Goal Programming and Its Variants

Goal Programming and Its Variants

John Wang (Montclair State University, USA), Dajin Wang (Montclair State University, USA) and Aihua Li (Montclair State University, USA)
DOI: 10.4018/978-1-59904-843-7.ch047
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Abstract

Within the realm of multicriteria decision making (MCDM) exists a powerful method for solving problems with multiple objectives. Goal programming (GP) was the first multiple-objective technique presented in the literature (Dowlatshahi, 2001). The premise of GP traces its origin back to a linear programming study on executive compensation in 1955 by Charnes, Cooper, and Ferguson even though the specific name did not appear in publications until the 1961 textbook entitled Management Models and Industrial Applications of Linear Programming, also by Charnes and Cooper (Schniederjans, 1995). Initial applications of this new type of modeling technique demonstrated its potential for a variety of applications in numerous different areas. Until the middle of the 1970s, GP applications reported in the literature were few and far between. Since that time, primarily due to influential works by Lee and Ignizio, a noticeable increase of published GP applications and technical improvements has been recognized. The number of case studies, along with the range of fields, to which GP has been and still is being applied is impressive, as shown in surveys by Romero (1991) and Aouni and Kettani (2001). It can be said that GP has been, and still is, the “most widely used multi-criteria decision making technique” (Tamiz, Jones, & Romero, 1998, p. 570).

Key Terms in this Chapter

Goal: This is the specified and definite target level of the objectives.

Linear Programming: It is a branch of mathematics that uses linear inequalities to solve decision-making problems involving maximums and minimums.

Objective Function: This is the function to be minimized or maximized, representing cost or profit, and so forth.

Goal Programming: It is an extension of linear programming that is capable of handling multiple and conflicting objectives.

Weighted GP: A weighted GP is a form of GP that uses penalty weights to find the optimal solution that minimizes the sum of the weights.

Priority Level: Priority levels separate the objectives of the model into categories that must be achieved in a particular order.

Pareto Efficient: It is the achieved value of the objective that cannot be improved without negatively affecting the level of another objective.

Penalty Weights: These are the values in weighted GP that measure how critical it is to the model that these values do not contain deviations.

Objective: An objective is an issue of importance that the model should address such as cost, profit, quality, and so forth.

Deviation Variable: A deviation variable represents the difference in distance between the desired target level and the actual achieved target level.

Preemptive or Lexicographic GP: This is a form of GP that ranks each goal according to its specified importance in the overall model.

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