Skill Vehicle Routing Problem With Time Windows Considering Dynamic Service Times and Time-Skill-Dependent Costs

Service processes in modern logistic systems tend to be highly specialized and intellectualized. However, some casual and unexpected behavior may occur, causing specific dynamic interactions among their many constituents. As such, the optimization and modeling of complex problems have become increasingly tough. Besides, technicians typically need to possess appropriate skills that match assigned tasks. Faced with real service scenarios, however, employees inevitably suffer from an increasing level of fatigue attributed to continuous work, resulting in a gradual decrease in the efficiency of workers over time. In this situation, the service time for a given task can no longer be treated as a constant, but instead, it should be treated as dynamic. Moreover, highly skilled technicians are usually paid higher than the junior ones with basic or lower skill level, which introduces new challenges in the optimization of service task schedules' problem. In this paper, we first present the skill vehicle routing problem considering dynamic service times and time-skill-dependent costs, in which the efficiencies of the workers are dynamically affected by their fatigue levels, and the costs, i.e., salaries paid to the employees, are related to skill levels and continuous work time. Furthermore, we develop a comprehensive and general mixed-integer linear programming dynamic-based model to formulate the proposed problem, which is directly solvable by MIP solvers for small-sized problems. We also initiate an iteratively dynamic neighborhood search (IDNS) algorithm that combines iterative partial optimization with dynamic neighborhood search to efficiently solve large-sized problems with near-optimal solutions. The comprehensive computational experiments were performed on the problems of different sizes to test the effectiveness and efficiency of the proposed model and solution approach. Some useful managerial insights were obtained from the computational results that can help decision-makers to determine cost-effective service routes and schedules in complex transportation-related issues.