A study on the interval goal programming with arbitrary penalty function

Interval goal programming (IGP) with a marginal penalty function was first proposed by Charnes and Collomb (1972), and further developed by Kvanli (1980), Jones and Tamiz (1995), Vitoriano and Romero (1999), Romero(2004) and Chang (2006). None of the above studies were able to formulate IGP with an S-shaped penalty function until a mixed integer method was proposed by Chang and Lin (2009). However, their method requires adding many extra binary variables when problem size gets large. This increases the computational burden in the solution process. In addition, any arbitrary penalty function can be seen in the fields of business and industry. However, none of the previous approaches have addressed any arbitrary penalty functions in IGP. For the above two reasons, this study proposes a method to formulate any arbitrary penalty function in which extra binary variables are no longer required. In order to demonstrate the usefulness of the proposed model, an illustration example is provided.

Project ID:PB10202-0134
External Project ID:NSC101-2410-H182-007-MY2