A heuristic algorithm for solving bi-level programming problems with application to large-scale location-arc routing in urban traffic lights maintenance

The present study developed a bi-level mathematical model to determine optimal routes for repair teams in charge of inspecting urban traffic lights. In this model, the municipality as the leader locates the construction sites of urban spare parts warehouses and repair centers to minimize the costs of constructing the facilities. At the follower level, the contractor determines the optimal routes for the repair teams. Bi-level models are strongly NP-hard in type. A heuristic algorithm is therefore developed to solve numerical examples, in which the leader first determines different decision-making strategies for the follower through generating a set of justified solutions. In response to the leader rsquo;s set of strategies, the follower presents a set of corresponding solutions. The individual solutions of the follower are then entered into the leader model and the corresponding values of the objective function are calculated. A solution with the optimal numerical value for the leader is ultimately selected as the Stackelberg equilibrium. The efficiency of the proposed model and algorithm was evaluated by presenting the computational results obtained from solving several random numerical examples of small, medium and large dimensions through generating the Stackelberg equilibrium and establishing a relationship between the leader and follower levels. The present findings are recommended to be used as a management tool by policymakers in the urban management sector.