A mixed integer programming model for optimizing multi-level operations process in railroad yards

• Develop a time-expanded multi-layer network flow model to describe complex yard operational plan.
• Construct a mixed integer programming model to optimize overall performance in yard operations.
• Adopt a cumulative flow count representation to model spatial capacity constraints in tracks.
• Propose a lot-sizing-based valid inequality formulation and assignment-based heuristic rules.

A typical railroad hump yard contains multiple layers of complex operations. The railcars coming with inbound trains through the yard need to be humped into different classification tracks according to the destination, and then assembled to generate the desired outbound trains. During this complex procedure, the processing time of railcars and various resource constraints at different railroad yard facilities could significantly affect the overall performance of yard operations, individually and in combination. It is theoretically challenging to represent a large number of practical operation rules through tractable mathematical programming models. This paper first presents a time-expanded multi-layer network flow model to describe the connection between different layers of yard operations. A mixed integer programming model is developed to optimize the overall performance by jointly considering tightly interconnected facilities. We adopt a cumulative flow count representation to model the spatial capacity constraints in terms of the number of railcars in classification yards. A novel lot-sizing modeling framework and related valid inequality formulations are introduced to model the assembling jobs for outbound trains. We also develop an aggregated flow assignment model and earliest due date-based heuristic rules to determine the humping jobs sequence for reducing the search space. Numerical experiments are conducted to examine the solution quality and computational efficiency under different types of formulation strategies.