  Cluster-wise linear regression (CLR), a clustering problem intertwined with
regression, is to find clusters of entities such that the overall sum of
squared errors from regressions performed over these clusters is minimized,
where each cluster may have different variances. We generalize the CLR problem
by allowing each entity to have more than one observation, and refer to it as
generalized CLR. We propose an exact mathematical programming based approach
relying on column generation, a column generation based heuristic algorithm
that clusters predefined groups of entities, a metaheuristic genetic algorithm
with adapted Lloyd's algorithm for K-means clustering, a two-stage approach,
and a modified algorithm of Sp{\"a}th \cite{Spath1979} for solving generalized
CLR. We examine the performance of our algorithms on a stock keeping unit (SKU)
clustering problem employed in forecasting halo and cannibalization effects in
promotions using real-world retail data from a large supermarket chain. In the
SKU clustering problem, the retailer needs to cluster SKUs based on their
seasonal effects in response to promotions. The seasonal effects are the
results of regressions with predictors being promotion mechanisms and seasonal
dummies performed over clusters generated. We compare the performance of all
proposed algorithms for the SKU problem with real-world and synthetic data.
