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Freight carriers rely on tactical plans to satisfy demand in a cost-effectiveway. For computational tractability in real large-scale settings, such plansare typically computed by solving deterministic and cyclic formulations. Animportant input is the periodic demand, i.e., the demand that is expected torepeat in each period of the planning horizon. Motivated by the discrepancybetween time series forecasts of demand in each period and the periodic demand,Laage et al. (2021) recently introduced the Periodic Demand Estimation (PDE)problem and showed that it has a high value. However, they made strongassumptions on the solution space so that the problem could be solved byenumeration. In this paper we significantly extend their work. We propose a newPDE formulation that relaxes the strong assumptions on the solution space. Wesolve large instances of this formulation with a two-step heuristic. The firststep reduces the dimension of the feasible space by performing clustering ofcommodities based on instance-specific information about demand and supplyinteractions. The formulation along with the first step allow to solve theproblem in a second step by either metaheuristics or the state-of-the-artblack-box optimization solver NOMAD. In an extensive empirical study using realdata from the Canadian National Railway Company, we show that our methodologyproduces high quality solutions and outperforms existing ones.

A Two-step Heuristic for the Periodic Demand Estimation Problem