Abstract
Keywords - Loading vehicles, non-identical items, packing, optimisation, integer linear programming
Abstract - This study considers the optimisation problem of loading vehicles with rectangular products. The objective of this model is to define a loading pattern, which maximise the used loading capacity of a vehicle. Thus, the number of vehicles needed to ship the clients orders is reduced, and so are the shipping expenses.
The solving method used is based on the cutting and packing approach in which small items (rectangular products) must be fitted into large objects (vehicles). An exact method is chosen to solve the problem: integer mathematical programming.
Different models were developed. The models contain different types of variables (integer or binary) and different constraint definitions. All combinations are tested with different initial data in order to identify the best variable and constraint definition. The model is completed by adding constraints to guide the search. These constraints improve the models solving capacities (bounds, ordinations, priorities).
The software used to carry out these solving procedures is ILOG Cplex.
Sets of examples found in related literature are used to compare the different models, adapting the main model to each particular case. The experiments proceed with random examples generated with information given to us by a Spanish company which produces and distributes thread to European countries.
The most adequate variables and the required additional constraints are given by the computation results. We have determined which combination of these factors is best for each problem, with respect to the set of available vehicles and the set of pallets to load.