Showing papers in "Management Science in 1960"
TL;DR: The paper presents a method of forecasting sales which has these desirable characteristics, and which in terms of ability to forecast compares favorably with other, more traditional methods.
Abstract: The growing use of computers for mechanized inventory control and production planning has brought with it the need for explicit forecasts of sales and usage for individual products and materials. These forecasts must be made on a routine basis for thousands of products, so that they must be made quickly, and, both in terms of computing time and information storage, cheaply; they should be responsive to changing conditions. The paper presents a method of forecasting sales which has these desirable characteristics, and which in terms of ability to forecast compares favorably with other, more traditional methods. Several models of the exponential forecasting system are presented, along with several examples of application.
1,773 citations
TL;DR: The problem of determining optimal purchasing quantities in a multi-installation model of this type, which arises when there are several installations, is considered.
Abstract: In the last several years there have been a number of papers discussing optimal policies for the inventory problem. Almost without exception these papers are devoted to the determination of optimal purchasing quantities at a single installation faced with some pattern of demand. It has been customary to make the assumption that when the installation in question requests a shipment of stock, this shipment will be delivered in a fixed or perhaps random length of time, but at any rate with a time lag which is independent of the size of the order placed. There are, however, a number of situations met in practice in which this assumption is not a tenable one. An important example arises when there are several installations, say 1, 2,..., N, with installation 1 receiving stock from 2, with 2 receiving stock from 3, etc. In this example, if an order is placed by installation 1 for stock from installation 2, the length of time for delivery of this stock is determined not only by the natural lead time between these two sites, but also by the availability of stock at the second installation. In this paper we shall consider the problem of determining optimal purchasing quantities in a multi-installation model of this type.
1,462 citations
TL;DR: This work presents an original method, going beyond the limits of classical mathematical analysis, for solving extremal problems and provides an application of mathematical methods to questions of organizing production which merits the serious attention of workers in different branches of industry.
Abstract: The author of the work “Mathematical Methods of Organizing and Planning Production”, Professor L. V. Kantorovich, is an eminent authority in the field of mathematics. This work is interesting from a purely mathematical point of view since it presents an original method, going beyond the limits of classical mathematical analysis, for solving extremal problems. On the other hand, this work also provides an application of mathematical methods to questions of organizing production which merits the serious attention of workers in different branches of industry.
This is the English translation of the famous 1939 article by L. V. Kantorovich, originally published in Russian.
758 citations
TL;DR: In this paper, a typical sequential probabilistic model may be formulated in terms of a an initial decision rule and b a Markov process, and then optimized by means of linear programming.
Abstract: Using an illustration drawn from the area of inventory control, this paper demonstrates how a typical sequential probabilistic model may be formulated in terms of a an initial decision rule and b a Markov process, and then optimized by means of linear programming. This linear programming technique may turn out to be an efficient alternative to the functional equation approach in the numerical analysis of such problems. Regardless of computational significance, however, it is of interest that there should be such a close relationship between the two traditionally distinct areas of dynamic programming and linear programming.
469 citations
TL;DR: In this article, a dynamic inventory model is formulated in which the demand distributions may change from period to period, and the optimal policy at each stage is characterized by a single critical number which also could vary in successive periods.
Abstract: A dynamic inventory model is formulated in which the demand distributions may change from period to period. The optimal policy at each stage is characterized by a single critical number which also could vary in successive periods. The dependence of the critical numbers as a function of stochastic ordering amongst distributions is developed under various conditions. Most of the studies are conducted under the assumption of linear purchasing cost. In §3 the possibility of convex purchasing cost is allowed.
303 citations
TL;DR: In this paper, conditions are given for the equality of the expected value of the objective function for the optimal solution and the value for the approximate solution; bounds on these values are also given.
Abstract: Consider a linear-programming problem in which the “right-hand side” is a random vector whose expected value is known and where the expected value of the objective function is to be minimized. An approximate solution is often found by replacing the “right-hand side” by its expected value and solving the resulting linear programming problem. In this paper conditions are given for the equality of the expected value of the objective function for the optimal solution and the value of the objective function for the approximate solution; bounds on these values are also given. In addition, the relation between this problem and a related problem, where one makes an observation on the “right-hand side” and solves the nonstochastic linear programming problem based on this observation, is discussed.
