A problem of primary significance to a variety of industries is the suppression of trim losses in cutting rolls of paper, textiles, cellophane, metallic foil, or other material, for the execution of business orders. This problem is amenable to solution by the application of mathematical tools. We shall illustrate the general treatment of such problems by demonstrating a numerical example.
The word “leadership” has been widely used. Political orators, business executives, social workers, and scholars employ it in speech and writing. Yet, there is widespread disagreement as to its meaning. Among social scientists, the theoretical formulations of the leadership concept have continued to shift, focusing first upon one aspect and then upon another. Much still needs to be done to develop a basic, systematic theory. The time seems ripe for attempting a careful statement of a frame of reference which may serve to make available research more meaningful, and which may guide future research and practice. Specifically, such a frame of reference can perform the useful function of pointing to the variables which need to be measured. It can help us to state hypotheses concerning the key variables underlying leadership effectiveness. It can also provide meaningful objectives for the development of more adequate leaders.
This paper is the result of a survey made during the summer of 1956. It is a progress report on applications of linear programming by a number of oil companies. Examples are presented of applications to a variety of problems arising in the areas of Drilling and Production, Manufacturing, and Marketing and Distribution. The examples were selected to illustrate both the power and the limitations of present linear programming methods when applied to actual problems.
There are many business situations where it might be necessary to keep the potential service level (preparedness) above requirements at least in some of the time intervals. For instance, a fleet of trucks (or cabs) or group of production machines, cannot be easily adjusted month by month and, therefore, during slack periods the potential service level may exceed requirements. In a manufacturing firm, there are certain functions to be performed, such as maintenance or clerical work (often overhead type functions), where again the potential service level is expensive to change. In fact, even in the case of production workers, the expense of hiring, training, firing, or the contractual obligations of guaranteed wage agreements may make it undesirable to change the level of employment during slack periods. The reader will readily find further illustrations of the type of planning problems we are describing here.
This is a progress report on the Air Force use of scientific procedures in programming and planning. The use of scientific methods, in the development of Air Force programs and plans and in the determination of the logistic support required, has occurred primarily in association with the use of large-scale electronic data processing systems. Therefore, in discussing progress I will be dealing for the most part with work done in connection with such systems.
The present paper summarizes the results of a detailed empirical investigation of the theory of economic equipment policy as applied to one important kind of industrial equipment, viz line-haul truck-tractor power units. The objective of this research was to ascertain, for a type of equipment which is perhaps best suited to exact replacement analysis, the quantitative importance to the firm of following optimal policies in replacement and in the choice of equipment type. Also it was desired to compare actual with optimal policies in a concrete case.
The primary purpose of this paper is to present for management an approach to the employment of large data-handling equipment in commercial problems. This approach is in the form of guideposts which, in a very general way, may indicate to people without a background in the data processing field, major requirements to consider or problems which will be encountered in connection with this employment. The problem arises in the military departments largely in connection with logistics and throughout non-military governmental and nongovernmental operations.
Both economists and businessmen are interested in knowing whether inventories are higher or lower than firms desire: Economists because it would provide a clue to the structure of business expectations, businessmen because it would give some indication of the future trend of business. In this paper a model is presented with the aid of which an estimate, however crude, of the amount of undesired inventory in the economy is made from market data.
Modigliani and Hohn [Modigliani, F., F. E. Hohn. 1955. Production planning over time. Econometrica 23 (1, January) 46–66.] have formulated a production planning and inventory control model that appears relevant to an important class of non-stochastic decision-making problems. It is the purpose of this note to suggest: (1) that the Modigliani Hohn problem may be studied in terms of linear programming as well as through the calculus model originally employed; (2) that by working through the stock-flow relationships, it is possible to effect certain conceptual and computational improvements over Edward Bowman's original method for converting this type of problem into the “transportation” form [Bowman, E. H. 1956. Production scheduling by the transportation method of linear programming. J. Oper. Res. Soc. America 4 (1, February) 100–103.]; and (3) that the linear programming version is especially suitable for tracing out the cost implications of stabilizing the work force at alternative levels. Like the “caterer problem” [Jacobs, W. 1954. The caterer problem. Naval Res. Logist. Quart. 1 (2, June) 154–165.] and the “warehousing problem” [Charnes, A., W. W. Cooper. 1955. Generalizations of the warehousing model. Oper. Res. Quart. 6 (4, December) 131–172.], this linear programming model represents another instance in which every basis is pure triangular and contains no elements but zero, +1, and −1.
Production of a given commodity is to be scheduled over time to meet known future requirements while minimizing total costs. The costs include both storage and production costs as functions of time. The unit production cost is an increasing function of the production rate. Previous solutions to this problem have involved complicated iterative procedures. A new approach brings out the basic principle involved and leads to a surprisingly simple solution. This coincides with a common-sense technique sometimes used in business.