In the 1970s, considerable progress was made in the field of Operations Research, and Multi-Criteria Decision-Making (MCDM) procedures were advanced in several directions, viz., utility theory, goal programming, etc. Goal programming is one of the techniques used for obtaining a possible ‘satisfactory’ level of achieving various objectives and an approach to avoid stretching one’s resources. This paper scans through the engineering applications of optimization with different modeling approaches. This helps the reader to obtain a broad picture of the multitude of applications of optimization techniques.

Scanning through the engineering applications of optimization with different modeling approaches, one gets a broad picture of the multitude of applications of optimization techniques. In the 1970s, considerable progress was made in the field of Operations Research, and Multi-Criteria Decision-Making (MCDM) procedures were advanced in several directions, such as utility theory, goal programming, interactive procedures, out-ranking methods and fuzzy programming. There are three broad categories of MCDM problems:

1. Decision under certainty (Deterministic modeling),
   
2. Decision under uncertainty (Stochastic modeling),
   
3. Decision under fuzziness (Fuzzy modeling).

Mathematical modeling and solution methodology of decision making under certainties are both discrete solution space and continuous solution space. The most popular technique for the solution of multi-criteria problems is Goal Programming (GP), which came into existence under continuous solution space methodology.

GP is one of the techniques for obtaining a possible ‘satisfactory’ level of achieving various objectives: an approach to avoid stretching one’s resources too much as it produces bad aftereffects, where a person or an organization instead of maximizing or minimizing an objective may be satisfied by setting up a reasonable goal for the objective to be achieved as closely as possible. GP is one of the most widely used techniques for solving many real-world managerial MCDM problems, particularly in case where the criteria are defined as linear analytic functions of decision variables belonging to a compact feasible set. In general, GP is used for solving linear decision models having more than a ‘single’ objective, i.e., multi-objective decision-making problems. In the early 1960s, Charnes and Cooper described GP as a workhorse which is strong and rugged and easy to use in comparison to a thoroughbred one requiring devoted attention by skilled attendant and used only by specially trained riders (Charnes and Cooper, 1961, 1968, 1975 and 1977). GP, which has received much attention from analysts like Yuji (1965), Sang (1972), Ignizio (1976, 1982 and 1983), Tiwari et al. (1986), Mondal (1988), and others, due to its ease of applicability to many real-world problems, has led to development of a systematic methodology.

Operations Management Journal, Relative Efficiencies of Schools, Data Envelopment Analysis, Government-Aided Schools, Linear Programming Model, Decision-Making Units, Organizational Units, Human Resources, Public Procurement Sectors, Government Schools, Education System.