263 citations
TL;DR: In this paper it is shown that a solution can be obtained by linear programming methods and this paper is of an expository nature.
Abstract: The problem of production and employment scheduling may be stated as follows. Given the monthly demands for the product turned out by a factory, what should be the monthly production rates and work force levels in order to minimize the total cost of regular payroll and overtime, hiring and layoffs, inventory and shortages incurred during a given planning interval of several months? This problem has received a classical solution in two papers by Holt, Modigliani, Muth, and Simon (Holt, C. C., F. Modigliani, H. A. Simon. 1955. A linear decision rule for production and employment scheduling. Management Sci. (October); Holt, C. C., F. Modigliani, J. F. Muth. 1956. Derivation of a linear decision rule for production and employment. Management Sci. (January).). These authors assumed quadratic cost functions. Their treatment of the problem will be referred to as “quadratic programming.” It appears, however, that in the majority of practical applications and theoretical models the cost functions are assumed to be...
231 citations
TL;DR: This paper refines proposals to give what is believed to be the shortest procedure for finding the shortest route when it is little effort to arrange distances in increasing order by nodes or to skip consideration of arcs into nodes whose shortest route to the origin has been determined earlier in the computation.
Abstract: The chief feature of the method is that it fans out from the origin working out the shortest path to one new node from the origin and never having to backtrack. No more than nn-1/2 comparisons are needed to find the shortest route from a given origin to all other nodes and possibly less between two fixed nodes.
Except for details and bias of various authors towards a particular brand of proof, this problem has been solved the same way by many authors. This paper refines these proposals to give what is believed to be the shortest procedure for finding the shortest route when it is little effort to arrange distances in increasing order by nodes or to skip consideration of arcs into nodes whose shortest route to the origin has been determined earlier in the computation.
In practice the number of comparisons is much less than indicated bounds because all arcs leading to nodes previously evaluated are deleted from further consideration. A further efficiency can be achieved in the event of ties by including least distances from origin to many nodes simultaneously during the fanning out process. However, these are shown as separate steps to illustrate the underlying principle.
218 citations
IBM1
TL;DR: This is a report of the results of some digital computer simulation studies of a simplified model of a job shop production process that found the average manufacturing times and predictability of completion times were used as measures of effectiveness.
Abstract: This is a report of the results of some digital computer simulation studies of a simplified model of a job shop production process. Such factors as the average effectiveness of schedules under the impact of random variations in processing times and the effect of changing operating policies are considered. The average manufacturing times and predictability of completion times were used as measures of effectiveness.
116 citations
TL;DR: In this paper, the authors describe a procedure to maximize a strictly concave quadratic function subject to linear constraints in the form of inequalities, where the unconstrained maximum is considered; when certain constraints are violated, maximization takes place subject to each of these in equational (rather than inequality) form.
Abstract: The article describes a procedure to maximize a strictly concave quadratic function subject to linear constraints in the form of inequalities. First the unconstrained maximum is considered; when certain constraints are violated, maximization takes place subject to each of these in equational (rather than inequality) form. The constraints which are then violated are added in a similar way to the constraints already imposed. It is shown that under certain general conditions this procedure leads to the required optimum in a finite number of steps. The procedure is illustrated by an example while also a directory of computations is given.
107 citations
TL;DR: In this paper, a heuristic procedure for balancing production assembly lines and a computer program for carrying out that procedure is presented. But this procedure is restricted to a single assembly process made up of elemental tasks with a time required per unit of product and an ordering with other tasks.
Abstract: This paper presents a heuristic procedure for balancing production assembly lines and a computer program for carrying out that procedure. This research was undertaken to investigate the application of complex information processing techniques (as used in producing the Chess Machine and Logic Theorist) to a typical industrial problem. The assembly line balancing problem is stated as: Given an assembly process made up of elemental tasks, each with a time required per unit of product and an ordering with other tasks, what is the least number of work stations needed to attain a desired production rate? The heuristic procedure for assembly line balancing consists of three phases: repeated simplification of the initial problem by grouping adjacent elemental tasks into compound tasks; solution of the simpler problems thus created by assigning tasks to work stations at the least complex level possible, breaking up the compound tasks into their elements only when necessary for a solution; smoothing the resulting b...
IBM1
TL;DR: In this paper, the problem of specifying an allowance for defects in a production lot is that of balancing the cost of producing too many items against the risk of not having enough to meet requirements.
