The Intermodal Railroad Blocking and Railcar Fleet-Management (IBRM) problem, introduced in 2025 by Kienzle, Bisaillon, Crainic, and Frejinger, integrates three consolidation processes (loading containers onto railcars, grouping railcars into blocks, assigning blocks to trains) with the management of a limited heterogeneous railcar fleet, and is solved in deterministic form as a scheduled service network design with resource management (SSND-RM) integer program on industrial instances from the Canadian National Railway. The authors explicitly leave open the extension of this integrated tactical planning problem to uncertainty and to operations: a contextual stochastic formulation at the tactical level, made difficult by demand distributions that are expected to be decision-dependent, and an operational short-horizon counterpart that adapts the tactical plan to unforeseen events such as equipment failures while managing the railcar fleet at finer temporal granularity. As of the cited literature, both directions remain open: existing stochastic service network design models treat demand uncertainty as exogenous and do not cover the integrated blocking and heterogeneous-fleet structure, while operational railcar work addresses isolated subproblems rather than network-wide adaptation of an integrated tactical plan.

Background

In freight railroads, a block is a group of railcars, possibly with different origins and destinations, that are coupled together and moved as a single unit between yards to reduce classification (re-sorting) work. Intermodal freight — containers on railcars — adds further coupling: containers of different types must be loaded onto railcars subject to physical loading rules, and railcars themselves are heterogeneous (e.g., single-platform vs multi-platform cars, each compatible with different container configurations). Tactical planning in this setting means building a repeatable plan, typically for a cyclic period such as a week, that is executed over a season: which extra train services to add to a given schedule, how to load containers onto railcars, how to group railcars into blocks, which blocks to use, how to route demand through the network, and how to allocate and reposition a limited heterogeneous railcar fleet. Kienzle, Bisaillon, Crainic, and Frejinger (2025) formalized this integrated question as the Intermodal Railroad Blocking and Railcar Fleet-Management (IBRM) problem and modeled it as a Scheduled Service Network Design with Resource Management (SSND-RM) problem — an integer linear program over a cyclic four-layer (container, car, block, train) continuous-time network representation, a modeling framework originating with Crainic, Hewitt, Toulouse, and Vu (2018). Because such formulations are hard to solve at scale, they computed high-quality warm-start solutions (initial feasible solutions fed to the solver) with a construction heuristic inspired by relax-and-fix (a method that solves a sequence of restricted problems in which some integer variables are temporarily relaxed) and could then solve realistic large-scale instances from the Canadian National Railway Company, a North American Class I railroad (the largest revenue category of North American freight railroads), with a general-purpose solver. Their experiments show that ignoring railcar fleet management or container loading constraints severely underestimates the capacity a railroad actually needs; the closest earlier work, intermodal block planning by Morganti, Crainic, Frejinger, and Ricciardi (2020), did not consider fleet management or extra service selection. Two modeling traditions border the open question. First, stochastic service network design: Hewitt, Crainic, Nowak, and Rei (2019) built a stochastic SSND-RM model with fleet sizing under scenario-based demand uncertainty, but for less-than-truckload (freight too small to fill a full truck, consolidated across shipments) and postal carriers, without the intermodal blocking and loading structure, and with demand distributions fixed in advance (exogenous uncertainty). Second, contextual stochastic optimization — methods that combine prediction from contextual features with decision-making under uncertainty, surveyed by Sadana, Chenreddy, Delage, Forel, Frejinger, and Vidal (2025) — and decision-dependent (endogenous) uncertainty, where the probability distribution of an uncertain quantity depends on the decision-maker's own choices. Frejinger and Hewitt (2025) argue that in transport systems demand is typically supply-dependent (the services a carrier decides to offer shape the demand it observes), making this coupling a fundamental open challenge for transport optimization rather than a technicality. The deterministic IBRM model assumes demand is known with certainty, which at the tactical planning level it is not; and the tactical plan, once executed, must confront unforeseen events (equipment failures, disruptions) that it does not anticipate.

Problem Statement

Formulate and solve the uncertainty-aware extensions of the Intermodal Railroad Blocking and Railcar Fleet-Management (IBRM) problem introduced by Kienzle, Bisaillon, Crainic, and Frejinger (2025), preserving its integrated structure (selection of extra train services, loading of containers onto railcars under loading rules, blocking of loaded and empty railcars, block selection, demand flow distribution, and management of a limited heterogeneous railcar fleet). The extension covers two open research directions identified by the authors, each making the integrated plan account for uncertainty across planning horizons: (1) at the tactical level, a contextual stochastic formulation of IBRM in which demand uncertainty is represented and, crucially, the demand distributions are treated as decision-dependent, since the services and plans chosen by the railroad shape the demand it observes; and (2) at the operational level, the corresponding shorter-horizon network-planning problem that adapts the tactical plan to unforeseen events such as equipment failures and manages the railcar fleet at a finer temporal granularity. Solutions should include formulations and algorithms that handle the decision-dependent uncertainty and the combinatorial richness of the integrated model at realistic Class I railroad scale. The research target covers both directions jointly: a formulation together with a solution algorithm for each, evaluated on representative instances at the scale of the industrial Canadian National Railway instances of the source study.

References

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