Rough Programming and Its Application to Production Planning

By rough programming, we mean the optimization theory dealing with rough decision problems. This paper constructs a general framework of rough chance-constrained programming. We also design a spectrum of rough simulations for computing uncertain functions arising in the area of rough programming. To speed up the process of handling uncertain functions, we train a neural network to approximate uncertain functions. Finally, we integrate rough simulation, neural network, and cultural algorithm to produce a more powerful and effective hybrid intelligent algorithm for solving rough programming models and illustrate its effectiveness by example of production planning.