A two-stage robust optimization approach for the mobile facility fleet sizing and routing problem under uncertainty

• A two-stage robust optimization approach is applied to the formulation of the MFFSRP for the first time.
• An enhanced version of the cutting plane method is proposed that exploits the special features of the problem.
• The performance of the proposed approach is examined in an experimental study.

We propose a two-stage robust optimization model for the mobile facility fleet sizing and routing problem with demand uncertainty. A two-level cutting plane based method is developed, which includes an algorithm to generate problem-specific lower bound inequalities in the outer level, and a hybrid algorithm in the inner level that combines heuristic and exact methods to solve the recourse problem. Numerical tests show that the design and operation from the proposed method outperforms other solution approaches. The efficiency of the proposed solution algorithm in identifying the optimal solution is quantified and the robustness of the proposed model is demonstrated for varying degrees of uncertainty in demand.