One-Stage Uncertain Linear optimization

Uncertainty is one of the intrinsic features of natural phenomenon and optimization is not an exception. Parameters in an optimization problem may be inaccurately presented, or due to variation after solving the problem, the current optimal solution may not be optimal or feasible for the new data. One of the approaches towards the uncertainty is the uncertainty theory initiated by Liu in 2007 and completed in 2011. This theory describes the uncertainty originated from human reasoning in mathematical axiomatic words. In this paper, we consider one-stage uncertain linear optimization problem, where the parameters linearly depend on several independent uncertain variables. A solution method is presented which is similar to the branch and bound method for the integer linear program. The presented methodology is explained by simple illustrative examples.