE DECISION IN A CASE AND ITS REPORTING, SOME OF THESE CASES WERE IN FACT DECIDED IN 1964 OR EARLIER. WHERE DECISIONS DISCUSSED HERE HAVE COME FROM LOWER OR INTERMEDIATE COURTS, THAT FACT IS NOTED. /AUTHOR/

This paper discusses the development and application of a multiple reorder inventory policy which can be stated as follows: reorder an optimal lot size Q when inventory (stock on hand) falls to R, R-Q, R-2Q,..., R-NQ; where R is the reorder level. If demands cause the inventory to fall below two reorder levels, say a jump from R+ ɛ to R-2Q+ɛ′ where ɛ and ɛ′ 0·5) and continuous inventory records are maintained. Tables, charts and nomographs to simplify clerical tasks can be obtained quite readily. In this formulation R and Q are not independent factors as in the usual Wilson formulation, but are obtained by minimizing a single cost functional subject to the constraint of a specified risk of out-of-stock condition or a specified level of service (Galliher and Simmond, 1957), (Morse et al., 1959). The particular application concerns the raw material inventories of a manufacturer of metal pressings who is required to offer “immediate service”. The demand distribution during the lead time closely approximates the exponential distribution, and lead times are constant for each raw material. The application of the multiple reorder policy results in a 30 to 35 per cent reduction in inventory for a 95 per cent service level. Measures of sensitivity and response are obtained, and the mean number of shortages is expressed in closed form. The policy is compared with the Wilson policy and shown to be more “effective” in that it results in lower inventories and a smaller number of orders for the case considered.

This paper considers dynamic single- and multi-product inventory problems in which the demands in each period are independent and identically distributed random variables. The problems considered have the following common characteristics. At the beginning of each period two order quantities are determined for each product. A “normal order” quantity with a constant positive lead time of λn periods and an “emergency order” quantity with a lead time of λe periods, where λe = λn - 1. The ordering decisions are based on linear procurement costs for both methods of ordering and convex holding and penalty costs. The emergency ordering costs are assumed to be higher than the normal ordering costs. In addition, future costs are discounted.

The paper is divided along the following lines. First, I illustrate the inventory models having Deterministic Demand and then consider the class of Probabilistic Demand Models. Within the latter class, I consider the single period steady state case, and then the N-period dynamic inventory model. For the N-period case, I then report results covering non-zero procurement lead time, demand rate varying each period, joint solution of the inventory-control-production scheduling decision, and a multi-echelon model. Finally, since in the previous consideration of probabilistic demand models, knowledge of the demand probability distribution and its parameters were assumed, I discuss a paper dealing with the use of Bayes estimates.

OVER the next several years, profits of manufacturers of electrical equipment should rise substantially as a result of the combined effects of rising sales, increasing prices and reductions in manufacturing costs. The demand for electrical equipment is expected to increase rapidly for the next several years. Purchases of generation, transmission and distribution equipment by utilities should rise significantly with the steady growth of the consumption of electricity and increasing number of large-scale power pools. Residential, commercial and industrial demand for electrical equipment should expand with prospects of rising housing starts and higher capital outlays for expansion, modernization and automation of factories and offices. With the increase in volume over the last several years, prices of electrical products have strengthened from severely depressed levels, and further improvement is expected. However, because of the long lead time on heavy-duty electrical equipment, the benefits to earnings from price improvements in the past three years are only now beginning to be reflected in earnings, and therefore, the rising trend of prices since 1962 should continue to be reflected in higher margins for several years to come. During the period of severe price competition and particularly since 1960, electrical equipment manufacturers invested heavily in new plants and more efficient machinery to reduce costs in the face of substantial declines in earnings from the lower volume and prices. For the next decade, the electric utility industry forecasts the use of electricity to rise at about 6.8%/4 a year, nearly a doubling of power consumption by 1975. This rapid growth, which parallels the historic growth rate, is based on many factors, including greater housing needs of a larger population, continued growth of the use of electrical appliances, expanded commercial facilities, and continued heavy outlays for new manufacturing machinery and equipment. To supply this increasing market for electricity, the demand for electrical generating, transmission and distribution equipment should rise at about 5%,,-7%c a year for the next several years. This improved operating environment will create rising earnings for the electrical equipment manufacturers.