Abstract: The problem of specifying an allowance for defects in a production lot is that of balancing the cost of producing too many items against the risk of not having enough to meet requirements. A model of these costs is here proposed.
Sufficient conditions are developed on the probability distribution of defectives for total cost to have a single minimum with respect to the allowance. A sequential algorithm is investigated and shown to produce an optimum allowance if certain further conditions on the probability are met. Next, it is shown for a special class of probability distributions that the above conditions are satisfied. This class is that for which the probability of an item being defective is independent of previous defects in the lot, and includes the binomial distribution. Finally some computational aspects of this algorithm are discussed, and an easily computable starting value is given.
TL;DR: In this paper, a linear programming formulation for on optimal steady state solution of sequential decision models has been proposed and a proof that an optimal solution exists involving only pure strategies is given.
Abstract: In Manne [Manne, A. S. 1960. Linear programming and sequential decisions. Management Sci. April.] has suggested a linear programming formulation for on optimal steady state solution of sequential decision models. In this note we offer a proof which appeals primarily to the properties of linear programs that an optimal solution exists involving only pure strategies.
TL;DR: Discussion on two early papers of Professor Kantorovich, from 1939 and 1949, that proved to be remarkable documents in the history of management science, of linear programming, and of economic theory in general.
Abstract: Discussion on two early papers of Professor Kantorovich, from 1939 and 1949, that proved to be remarkable documents in the history of management science, of linear programming, and of economic theory in general. The 1949 paper discusses transportation models for a single commodity and for many commodities including empty vehicles, and a single-commodity model for a capacitated network, with applications to sections of the Russian railroad network. All problems considered in the 1939 paper reprinted in this issue are what would now be called linear programming problems. The coefficient matrices of the problems labeled “A” and “B” exhibit special structures somewhat similar to that of the transportation problem matrix. Problem “C,” while appearing still to have a somewhat special structure, is in fact equivalent to the general linear programming problem.
TL;DR: In this paper, the problem of allocation under uncertain demand, when the latter has a continuous distribution function, is treated and a necessary and sufficient condition for optimality is given, and a numerical example is solved.
Abstract: The problem of allocation under uncertain demand, when the latter has a continuous distribution function, is treated. A necessary and sufficient condition for optimality is given, and a numerical example is solved. This solution is compared with the L.P. solutions obtained under the assumptions of constant demand and demand with discrete d.f. It is seen that considerable savings can be realized by considering d.f.'s as continuous if they so occur in nature.
TL;DR: This paper makes use of a device proposed by Fulkerson and Ford for maximal multi-commodity network flows and develops a compact network representation of the set of possible activities which permits generating just the activity to enter the basis on each iteration without explicitly generating the others.
Abstract: This paper makes use of a device proposed by Fulkerson and Ford for maximal multi-commodity network flows Ford, L. R. Jr., D. R. Fulkerson. 1958. A suggested computation for maximal multi-commodity network flows. The RAND Corporation, Paper P-1114, March 27, 1958. Also Management Sci.51 97--101.. A machine-job scheduling model is formulated that avoids the usual in-process inventories and thereby has fewer equations. The activities are the possible sequence for each job of machine steps and interspersed delays; this, of course, greatly multiplies the number of activities. However, a compact network representation of the set of possible activities is developed which permits generating just the activity to enter the basis on each iteration without explicitly generating the others. This is done by using one of the efficient procedures that now exist for computing the shortest route through a network Dantzig, George B. 1960. On the shortest route through a network. Management Sci.62; Moore, E. F. The shortest path through a maze. Unpublished mimeographed report, 16 pages; Bellman, Richard. 1958. On a routing problem. JORSA, XVI1 87--90., Ford, L. R. Jr. 1956. Network flow theory. The RAND Corporation, Paper P-923.
TL;DR: In this paper, the authors investigate how the theory of self-regulating systems applies to human organizations in general and to one industrial plant in particular, finding that feedbacks of information on performance and objectives have much influence on two types of executive decision processes: programming of routine work and innovation in the organization of executive functions.
Abstract: The research reported is an attempt to discover to what extent the theory of self-regulating systems applies to human organizations in general and to one industrial plant in particular. Feedbacks of information on performance and objectives were found to have much influence on two types of executive decision processes: programming of routine work and innovation in the organization of executive functions. The control pattern included multiple, decentralized control loops. This combination worked adequately in an area---safety---where the results of decisions could not be forecasted with any accuracy.
