Traveling salesperson problem with unique pricing and stochastic thresholds

In this variant of traveling salesperson person problem, only the customers who accept to pay a unique service fee are serviced. Each customer has a random price acceptance threshold and accepts to pay any fee lower than this threshold. To address this issue, a chance-constrained stochastic model is developed and two exact methods, one based on a Branch & Cut scheme, and the other on Logic Based Benders Decomposition, are built. Numerical tests show that, on small instances both methods are efficient but on larger instances with 100 customers, Logic Based Benders Decomposition dominates clearly the Branch & Cut method.