Prior to the start of any precast concrete project a complete review of contract requirements is necessary. Contract requirements usually encompass the architectural and structural plans, the project specifications, and the precast firm's proposal defining the conditions of the contract. It is most important that the contract proposal be carefully reviewed. Many times items are deleted or additional considerations are involved. Sometimes the precaster furnishes his product FOB job-site and this has an important bearing on the overall requirements of the project. The contract requirements should be checked carefully to discover any special conditions that may exist. For example, special conditions may concern the hardware cast into the panels, the hardware used to attach the panels, the limitations posed by the project relative to the overall production (e.g., certain items required prior to others), or the specified delivery dates. Job organization. The first step toward job organization is to locate and define all of the precast concrete members required. Next, a thorough review should be made to determine what standardization can be achieved. Standardization is desirable not only for ease of fabrication and erection, but also for general improvement of the job. Often the job can be made less costly by slightly altering the materials, the shapes or the design. Erection procedures also must be checked during this initial review because they can exert considerable influence on the way a job is to be handled. Before shop drawings are started, engineering personnel should meet with production and erection people to discuss overall job problems as well as possible modifications or changes. At this time it may be advisable to meet with the contractor and architect to examine and agree upon any desired changes. The amount of lead time available for the project must be calculated at this stage because production availability may be the prime factor in organizing the job. The

The application of probability methods in power system reliability evaluation started over thirty years ago. The bulk of the work has been in the static capacity area and the first major paper on spinning reserve evaluation appeared in 1962(1). A second paper(2) illustrated the application of this approach in a medium size utility. Both these papers illustrated the development of a risk index which includes the probabilities of capacity deficiencies and unforeseen load conditions. In a more recent paper(3), Markov processes were used to determine the transient probabilities associated with a generating unit containing a single derated state. The general expressions are rather complicated and it is difficult to extend this approach to include units with more than one derated state. The discussion to Reference 3 proposes a state space model which assumes that the lead times are small relative to the unit repair times and therefore it is reasonable to assume that no repairs will be made during this lead time. This method though approximate can be applied to units with several derated states.

Budget and technical considerations require the formulation of specific criteria in designing water level data networks that are to be measured over a long time period. Specific purposes or uses of longtime water levels relate to various intensities of hydrologic studies. Specific criteria in terms of measurement frequency and observation point density for purposes of storage and storage fluctuation for five intensities of hydrologic investigations were developed subjectively and are presented, each related to needed geologic detail. The lead time for data collection varies from 1 to 15 years, depending on the intensity of the study and the resulting decision type. Application of the criteria in California's groundwater basins confirms the utility of the concept, but identifies the need for a definition of accuracies of contour maps constructed from various point densities and other study input, for close control of measurement points, for broad judgment at boundaries, and for specifications of needed accuracy of interpreted information by users.

Open burning of retired railroad freight cars has been the accepted practice for removing the wood to prepare metal components for scrap and salvage operations. New legislation and enforcement zeal threaten the survival of the dismantling industry unless economical alternative methods involving acceptable emission levels are employed. A search for technologically feasible alternatives produced a listing of 39 methods, ranging from simple modifications of existing practice to complex automated, fully mechanized systems. All of the alternative methods satisfied the requirement that pollutant emission be at legally acceptable levels or entirely eliminated. A second requirement of short lead time for implementation led to the rejection of experimental processes and fully mechanized, automatic systems at this time. On the basis of eight other cost-effectiveness criteria, a qualitative screening resulted in the rejection of all but eleven methods. These final, candidate methods were evaluated by application of a forced decision model often used in value engineering. The eight criteria and eleven candidate methods were the arguments of a two-dimensional distribution matrix in which the scores were determined from the decision model exercise. The two highest scoring methods were emission-controlled wood incineration within the confines of each car by means of a special stack or hood configuration; and the use of high-pressure water jets to out away the wood. These methods have been demonstrated in principle by actual field tests performed on box cars in scrap yards. (Authors' Abstract)

Medical manpower projections indicate that by 1991 there will be one doctor to 500 population instead of the 1: 721 ratio in 1976. There are many variables; projections, while hazardous, are necessary for planning because of the long lead time. Productivity is equally important. There is no evidence that the rapidly rising female intake will reduce productivity in the next 15 years.

THIS PAPER HAS a twofold purpose. The first is to evaluate the impact of federal expenditure and tax policies during the 1957-60 recession and recovery. The second is to explore the possible effect that alternative expenditure and tax policies might have had on economic stability during this period. The paper tries to answer two questions: What were the shortcomings of fiscal policy during the 1957-60 recession and recovery? To what extent might it be possible to remove these shortcomings in the future and therefore increase the effectiveness of fiscal measures as a countercyclical force? The analysis of 1957-60 fiscal policy will be carried out in Part II. It will be argued that the major shortcoming of this policy was the timing of discretionary expenditure measures. To a large extent, these discretionary measures were either not taken until the recession trough had been reached or, if they were taken before the trough, produced the great bulk of their effects after the trough. Relatively little scope appears to exist for increasing the built-in flexibility of the fiscal system, which, indeed, turned in a fairly good performance. The long lead time between the enactment of discretionary fiscal measures and their impact on public and private spending, however, poses a difficult problem in the effective use of the fiscal system as an instrument for combating recession. Part III of the paper attempts to assess three different approaches that have been urged as solutions to this problem of the long lead time of discretionary expenditures. These approaches are (1) the

Consider an inventory item for which the procurement (or production setup) lead time is nonzero. One of the commonly used methods of determining the reorder point of such an item is to specify the probability of a stockout or a desired service level (fraction of demand that is to be instantaneously satisfied) and then select the reorder level that will provide such service. However, such an approach has assumed that the probability distribution of demand during the lead time is exactly known. In many inventory situations this assumption is not justified, particularly in the case of a slow moving item with limited available sales history. For such a situation this paper explores the use of a Bayesian approach to selecting a reorder point.