TL;DR: A survey of the current relationship between the many different problem areas investigated by means of Game Theory and the study of Industrial Organization is presented.
Abstract: A survey of the current relationship between the many different problem areas investigated by means of Game Theory and the study of Industrial Organization is presented. Several examples are provided to illustrate the nature and relevance of work on 1 two-person constant-sum games; 2 the extensive form of a game; 3 theories of solution for n-person games; 4 theories of solutions for games against nature; and 5 theories of solution for dynamic games. The nature and state of the current applications of game theory to organizational problems and to parts of the behavorial sciences are summarized.
TL;DR: An illustration concerned with the allocation of an advertising budget among competing media will be presented and an attempt will be made to show the relationship between demand and production theory on the one hand and programming on the other.
Abstract: Much of the importance of the new dynamic programming methods has remained unnoticed because of the apparent complexity of the underlying mathematics. This is indeed unfortunate because the essence of the programming methods for certain classes of problems is not new to practicing economists. Dynamic programming methods can provide an efficient computational algorithm for problem types frequently encountered in consumer demand and production theory. In this paper the following approach will be utilized. First, an illustration concerned with the allocation of an advertising budget among competing media will be presented that will enable the reader to study the relationship between dynamic programming and simple combinatorial analysis. Second, an attempt will be made to show the relationship between demand and production theory on the one hand and programming on the other. Third, an advertising budget allocation problem much like the simpler one discussed in the first section will be cast in terms of the dy...
TL;DR: It is pointed out that many industrial problems which involve optimization, may be characteristically similar, and it is desirable to study the sesitivity of the function to be optimized by computing an optimal range, for which a general approximation is suggested.
Abstract: With reference to previous publications on the advisability of defining an economic production range in case of batch production, it is pointed out that many industrial problems which involve optimization, may be characteristically similar. It is therefore desirable to study the sesitivity of the function to be optimized by computing an optimal range, for which a general approximation is suggested.
TL;DR: This paper describes an algorithm for the solution of mathematical programming problems having a linear objective function and non-linear constraints, basically an adaptation of the simplex method to the case of non- linear constraints.
Abstract: This paper describes an algorithm for the solution of mathematical programming problems having a linear objective function and non-linear constraints. The algorithm is basically an adaptation of the simplex method to the case of non-linear constraints. Certain complications are, however, introduced through non-linearity in the constraints, and it is shown how these can be overcome.
TL;DR: The history of the development of accounting and auxiliary calculations illustrates the consequences of permitting a measuring and communicating system to become institutionalized.
Abstract: The possibility of measuring does not necessarily lead to the presentation of relevant information for decision-making in business. This is demonstrated by reference to accounting methods and to profit computation in particular. Accounting processes have become formalized to the point where they misrepresent financial results and position; the probability that resources will be used efficiently and that equity between parties of interest will be served is materially reduced by lack of care in the definition of significant concepts and the concurrent acceptance of procedures which have directly opposite justifications and consequences. As the speed of information processing increases and computational refinements develop, a corresponding effort is necessary to redefine in operationally relevant terms, or to sharpen the definition of, such key concepts as profit, capital, cost. The history of the development of accounting and auxiliary calculations illustrates the consequences of permitting a measuring and communicating system to become institutionalized. Some suggestions for improving the relevance of accounting and similar information are made.
TL;DR: In the context of such subjects as optimization of equations, techniques of mathematical programming, and the like, "The Sociological Impact of Automation in the Office" may appear somewhat out of place as mentioned in this paper.
Abstract: In the context of such subjects as optimization of equations, techniques of mathematical programming, and the like, “The Sociological Impact of Automation in the Office” may appear somewhat out of place. This is because there has been a lag in the feedback process between the conventional social scientists and the operations research and management science people. Some work involving high-speed electronic computers, as that concerned with nuclear fission, has begun to achieve a closed loop, with the social implications of the scientific advances taken so seriously as to affect the actual pattern and direction of research in some cases. Inclusion at this conference of a paper on office automation in relation to its significance for the workers involved indicates that OR and TIMS people are becoming aware that their activities may have social consequences worthy of consideration. Management Technology, ISSN 0542-4917, was published as a separate journal from 1960 to 1964. In 1965 it was merged into Manageme...
