Multiple Criteria Problems in Linear Programming

A primary in modern decision analysis is the treatment of multiple objectives. The question becomes one of value trade-offs in the social structure of varying interests. A formal decision analysis capable of handling such situations is a new entrant in the field of management technology.

The organizational goals depend very much on the character and type of organization, the philosophy of management, and environmental conditions. Profit maximization, which is regarded as the sole objective of the business firm, is one of the most widely accepted goals of management, but is not always the only goal. The various formal solution techniques that have been needed for decision analysis are concerned primarily with making the right selection from a set of alternatives. However, in recent years, the nature of major decision problems has changed drastically and the adequacy of many solution techniques has been questioned.

Goal programming is a special extension of linear programming which is capable of handling a decision problem with multiple goals and multiple sub-goals. Often goals, set by management are achievable only at the expense of other goals. In goal programming, instead of trying to maximize or minimize the objective criterion directly, as in linear programming, the deviations between goals and what can be achieved within the given set of constraints are minimized. Thus the objective function becomes the minimization of these deviations, based on the relative importance of priority assigned to them. The true value of goal programming lies its ability to solve problems involving multiple, conflicting goals according to the manager’s priority, with a greater emphasis on ‘satisfying’ rather than “maximizing”.

Another extension of linear programming is in the solution of problems involving multiple objectives and is termed multiple objective linear programming. In this technique the ordering of the objectives is very crucial in obtaining the optimal solution. Forestry management, manpower allocation, water resource problems, and media selection problems in advertising are some of the areas in which the techniques mentioned above are being used.

Work Improvement:

The goal of work improvement is the economizing of effort. The key to the attainment of this goal is an awareness of exactly what an operation involves, the details of what must be done, and an inquiring mind that searches for “the best way”.

The inquiring mind needs certain questions to guide its thinking. Four such questions have proved useful in all work improvement:

1. Can some elements of the work be eliminated? If there is any step that need not be done at all or any motion that is completely a wasted one, it should be eliminated.
2. Can some parts of the operation be combined? If two parts of an operation can be done jointly, combining them will improve it.
3. Can the sequence be changed? Anyone who has purchased disassembled furniture and has failed to follow the closed instruction will be especially conscious of failing to give proper consideration to sequence.
4. Can the operation be simplified? The simple way is usually the easiest, least expensive, and best way.

In using the four questions, it is mandatory to describe in detail exactly what is being done. One cannot improve an operation that one does not visualize and analyze.

Certain key ideas have helped guide though about work improvement. Use symmetrical motions which have corresponding size, shape, and relative position when viewed from the center. The numeral “8” and the letter “S” are symmetrical when divided by a horizontal line through the center. Opposite motions contribute to the balancing of members of the body. Ballistic motions in which movement is “free” uncontrolled are best. Continuous curved motions require less effort. Rhythm, a term generally understood from its musical usage, is generally applicable in motion study. Momentum can help once an item is in motion. Gravity is a basic law of nature that is very beneficial to a worker if he finds out how it is to his advantage instead of having to fight it. The definite location for tools, materials, persons, and work in process is particularly important in planning the workplace.