This paper is a follow-up to a paper on the scheduling of heat-exchanger network cleaning. In the first part (Lavaja, J. H.; Bagajewicz, A Ind. Eng. Chem. Res. 2004, 43, 3924-3938), a new mixed-integer linear model for the planning of heat-exchanger cleaning in chemical plants was presented. This model minimizes the net present value of the combined costs of cleaning and energy; it takes into account changes in production rates and even changes in the properties and flows of the different streams throughout time. The model is extended here to allow the consideration of throughput reduction throughout the time horizon in cases where the maximum capacity of the furnace is reached. Results show that throughput reduction may be advisable at times. Multipurpose/multiperiod operation of the network under critical conditions is also addressed.