Split delivery and pickup vehicle routing problem with two-dimensional loading constraints

In this paper, we address the distribution problem of liquefied petroleum gas (LPG). In particular we are targeting the optimization of pickup and split delivery of gas bottles to a set of customers with loading constraints. The problem combines the loading of a heterogeneous fleet of vehicles through set of different size racks and then the establishment of divisible deliveries (split delivery: SDVRP). The problem discussed in this paper can be presented as a Multi-depot Two-Loading Split Delivery and Pickup using Heterogeneous fleet of Vehicles with Time Windows vehicle Routing Problem and with Multi-Product (2L-SDP-HVRPTW-MP). After proposing a mathematical formulation for this problem (MILP), we tested our model firstly by a small instances using ILOG CPLEX solver following this by testing and discussing numerical results.