Bi-Level Decision Making in Random Phenomenon

Random phenomena are events for which the possible outcomes are known, but the actual outcome in a given situation is not known. However, while individual outcomes are uncertain, a regular distribution can be seen after many repetitions. Random phenomena can be found in many problems, such as random networks (Jae-Hyeok et al., Acs Appl Mater Interfaces 7(3):1560–1567, 2015), stochastic processes (Barone-Adesi, Stochastic processes. Wiley encyclopedia of management. John Wiley & Sons, Hoboken, 2015; Papoulis, Probability, random variables and stochastic processes stochastic processes. McGraw-Hill, New York, 1991), and random noise (Stratonovich and Silverman, Topics in the theory of random noise. Gordon and Breach, New York, 1967). To describe bi-level decision making models with random phenomena, this chapter examines a practical example from a regional water resources allocation problem (RWRAP). The first section introduces the background to the problem, gives the bi-level problem description and discusses the random phenomena in the RWRAP. Then, several bi-level decision making models with random coefficients are developed and the transformation methods and properties are discussed. To solve the bi-level models, several algorithmic designs are outlined and numerical examples are given to illustrate the effectiveness of the algorithms. A real-world RWRAP construction site case is then described to demonstrate the practical effectiveness of the methods.