  Freight carriers rely on tactical plans to satisfy demand in a cost-effective
way. For computational tractability in real large-scale settings, such plans
are typically computed by solving deterministic and cyclic formulations. An
important input is the periodic demand, i.e., the demand that is expected to
repeat in each period of the planning horizon. Motivated by the discrepancy
between 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 strong
assumptions on the solution space so that the problem could be solved by
enumeration. In this paper we significantly extend their work. We propose a new
PDE formulation that relaxes the strong assumptions on the solution space. We
solve large instances of this formulation with a two-step heuristic. The first
step reduces the dimension of the feasible space by performing clustering of
commodities based on instance-specific information about demand and supply
interactions. The formulation along with the first step allow to solve the
problem in a second step by either metaheuristics or the state-of-the-art
black-box optimization solver NOMAD. In an extensive empirical study using real
data from the Canadian National Railway Company, we show that our methodology
produces high quality solutions and outperforms existing ones.
