Scheduling railway freight delivery appointments using a bid price approach

This paper proposes a method for establishing aggressive but achievable delivery appointment times for railroad shipments, taking into account individual customer needs and forecasted available train capacity. The concept of scheduling appointment times is directly patterned after current motor carrier industry practice, so that customers can plan for rail or truck deliveries in the same way. A shipment routing problem is decomposed into a deterministic ‘dynamic car scheduling’ (DCS) process for shipments already accepted and a stochastic ‘train segment pricing’ (TSP) process for forecasting future demands which have not yet called in and for which delivery appointments have yet to be scheduled. Both are formulated as multi-commodity network flow (MCNF) problem, where each shipment is treated as a separate commodity. Gain coefficients represent recapture probabilities that a specific customer will accept a carrier's service offer. A comparision with a widely used revenue management formulation is given. A Lagrangian heuristic for obtaining a primal solution is also described. The problem is solved within a 1% gap using the subgradient algorithm.