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The paper presents an optimization model and its implementation using a hybrid approach for the Capacitated Vehicle Routing Problem with Pick-up and Alternative Delivery (CVRPPAD). The development of the CVRPPAD was motivated by postal items distribution issues. The model proposed combines various features of Vehicle Routing Problem variants. The novelty of this model lies in the introduction of alternativeness of item delivery points, differentiation of delivery point types in terms of their capacity (parcel lockers) and possibility of collecting the items during the execution of delivery routes. The model also takes into account a possibility of introducing time windows related to delivery time. The proposed data structure in the form of sets of facts facilitates the implementation of the model in all environments, Constraint Logic Programming (CLP), Mathematical Programming (MP), metaheuristics, databases, etc. The model is implemented in the MP, hybrid CLP/MP, and hybrid CLP/heuristic environments. The hybrid CLP/MP approach is the authors’ original solution, which has already been used to solve Supply Chain Management problems, scheduling problems, routing problems etc. For large size problems, considering their combinatorial character, the proposed CLP/MP approach is ineffective. Its effectiveness will improve when MP is replaced by a heuristic. All implementations were performed on the same data instances (facts), which made it possible to compare them according to the solution search time, number of decision variables and number of constraints. The directions into which the model can be further developed were also presented.

Capacitated vehicle routing problem with pick-up and alternative delivery (CVRPPAD): model and implementation using hybrid approach