Flow-based integer linear programs to solve the weekly log-truck scheduling problem

In this paper we present the solution to a weekly log-truck scheduling problem (LTSP) integrating the routing and scheduling of trucks where all goods are transported in full truckloads. We must take into account pick-up and delivery requirements, multiple products, inventory levels, and lunch breaks. The objective is to minimize the overall transportation cost including wait times and the empty and loaded distance traveled. Our solution is based on a two-phase approach. The first phase involves an integer linear program that determines the destinations of full truckloads. The second phase uses an implicit integer linear program based on an arc formulation to ensure that the trucks are routed and scheduled at a minimum cost. Experiments have been conducted using Cplex 12.4.0, and almost all instances were solved within six hours with a reasonable gap.