This paper deals with short-time planning and scheduling in multipurpose plants subject to a variable demand profile. In this case, production delays are often due to equipment overload, and this paper addresses a two-level approach that is intended to help managers engineer a scheduling solution that fulfills a compromise between products' demands and plant loading. At the first level, once a product's demand and raw-material delivery plan are defined, backward and forward explosion procedures are developed in such a way that time windows, defined by the earliest starting time and latest finishing time for each batch, are generated. Those time windows are submitted to an extended capacity analysis, based on constraint-propagation mechanisms, which is intended to reduce the time windows. If, after the capacity analysis, the problem is still feasible and the plant loading is accepted, then a scheduling procedure is launched. The scheduling approach is based on a uniform discrete time representation that is intended to explore plant features, such as, zero-wait policies, limited storage; and/or low equipment demand. The mixed integer linear problem (MILP) approach, combined with the time-window shortening procedure at the planning level, leads to smaller MILP problems, thereby reducing the solution time.