A new framework for simulation-based goal programming using retrospective optimization

In this paper, we present a simulation-based goal programming framework to address stochastic optimization problems involving multiple performance measures. We specifically consider the weighted goal programming and min–max goal programming formulations, which are widely used in the field of goal programming. Due to the analytical intractability of the objective functions in this stochastic optimization model, traditional mathematical programming techniques cannot be readily applicable. To overcome this challenge, we propose using retrospective optimization algorithms, a type of simulation–optimization approach. To establish the validity of our method, we provide a convergence analysis of the proposed algorithms, demonstrating their ability to converge to a globally optimal solution under specific conditions. In addition to the theoretical development, we conduct numerical experiments using benchmark test functions and a stochastic inventory optimization problem to illustrate the effectiveness of our framework. The empirical results demonstrate that our approach performs competitively compared to existing benchmark solution methods.