We present a new aggregation operator called the generalized ordered weighted proportional averaging (GOWPA) operator based on an optimal model with penalty function, which extends the ordered weighted geometric averaging (OWGA) operator. We investigate some properties and different families of the GOWPA operator. We also generalize the GOWPA operator. The key advantage of the GOWPA operator is that it is an aggregation operator with theoretic basis on aggregation, which focuses on its structure and importance of arguments. Moreover, we propose an orness measure of the GOWPA operator and indicate some properties of this orness measure. Furthermore, we introduce the generalized least squares method (GLSM) to determine the GOWPA operator weights based on its orness measure. Finally, we present a numerical example to illustrate the new approach in an investment selection decision making problem.