Adaptive large neighborhood search for the time-dependent profitable pickup and delivery problem with time windows

The rise of e-commerce has increased the demands placed on pickup and delivery operations, as well as customer expectations regarding the quality of services provided by those operations. One strategy a logistics provider can employ for meeting these increases in demands and expectations is to complement and coordinate its fleet operations with those of for-hire, third-party logistics providers. Herein, we study an optimization problem for coordinating these operations: the time-dependent profitable pickup and delivery problem with time windows. In this problem, the logistics provider has the opportunity to use its fleet of capacitated vehicles to transport shipment requests, for a profit, from pickup to delivery locations. Owing to demographic and market trends, we focus on an urban setting, wherein road congestion is a factor. As a result, the problem explicitly recognizes that travel times may be time-dependent. The logistics provider seeks to maximize its profits from serving transportation requests, which we compute as the difference between the profits associated with transported requests and transportation costs. To solve this problem, we propose an adaptive large neighborhood search algorithm. The results of our extensive computational study show that the proposed algorithm can find high-quality solutions quickly on instances with up to 75 transportation requests. Furthermore, we study its impact on profits when explicitly recognizing traffic congestion during planning operations.