In this paper, we present a new computation scheme for pessimistic bilevel optimization problem, which so far does not have any computational methods generally applicable yet. We first develop a tight relaxation and then design a simple scheme to ensure a feasible and optimal solution. Then, we discuss using this scheme to compute linear pessimistic bilevel problem and several variants. We also provide numerical demonstrations on instances of those linear pessimistic bilevel problems. Because of its simplicity and convenient interfaces to existing algorithms of the regular (optimistic) bilevel problem, we believe that the developed scheme is of a great significance in solving pessimistic bilevel optimization problems arising from various practical systems.
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