Solving the bi-objective optimisation problem with periodic delivery operations using a lexicographic method

Periodic deliveries are typical in a number of real-life applications. Minimising the number of vehicles required to make deliveries to a set of customers with known delivery frequencies is called the problem of vehicle minimisation for periodic deliveries (VMPD). Catering to the welfare of vehicle drivers has now become very important. Consequently, this work integrates the vehicle load balance factor into the VMPD problem by considering both the number of vehicles required to make periodic deliveries and the load balance between vehicles. This work presents integer programming formulations and applies a lexicographic method to this bi-objective VMPD problem. This work also examines whether decomposition can significantly reduce the size and difficulty of basic integer programming formulation in order to output close-to-optimal schedules for large problems within a reasonable computational time. A greedy balancing algorithm is also proposed to use it along with a decomposed integer programming formulation to yield a satisfactory solution in a relatively short time. Computational experiments demonstrate the better competitiveness of the proposed approaches compared to that of the existing approaches.