Analysis on upper and lower bounds of stochastic Linear Programming problems

Business managers are often required to use LP problems to deal with uncertainty inherent in decision making due to rapid changes in today's business environments. Uncertain parameters can be easily formulated in the two-stage stochastic LP problems. However, since solution methods are complex and time-consuming, a common approach has been to use modified formulations to provide upper and lower bounds on the two-stage stochastic LP problem. One approach is to use an expected value problem, which provides upper and lower bounds. Another approach is to use ‘wait-and-see’ problem to provide upper and lower bounds. The objective of this paper is to propose a modified approach of ‘wait-and-see’ problem to provide an upper bound and to compare the relative error of optimal value with various upper and lower bounds. A computing experiment is implemented to show the relative error of optimal value with various upper and lower bounds and computing times.