Uncertain random assignment problem

•An uncertain random simulation algorithm is designed to estimate the critical values of uncertain random variables.•We propose an uncertain random assignment problem where uncertain variables and random variables coexist.•An optimization approach is presented to obtain the lower-bound value and upper-bound value for the optimal assignment. This paper proposes an uncertain random assignment problem in which random variables coexist with uncertain variables. Critical values of uncertain random variables are used to rank uncertain random variables. An uncertain random simulation algorithm is developed in order to obtain chance distributions and critical values of uncertain random variables. An α-optimistic model is presented. A combined optimization approach is designed to solve the α-optimistic model. This approach incorporates uncertain random simulation into branch and bound algorithm. Finally, an example application of the approach is presented.