A paint manufacturing firm's customers typically place orders for two or more products
simultaneously. Each product belongs to a family that denotes batching compatibility
during manufacturing. Further, products can be split into several sublots to allow
overlapping production in a two-stage hybrid flow shop wherein various identical,
capacitated machines operate in parallel at each stage. We present a mixed-integer
linear program (MILP) for this integrated batching and lot streaming problem with
variable sublots, incompatible job families, and sequence-dependent setup times. The
model determines the number and size of sublots for each product and the production
sequencing for each sublot such that the total weighted completion time is minimised.
To promote practical implementation, we develop and evaluate heuristics to efficiently
solve this problem.