We study the problem of generating daily production schedules in a two
-stage production system that is typical of many processing industries
. We first describe the problem as it occurs in practice, and then pre
sent an integer programming model that maximizes a weighted sum of the
customer orders to be processed in a day's work when a priori product
ion sequences are specified at some stations. Bounds on the optimal so
lution are obtained by a lagrangian relaxation, and two heuristic proc
edures are developed and tested empirically. We show how these procedu
res can be incorporated in an interactive solution scheme to generate
good production schedules.