A novel behavioral penalty function for interval goal programming with post-optimality analysis

Goal programming (GP) is a multi-objective extension of linear programming. Interval GP (IGP) is one of the earliest methods to expand the range of preferred structures in GP. The decision maker's (DM's) utility or preference in IGP is investigated by incorporating a widening range of underlying utility functions, commonly known as penalty functions. The basic idea of these functions is that undesirable deviations from the target levels of the goals are penalized regarding a constant or variable penalty value. The main concern with introducing the penalty functions is providing a wide range of a priori preference structures. Yet, the evaluation of how undesirable deviations are penalized based on DM's behavioral preferences is not sufficiently addressed in the penalty function types developed in the GP literature. In real-world scenarios involving risk, the achievement levels of decision-making attributes are typically associated with the behavior of the DM. In such scenarios, the DM's unavoidable attitude toward risk should be integrated into the decision-making process. We introduce the concept of behavioral penalty functions into the IGP approach, incorporating a risk aversion parameter tailored to the nature of each attribute to address this gap. This concept offers an innovative framework for capturing the preferences of the DMs and their various attitudes toward risk within the IGP approach. In this paper, we first introduce the concept of behavioral penalty functions. Next, we develop a behavioral utility-based IGP model. Finally, we present a portfolio selection case study to demonstrate the applicability and efficacy of the proposed procedure, followed by a post-optimality analysis and comparisons with other GP approaches.