Goods Consumed During Transit in Split Delivery Vehicle Routing Problems: Modeling and Solution

Abstract

This article presents the modeling and solution of an extended type of split delivery vehicle routing problem (SDVRP). In SDVRP, the demands of customers need to be met by efficiently routing a given number of capacitated vehicles, wherein each customer may be served multiple times by more than one vehicle. Furthermore, in many real-world scenarios, consumption of vehicles en route is the same as the goods being delivered to customers, such as food, water and fuel in rescue or replenishment missions in harsh environments. Moreover, the consumption may also be in virtual forms, such as time spent in constrained tasks. We name such a real-world SDVRP as Split Delivery Vehicle Routing Problem with Goods Consumed during Transit (SDVRP-GCT). In this paper, we give mathematical formulas to model SDVRP-GCT and provide solutions by extending three ant colony algorithms. To the best of our knowledge, this is the first research work specifically focussing on the SDVRP-GCT problem and its solutions. To assess the effectiveness of our proposed ant colony algorithms, we first apply them on widely adopted SDVRP benchmarking instances on different scales and their correspondingly extended SDVRP-GCT instances. Then, we formulate a real-world SDVRP-GCT instance for further assessment. Based on the extensive experimental results, we discuss the pros and cons of our proposed solutions and subsequently suggest their preferable application scenarios. In summary, our proposed solutions are shown as highly efficient in solving SDVRP-GCT instances.

Review of research on vehicle routing problems

“…Local search algorithm for routing and a genetic algorithm and several construction heuristics for packing [28] An enhanced neighborhood search algorithm (ENS) incorporated with the maximumspace-utilization-based tabu search packing algorithm (MSUTS) [29] Q-learning theory and differential evolutionary algorithms for designing memetic algorithm [30] Sub-heuristic algorithm Novel genetic quantum algorithm [31] Three ant colony algorithms [32] Memetic algorithm [33] Generic heuristic algorithm Adaptive large neighborhood search (ALNS) [34] Branch and Cut Algorithm [35]…”

A Novel Macro and Micro Scheduling Model for Regulated Safety Inspections Based on Probability Integral Transform and Modified Bin Packing Algorithm

“…The Split Delivery Vehicle Routing Problem (SDVRP) was introduced as BPPIF variant in many studies [33,[39][40][41] where the demand at each customer can be split among multiple vehicle visits for better vehicle utilization and less routing costs as well as to estimate the minimum fleet size that is required to perform all deliveries.…”

Improved Ant Colony Algorithm for the Split Delivery Vehicle Routing Problem

“…In recent years, metaheuristic algorithms have attracted considerable attention due to their excellent performance. The currently proposed metaheuristic algorithms mainly include the tabu search algorithm [8,9], genetic algorithm [10,11], particle swarm optimization algorithm [12,13], variable neighborhood search algorithm [14,15], large neighborhood search algorithm [16,17], ant colony algorithm [18][19][20], chimp optimization algorithm [21], and mayfly algorithm [22]. We focus on the ant colony algorithm because it has performed well on many optimization problems [23][24][25][26].…”

“…This threshold is used to control the ants' strategy of choosing the next customer, thus enabling the algorithm to better balance convergence speed and global search ability. However, most of the existing thresholds are set to a fixed value [18,20]. Some scholars [27] divide several fixed intervals according to the number of iterations, and different control thresholds are used in different intervals.…”

“…Pheromones are very important in ant colony algorithms, and the improvement of pheromone processing in ant colony algorithms has been the focus of scholars. To prevent a traditional ant colony algorithm from falling easily into a local optimum, a recent study [20] improved the pheromone update strategy and prevented the algorithm from entering a local optimum prematurely by adjusting the pheromone content. Experiments show that the max-min ant colony algorithm has the best pheromone processing performance.…”