A new MILP model for vehicle routing-loading problem under fragility, LIFO, and rotation constraints

Simultaneous optimization of vehicle routing and loading decisions in three-dimensional case is one of the important problems in logistics and has received great attention from researchers. To the best of our knowledge, optimization models presented in the literature for this problem either are too complicated or do not include important loading assumptions such as item fragility, last-in-first-out arrangement, and the possibility of rotation. To overcome the shortcoming of the existing models, in this paper, we present a novel mixed-integer linear programming (MILP) model which not only involves important loading assumptions, but also does not have the complexity of previous models. Moreover, we provide valid inequalities to strengthen the LP relaxation bound and accelerate the solution process. Further, we show that how a restricted version of our model can be incorporated in loading procedures of meta-heuristic algorithms to improve their efficiency. Computational results over instances, taken from the literature, show the performance of the proposed approach.