A Model and Algorithm for the Courier Delivery Problem with Uncertainty

Abstract

We consider the Courier Delivery Problem, a variant of the Vehicle Routing Problem with time windows in which customers appear probabilistically and their service times are uncertain. We use scenario-based stochastic programming with recourse to model the uncertainty in customers and robust optimization for the uncertainty in service times. Our proposed model generates a master plan and daily schedules by maximizing the coverage of customers and the similarity of routes in each scenario while minimizing the total time spent by the couriers and the total earliness and lateness penalty. The computational results show that our heuristic improves the similarity of routes and the lateness penalty at the expense of increased total time spent when compared to a solution by independently scheduling each day. Our experimental results also show improvements over current industry practice on two real-world data sets.

Models and Algorithms for Stochastic and Robust Vehicle Routing with Deadlines

“…This solution framework also offers the capability to solve the SVRP-D exactly if the probability for the tail of the convolution of the travel times can be computed. Third, we perform extensive computational experiments to evaluate the proposed Table 1 Summary of the related literature Author(s) Problem Uncertainty Recourse Deadline Network Approach description function restriction Laporte et al (1992) stochastic scenarios cost one deadline m-TSP branch-and-cut Lambert et al (1993) stochastic scenarios (2) cost one deadline m-TSP heuristic Kenyon and Morton (2003) stochastic scenarios (30) cost/prob one deadline m-TSP SAA/branch-and-cut Verweij et al (2003) stochastic scenarios (1000) cost one deadline SPP/TSP SAA/branch-and-cut Thomas (2008, 2009) stochastic scenarios (2) cost multiple deadlines PTSP heuristic Montemanni et al (2007) robust interval regret N/A TSP branch-and-cut/Benders Sungur et al (2010) stochastic scenarios (n/a) cost time windows VRP heuristic Lee et al (2012) robust budget of uncertainty n/a time windows VRP column generation Agra et al (2013) robust budget of uncertainty n/a time windows VRP column generation Jaillet et al (2014) robust unsatisfactory index n/a time windows SPP/TSP iterative procedure and their reformulation schemes. The algorithm for these problems are presented in Section 4 and the computational experiments are shown in Section 5.…”

“…They discussed several models with different recourses and proposed a heuristic to solve them. A more general case when time windows are imposed were considered in some studies (e.g., Russell and Urban (2008), Li et al (2010), Sungur et al (2010) and Taş et al (2013)). Since these problems are highly complicated, these studies limit themselves to the development of heuristics.…”

A decomposition approach for commodity pickup and delivery with time-windows under uncertainty

“…However, they consider in this paper an information-sparse scenario without implementation of intelligent transportation systems. Sungur et al (2010) consider the courier delivery problem with probabilistic customer arrivals and uncertain travel times, and use an approach that combines stochastic programming with recourse to model customer arrival uncertainty and robust optimization to capture uncertainty in travel times. This scenario-based approach maximizes customer coverage and route similarity over scenarios, and minimizes earliness and lateness penalties and total travel times.…”

“…While there has been extensive work on capturing specific types of uncertainty (such as demand uncertainty or travel time uncertainty) separately, there is relatively less work (for example, Sungur et al (2010) and Ordonez and Zhao (2011)) on capturing both types of uncertainty and generating robust solutions. Moreover, most models require knowledge of uncertainty distributions, whereas in practice, data generated from the field has only partial knowledge of the underlying distribution.…”

An Adaptive Memory Programming Framework for the Robust Capacitated Vehicle Routing Problem

“…The authors determine vehicle routes that satisfy the vehicle capacities and specified delivery time windows for all possible realizations of the uncertain problem data. Variants of the model were applied to a bioterrorism emergency planning problem (Shen et al 2009) and a courier delivery problem (Sungur et al 2010). The formulation from Sungur et al (2008) optimizes in view of the scenario where all customer demands and travel times attain their worst-case realizations simultaneously, which may 4 Article submitted to Transportation Science; manuscript no.…”