The two inventory echelons under consideration are the depot, D, and k tender ships E1, …, Ek. The tender ships supply the demand for certain parts of operational boats (the customers). The statistical model assumes that the total monthly demands at the k tenders are stationary independent Poisson random variables, with unknown means λ1, …, λk. The stock levels on the tenders, at the heginning of each month, can be adjusted either by ordering more units from the depot, or by shipping bach to the depot an excess stock. There is no traffic of stock between tenders which is not via the depot. The lead time from the depot to the tenders is at most 1 month. The lead time for orders of the depot from the manufacturer is L months. The loss function due to erroneous decision js comprised of linear functions of the extra monthly stocks, and linear functions of shortages at the tenders and at the depot over the N months. A Bayes sequential decision process is set up for the optimal adjustment levels and orders of the two echelons. The Dynamic Programming recursive functions are given for a planning horizon of N months.

A computerized cost-minimization model was used to study the importance of lead time unreliability (variability of lead time from mean lead time) in inventory management. Using different combinations of stockout cost, demand variability, mean lead time, and variability of lead time around the means, changes in optimum safety stock and in inventory costs were observed. Lead time unreliability was found to be of greater importance than either the mean lead time or the variability of demand in explaining inventory cost behavior. Managers and researchers involved in the development of inventory theory are urged to note the great financial damage that may result from ignoring lead time unreliability; a dollar measure of this penalty is included in the presentation.

This is an unclassified treatment of some problems in military worth which arise in the development of large systems. Recent studies in measures of effectiveness and value theory have been used to define this part of the discussion. Although the discussion will have points in common with many “large” systems, the model used in this discussion is a typical real-time digital data system for executive use. Factors and constraints such as fund limits, pricing, service life, lead time and environment are treated. A typical practical attack on the problem of measuring the military worth of such a system is included. Most systems in this class have not yet accumulated sufficient life in service for measurement and determination of results of plans to “maximize” their military worth. Accordingly, this part of the discussion is restricted to some suggestions concerning defining and measuring military worth of these systems.

An exact expression for protection and potential lost sales is obtained for a reorder level system of inventory control in which the demand is normally distributed and the lead time gamma distributed. The accuracy of an approximate method is explored.

This paper develops a linear periodic review inventory model in which the reorder rule is an extension of the “order up to S” or (S, T) policy where S varies as a general linear function of demand and net inventory. Stationary and non-stationary demand processes are considered. Lead time is assumed to be an integral multiple of the review period and, at most, an independent and identically distributed random variable. Analysis of the model includes stability, transient response, steady-state response, and the effects of common nonlinearities.

The objective of this paper is to determine the optimum inventory policy for a multi-product periodic review dynamic inventory system. At the beginning of each period two decisions are made for each product. How much to “normal order” with a lead time of λn periods and how much to “emergency order” with a lead time of λe periods, where λe = λn - 1. It is assumed that the emergency ordering costs are higher than the normal ordering costs. The demands for each product in successive periods are assumed to form a sequence of independent identically distributed random variables with known densities. Demands for individual products within a period are assumed to be non-negative, but they need not be independent. Whenever demand exceeds inventory their difference is backlogged rather than lost. The ordering decisions are based on certain costs and two revenue functions. Namely, the procurement costs which are assumed to be linear for both methods of ordering, convex holding and penalty costs, concave salvage gain functions, and linear credit functions. There is a restriction on the total amount that can be emergency ordered for all products. The optimal ordering policy is determined for the one and N-period models.

Summary The periodic review, single item, stationary (s, S) inventory model is considered. There is a fixed lead time, a linear purchase cost, a fixed set‐up cost, a holding and shortage cost function, a discount factor 0 < α≤ 1 and backlogging of unfilled demand. The solution for the total expected discounted cost for the finite period (s, S) model is found. In addition the time dependent behaviour of the inventory process is found. Further a limit theorem is given, which relates the total expected cost for the finite period (s, S) model with no discounting to the average expected cost per period for the infinite period (s, S) model. As a by‐product we obtain known results for the infinite period (s, S) model. Copyright

In new military systems, the development time required must be made as short as possible. In examining this critical problem, perhaps it is useful to first attempt to separate those elements of lead-time of an organizational or administrative nature from those primarily associated with technology. This paper recognizes the importance of administrative lag factors, but focuses its attention on suggestions for more realistically estimating technological lags.