This paper discusses a multi-compartment vehicle routing problem (MCVRP) that occurs in the context of grocery distribution. Different temperature-specific product segments (e.g., frozen or ambient) are transported from a retail warehouse to outlets. Different temperature-specific product segments can be transported together using multicompartment vehicles. These trucks are technically able to have different temperature zones on the same truck by separating the capacity of a vehicle flexibly into a limited number of compartments. On one hand, this leads to a cost saving as different product segments ordered by one outlet can be delivered jointly using only one truck. This impacts the routing and the number of stops-i.e., the transportation costs and unloading costs. On the other hand, more than one shipping gate has to be approached at the warehouse to collect and load different product segments. As a consequence, the number of segments on each truck and therefore the number of compartments impact loading, transportation, and unloading costs.An extended MCVRP with flexible compartments is presented to account for these loading and unloading costs. To solve the problem that arises, a large neighborhood search (LNS) tailored to the extended model is defined. The LNS includes problem-specific extensions in terms of the removal and reinsert operators as well as the termination criteria. It is tested using a case study with a retailer, benchmark data, and randomly generated data. Results are also compared to existing approaches. In line with the analyses performed for the model introduced, it is shown that the integration of loading and unloading costs into the model impacts routing considerably, and ultimately results in significant savings potential for retailers.

During recent years, several companies have introduced small autonomous delivery robots and evidenced their technical applicability in field studies. However, a holistic planning framework for routing and utilizing these robots is still lacking. Current literature focuses mainly on logistical performance of delivery using autonomous robots, ignoring real world limitations, and does not assess the respective impact on total delivery costs. In contrast, this paper presents an approach to cost‐optimal routing of a truck‐and‐robot system for last‐mile deliveries with time windows, showing how to minimize the total costs of a delivery tour for a given number of available robots. Our solution algorithm is based on a combination of a neighborhood search with cost‐specific priority rules and search operators for the truck routing, while we provide and evaluate two alternatives to solve the robot scheduling subproblem: an exact and a heuristic approach. We show in numerical experiments that our approach is able to reduce last‐mile delivery costs significantly. Within a case study, the truck‐and‐robot concept reduces last‐mile costs by up to 68% compared to truck‐only delivery. Finally, we apply sensitivity analyses to provide managerial guidance on when truck‐and‐robot deliveries can efficiently be used in the delivery industry.

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Multi-compartment vehicles (MCVs) can deliver several product segments jointly. Separate compartments are necessary as each product segment has its own specific characteristics and segments cannot be mixed during transportation. The size and position of the compartments can be adjusted for each tour with the use of flexible compartments. However, this requires that the compartments can be accessed for loading/unloading. The layout of the compartments is defined by the customer and segment sequence, and it needs to be organized in a way that no blocking occurs during loading/unloading processes. Routing and loading layouts are interdependent for MCVs. This paper addresses such loading/unloading issues raised in the distribution planning when using MCVs with flexible compartments, loading from the rear, and standardized transportation units. The problem can therefore be described as a two-dimensional loading and multi-compartment vehicle routing problem (2L-MCVRP). We address the problem of obtaining feasible MCV loading with minimal routing, loading and unloading costs. We define the loading problem that configures the compartment setup. Consequently, we develop a branch-and-cut (B&C) algorithm as an exact approach and extend a large neighborhood search (LNS) as a heuristic approach. In both cases, we use the loading model in order to verify the feasibility of the tours and to assess the problem as a routing and loading problem. The loading model dictates the cuts to be performed in the B&C, and it is used as a repair mechanism in the LNS. Numerical studies show that the heuristic reaches the optimal solution for small instances and can be applied efficiently to larger problems. Additionally, further tests on large instances enable us to derive general rules regarding the influence of loading constraints. Our results were validated in a case study with a European retailer. We identified that loading constraints matter even for small instances. Feasible loading can often be achieved only through minor changes to the routing solution and therefore with limited additional costs. Further, the importance to integrate loading constraints grows as the problem size increases, especially when a heterogeneous mix of segments is ordered.