In this paper, we introduce two algorithms to address the two-echelon capacitated location-routing problem (2E-CLRP). We introduce a branch-and-cut algorithm based on the solution of a new two-index vehicle-flow formulation, which is strengthened with several families of valid inequalities. We also propose an adaptive large-neighbourhood search (ALNS) meta-heuristic with the objective of finding good-quality solutions quickly. The computational results on a large set of instances from the literature show that the ALNS outperforms existing heuristics. Furthermore, the branch-and-cut method provides tight lower bounds and is able to solve small- and medium-size instances to optimality within reasonable computing times.

There are different transportations in the city logistics (e.g., passengers, freights, and wastes), which are handled respectively by single-purpose vehicles (SVs) of the corresponding type. The multi-purpose vehicle (MV) is a future concept whose load modules can be changed for different urban transportations. MVs enable the sequential sharing of different mobilities, thus theoretically improving the efficacy of the city logistics by higher utilization of vehicles. A variant model of the Pick-up and Delivery Problem with Time Windows is established to describe the sequential sharing problem considering both MVs and SVs with the features of multiple depots, partial recharging strategies, and fleet sizing. In the problem, MVs can change their load modules for all types of objects carried by SVs. An adaptive large neighborhood algorithm (ALNS) is developed with new mechanisms for MVs. The proposed ALNS is tested by 15 artificial data cases and compared with the MIP solver. The results show the proposed ALNS is time-effective and validated to find good solutions. / Det finns olika transporter i stadslogistiken (t.ex. passagerare, gods och avfall), som hanteras av enskilda fordon (SV) av motsvarande typ. Multifunktionsfordonet (MV) är ett framtida koncept vars lastmoduler kan ändras för olika stadstransporter. MV möjliggör sekventiell delning av olika mobiliteter, vilket på ett teoretiskt sätt förbättrar stadslogistikens effektivitet genom högre användning av fordon. En variantmodell av Pick-up and Delivery Problem with Time Windows är etablerad för att beskriva det sekventiella delningsproblemet med beaktande av både MV och SV med funktionerna i flera depåer, partiella laddningsstrategier och flottans storlek. I problemet kan MV: er ändra sina belastningsmoduler för alla typer av objekt som bärs av SV: er. En adaptiv stor stadsdelalgoritm (ALNS) har utvecklats med nya mekanismer för MV. Den föreslagna ALNS testas av 15 artificiella datafall och jämförs med MIP-lösaren. Resultaten visar att det föreslagna ALNS är tidseffektivt och validerat för att hitta bra lösningar.