Assessing Feasibility in Service Teams Transport Scheduling with Dedicated and Flexible Dispatch Approaches

The research problem addressed in this paper concerns the formulation of feasibility conditions for planned service missions in networks where fulfilling customer orders requires the coordinated participation of multiple resources—referred to as the Service Teams Transport Scheduling (STTS) problem. The study examines feasibility conditions (sufficient and necessary) for routing and scheduling mobile service teams, taking into account constraints arising from service time windows arrangement, vehicle and team availability, and the applied vehicle dispatching strategies. Due to the NP-hard nature of the problem, which limits the possibility of determining service distribution plans in real time, it becomes essential to develop necessary feasibility conditions that can be used in preliminary tests prior to the final search for a feasible service mission plan. By introducing a graph-based representation of time-window arrangement, the study establishes necessary feasibility conditions derived from chromatic number analysis of the corresponding graphs. The feasibility verification approach, based on these conditions, was validated through a series of experiments. The approach combines discrete optimization and declarative modeling to support algorithmic decision-making in real-world service logistics.