We study the problem of scheduling drayage operations in synchromodal transport. Besides the usual decisions to time the pick-up and delivery of containers, and to route the vehicles that transport them, synchromodal transport includes the assignment of terminals for empty and loaded containers. The challenge consists of simultaneously deciding on these three aspects while considering various resource and timing restrictions. We model the problem using mixed integer linear programming (MILP) and design a matheuristic to solve it. Our algorithm iteratively confines the solution space of the MILP using several adaptations, and based on the incumbent solutions, guides the subsequent iterations and solutions. We test our algorithm under different problem configurations and provide insights into their relation to the three aspects of scheduling drayage operations in synchromodal transport.

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We consider a Logistic Service Provider (LSP) that transports freight periodically in a long-haul round-trip. At the start of a round-trip, the LSP consolidates freights in a long-haul vehicle and delivers them to multiple destinations in a region. Within this region, the LSP picks up freights using the same vehicle and transports them back to the starting location. The same region is visited every period, independent of which freights were consolidated. Consequently, differences in costs between two periods are due to the destinations visited (for delivery and pickup of freights) and the use of an alternative transport mode. Freights have different time-windows and become known gradually over time. The LSP has probabilistic knowledge about the arrival of freights and their characteristics. Using this knowledge, the goal of the LSP is to consolidate freights in a way that minimizes the total costs over time. To achieve this goal, we propose the use of a look-ahead policy, which is computed using an Approximate Dynamic Programming (ADP) algorithm. We test our solution method using information from a Dutch LSP that transports containers daily, by barge, from the East of the country to different terminals in the port of Rotterdam, and back. We show that, under different instances of this real-life information, the use of an ADP policy yields cost reductions up to 25.5% compared to a benchmark policy. Furthermore, we discuss our findings for several network settings and state characteristics, thereby providing key managerial insights about look-ahead policies in intermodal long-haul round-trips.

Abstract. Logistic Service Providers (LSPs) offering hinterland transportation face the trade-off between efficiently using the capacity of longhaul vehicles and minimizing the first and last-mile costs. To achieve the optimal trade-off, freights have to be consolidated considering the variation in the arrival of freight and their characteristics, the applicable transportation restrictions, and the interdependence of decisions over time. We propose the use of a Markov model and an Approximate Dynamic Programming (ADP) algorithm to consolidate the right freights in such transportation settings. Our model incorporates probabilistic knowledge of the arrival of freights and their characteristics, as well as generic definitions of transportation restrictions and costs. Using small test instances, we show that our ADP solution provides accurate approximations to the optimal solution of the Markov model. Using a larger problem instance, we show that our modeling approach has significant benefits when compared to common-practice heuristic approaches.

We study the planning problem of selecting services and transfers in a synchromodal network to transport freights with different characteristics, over a multi-period horizon. The evolution of the network over time is determined by the decisions made, the schedule of the services, and the new freights that arrive each period. Although freights become known gradually over time, the planner has probabilistic knowledge about their arrival. Using this knowledge, the planner balances current and future costs at each period, with the objective of minimizing the total costs over the entire horizon. To model this stochastic and multi-period tradeoff, we propose a Markov Decision Process (MDP) model. To overcome the computational complexity of solving the MDP, we propose an Approximate Dynamic Programming (ADP) approach. Using different problem settings, we show that our look-ahead approach has significant benefits compared to a benchmark heuristic.