Multi-Depot Pickup and Delivery Problem with Resource Sharing

Abstract

Resource sharing (RS) integrated into the optimization of multi-depot pickup and delivery problem (MDPDP) can greatly reduce the logistics operating cost and required transportation resources by reconfiguring the logistics network. This study formulates and solves an MDPDP with RS (MDPDPRS). First, a bi-objective mathematical programming model that minimizes the logistics cost and the number of vehicles is constructed, in which vehicles are allowed to be used multiple times by one or multiple logistics facilities. Second, a two-stage hybrid algorithm composed of a k-means clustering algorithm, a Clark-Wright (CW) algorithm, and a nondominated sorting genetic algorithm II (NSGA-II) is designed. The k-means algorithm is adopted in the first stage to reallocate customers to logistics facilities according to the Manhattan distance between them, by which the computational complexity of solving the MDPDPRS is reduced. In the second stage, CW and NSGA-II are adopted jointly to optimize the vehicle routes and find the Pareto optimal solutions. CW algorithm is used to select the initial solution, which can increase the speed of finding the optimal solution during NSGA-II. Fast nondominated sorting operator and elite strategy selection operator are utilized to maintain the diversity of solutions in NSGA-II. Third, benchmark tests are conducted to verify the performance and effectiveness of the proposed two-stage hybrid algorithm, and numerical results prove that the proposed methodology outperforms the standard NSGA-II and multi-objective particle swarm optimization algorithm. Finally, optimization results of a real-world logistics network from Chongqing confirm the applicability of the mathematical model and the designed solution algorithm. Solving the MDPDPRS provides a management tool for logistics enterprises to improve resource configuration and optimize logistics operation efficiency.

Pickup and delivery problem in the collaborative city courier service by using genetic algorithm and nearest distance

“…This relation occurs in all models. Comparing among models, the proposed model is the best model in creating low total travel distance rather than the previous models, the KMGA model [6] and SNLIFO [12]. This condition occurs in almost all number of orders, although in the beginning, the total travel distance of the proposed model is little bit higher than the previous models.…”

“…Pickup and delivery problem in the collaborative city courier service by using … (Purba Daru Kusuma) 1033 [6] and 30 percent lower than the SNLIFO model [12]. Figure 1(b) shows that the number of orders does not have relation to the outsourcing rate for the previous models [6], [12].…”

“…In this simulation, this proposed model is compared with the existing PDP models. The first compared model was acronymized as KMGA because it used K-means clustering and non-dominated sorting genetic algorithm (NSGA II) [6]. This model conducted resource sharing method.…”

“…The explanation of (3) to ( 7) is as; (3) declares that the vehicle's initial location is its depot or home, (4) shows that when all orders have been delivered, the vehicle will return to its depot. Else, the vehicle's next location is its nearest target node, (5) shows that vehicle's target nodes are the joint of pickup target nodes and delivery target nodes, (6) shows that the vehicle's pickup target nodes are all of vehicle's order pickup location where these orders have not been picked up, (7) shows that the vehicle's delivery target nodes are all of vehicle's order delivery locations where these orders have been picked up but have not been delivered.…”

“…The solution was developed by using quantum evolution algorithm. Wang et al [6] developed multi-depot PDP model where resource sharing is allowed. The system consisted of several logistic service providers.…”