An integrated approach for three-dimensional capacitated vehicle routing problem considering time windows

Purpose As a critical problem in sophisticated distribution systems, vehicle routing plays a pivotal role in dealing with time windows and capacities constraints. The purpose of this paper is to addresses a new integrated model to incorporate both three-dimensional and time windows aspects of the routing problem. First, capacitated vehicle routing decisions are made subject to a soft time interval to meet the customers' demands. Afterward, these decisions are entered into the three-dimensional loading problem. Design/methodology/approach The problem is solved using generalized algebraic modeling system software in small-size problems. The problem is NP-hard and requires an efficient solution methodology. For this purpose, a hybrid algorithm has been proposed to solve the large-size problems. The efficiency of this algorithm is checked by making comparisons with exact solutions for small and medium size test problems, and with the related literature for large size problems. Findings The numerical experiments show that the proposed model covers more effectively the broader aspects of the transportation problem. Furthermore, the proposed algorithm supports competitive and satisfactory results by giving reasonable outputs in comparison with previous studies. Originality/value The main purpose of this integration is to achieve minimum total transportation costs, which cannot be guaranteed without applying two referred constraints, simultaneously.