Extended goal programming approach for solving multi-objective de novo programming problems

A new proposal has been made in this study to solve the multi-objective de novo programming problem using extended goal programming, which includes minmax and weighted goal programming. In the proposal, goal functions are created by fixing each objective function of the multi-objective de novo programming model to its own positive ideal solution. Additionally, the normalization constant is determined using positive and negative ideal solutions in the proposal. The proposed approach made it possible to determine the range in which "efficiency and equity" are balanced in the transition from max. efficiency to max. equity. The applicability of the proposed approach is demonstrated in an illustrative example, and considering the obtained results, the optimal point that represents both poles of the extended GP equally is obtained. Through this optimal point, the optimal feasible amount of each constraint is calculated from the extended goal programming perspective.