Management science embodies the use of engineering and mathematical skills to solve the complex problems of the modern organization. While engineering and mathematical skills were used in business problems before, World War II and the development of the computer brought them to the forefront. If we are to consider the behavioral science approach as a school of management theory, we should also consider the quantitative or mathematical approach as another tool for improving the efficiency of the business organization.
The logistics of a modern global war such as World War II called for more precise methods than ever before. Afterwards, the applications developed by the US government during the war were applied to peacetime production Operations research was one such approach, which today has taken on meaning as a tool of management decision-making. The basis of the management science approach is the construction of models to aid the manager in carrying out his functions Management science, like behavioral science, is one tool for the solution of problems in business or any other system.
Two kinds of models may be employed to describe a situation mathematically the descriptive model shows how a system works merely describes things as they are and in itself is incapable of showing how they should or could work. This model is used for analysis because it clearly portrays the situation as it is for someone who wishes to change it. The normative model is specifically designed and one constructed to select the best alternatives based on some previously determined criterion which has been included in the model. It tells how the system should be in order to attain a specific objective. A normative model may also be referred to a maximizing or an optimizing model, since its purpose is to choose from a set of alternatives to best determine the path to be followed in attaining objectives.
Here is a simple illustration of the two models. A shoemaker with his own shop who works by himself can produce a pair of shoes every four hours. Ile can sell all the shoes he produces for $20 a pair, so his production can be considered a straight line.
If his materials and overhead for an eight-hour day amount to $5 per pair of shoes, his profit can also be shown as a straight line working five days, the shoemaker can produce ten pairs of shoes. If he sells all of them, his total revenue would be $200 for the week because his costs were $50; his profit would be $150, since revenue minus cost lesves profit.
Assume that this man has several choices of product, given the same tools and materials He can manufacture belts, pocketbooks, sandals, and boots Each of these may call for a different quantity of leather and other finishing materials, each will take a different length of time to produce, and each will sell for a different price In addition, let us suppose that he could only sell a certain quantity of each of these products, where he could sell all the shoes he could produce. In other words, he has choices with given restraints a model of this new sination would then be a normative model. By simply looking at this, we may ascertain what the shoemaker should produce to get the best out of his right hour day if he could sell everything he could make. If he produced two pocketbooks and two belts, he would make $50 profit. But if he could sell only one pocketbook and five belts a week, how much of each should be produced in a week for the best return? Realistically, restraints must be included, such as an eight-hour day times five days or a total work week of forty hours. Consider also that one may not be able to sell all that is or could be produced. The problem could be further complicated in that the shoemaker enjoys making shoes and wishes to produce at least one pair a day or five pairs a week for his personal satisfaction regardless of the profit involved.
This is a very simple case, compared to real problems solved by the techniques of management science. When a problem involves exact relationships and all the costs are known, as in our example, it is known as a deterministic model. If the shoemaker had not known how many of each item he could sell, he would have been faced with a stochastic model or a probabilistic model. He would then have had to use the mathematics of statistics to estimate the probability of selling particular quantities of shoes, sandals, belts, and pocketbooks. Contrast this simple problem with that of the automobile manufacturer with 100,000 employees in plants in five states producing eight lines of cars with six variations in each line-compounded by the vast combinations of colors and accessories possible for each. Add to this the competition and external factors such as a declining economy and possible shortages of materials due to strikes. In this case, many models would have to be constructed and compared to give a possible solution. Mathematics and statistics are used in many management situations: in product-mix problems like the one just described; in waiting-line or queuing theory to eliminate delays or dissatisfactions that arise from lack of materials for processing or lack of integration of production facilities; in inventory models to determine how much, when, and where inventory should be produced and held; in transportation models to determine the best places to manufacture and stock goods at the lowest cost. The management science approach at best solves part of the total problem confronting the management of a business firm. The classical and behavioral approaches, together with mathematical methods, join in the functions next to be discussed.