TL;DR: An overall examination of the operations of a textile mill, operated by the Pepperell Mfg.
Abstract: The present study encompassed an overall examination of the operations of a textile mill, operated by the Pepperell Mfg. Co. and engaged in the production of blankets. It was hoped at the outset that application of the mathematical methods of operations research might yield findings and insights pointing to a potentially more profitable management of existing facilities. These hopes were subsequently amply fulfilled. Management Technology, ISSN 0542-4917, was published as a separate journal from 1960 to 1964. In 1965 it was merged into Management Science.
TL;DR: In this paper, the authors describe a method of computing the number of spare parts of each kind to have at each field station in a maintenance system, where the variables considered are: (1) the replenishment time from a central warehouse to field stations, (2) a specified protection level, and (3) the predicted usage rate for each part-station combination.
Abstract: The authors describe a method of computing the number of spare parts of each kind to have at each field station in a maintenance system. One-at-a-time replenishment is used and the variables considered are: (1) the replenishment time from a central warehouse to field stations, (2) a specified protection level (maximum number of shortages per year), and (3) the predicted usage rate for each part-station combination. The method employs multi-channel queuing theory in a routine programmed for Univac I. Of basic interest is the technique of predicting part-station usage from the number of landings per time period, rather than from hours flown, a modification of usual airline practice that allows usage predictions to be tied directly to a given station, and, furthermore, allows allocations of parts to stations to be revised as schedules change. Thus, the procedure bases inventory levels at each station on future needs, rather than on past history—a poor predictor as plane types and schedules are revised. The m...
TL;DR: In this paper, the relation between productivity, efficiency and size of a technical organization as affected by internally generated and circulated paperwork is analyzed and it is shown that there exists an upper bound to total productive output which is independent of the number of employees.
Abstract: The relation between productivity, efficiency and size of a technical organization as affected by internally generated and circulated paperwork is analyzed It is shown that there exists an upper bound to total productive output which is independent of the number of employees; and that as the organization size is increased the efficiency generally first rises and then falls off inversely proportionally to the number of employees
TL;DR: The purpose of this paper is to present and analyze the difficulties encountered in a single, but representative, area of decision-making, namely, equipment replacement.
Abstract: A great deal of time and effort has been devoted to the development of quantitative methods for the solution of business management problems. Unfortunately, a tremendous difference exists between the rate at which these methods are being generated and the rate at which they are being applied. This suggests that there exist problems of application which industry is not able to overcome. The purpose of this paper is to present and analyze the difficulties encountered in a single, but representative, area of decision-making, namely, equipment replacement. It is hoped a presentation and analysis of these difficulties will have some effect on the nature of future research activities.
TL;DR: This paper discusses the variety of subjects studied: demand prediction, inventory control, procurement and other decision rules, management control systems, etc.
Abstract: The complexities of the Air Force pose a very hard challenge for the development and application of management science. At the same time, they provide a wide range of problems to study. RAND has been engaged in logistics research for the Air Force since 1953. This paper discusses the variety of subjects studied: demand prediction, inventory control, procurement and other decision rules, management control systems, etc. These have made use of many traditional tools of analysis and management science. In addition, simulation techniques have been found particularly useful in fitting together pieces of separate research into a systems context for feasibility and consistency tests.
TL;DR: In this article, the authors developed an application of linear programming to the problem of the distribution of a certain investment which is restricted to a fixed amount among the various productive processes or departments.
Abstract: We develop an application of linear programming to the problem of the distribution of a certain investment which is restricted to a fixed amount among the various productive processes or department...
TL;DR: The weapon systems management concept, and more particularly its civilian counterpart the product mission concept, is presented as a possible frame of reference for top management and systems analysts to use in long-range planning.
Abstract: This paper is concerned with the lack of significant progress in the application of electronic computers for expanding the scope of systems of information flow. The weapon systems management concept, and more particularly its civilian counterpart the product mission concept, is presented as a possible frame of reference for top management and systems analysts to use in long-range planning. The functions necessary for successful product mission accomplishment are outlined and the role of systems analysts in the performance of these functions is emphasized. The feasibility of long-range planning for systems of information flow without reference to existing applications or hardware is also discussed.