5042
Ind. Eng. Chem. Res. 2001, 40, 5042
Reply to Comments on “An Improved Continuous-Time Formulation for the Short-term Scheduling of Multipurpose Batch Plants” P. Castro,† A. P. F. D. Barbosa-Po´ voa,*,‡ and H. Matos† Departamento de Engenharia Quı´mica and Centro de Estudos de Gesta˜ o, Instituto Superior Te´ cnico, 1049-001 Lisboa, Portugal
Sir: The paper by Ierapetritou and Floudas3 did not give the exact values of the parameters used in their examples. Unfortunately, as illustrated by Tables 1 and 2 of Ierapetritou and Floudas,2 very slight differences in the parameter values lead to different values of the objective function. In particular, the values used by Ierapetritou and Floudas3 allow bigger batch sizes, which consequently results in higher profit. This effect caused misleading interpretations not only in our paper1 but also in theirs.3 For instance, in the last paragraph of p 4348, Ierapetritou and Floudas state that “the proposed formulation has the following advantages compared to the previously presented continuous-time formulations for short-term scheduling: ... (iii) the scheduling found from the solution of the proposed formulation corresponds to a higher profit value and consequently better utilization of the available resources, namely 71.518 compared to 71.45 and 71.47 presented by the two other formulations”. Similar statements were repeated until the conclusions on p 4355, where Ierapetritou and Floudas state that “Moreover, better objective values can be easily accomplished, since the models are easier to solve to optimality.” In view of the above analysis, this is clearly misleading. Using the batch sizes of the optimal schedules of Ierapetritou and Floudas3 coupled with our problem * To whom all correspondence should be addressed. † Departamento de Engenharia Quı ´mica. ‡ Centro de Estudos de Gesta ˜ o.
data does lead to schedules that violate time horizon constraints. This formed the basis for the comparison between the two formulations in section 6 in Castro et al.1 It is now evident that the apparent problems were caused by the slight differences in the data used. Although more nodes are required by our formulation to reach the solution, the required CPU times are very similar for four, five, and six event points if differences in computer performance are taken into account (Table 1 of ref 1). Thus, it seems unwarranted to conclude that our approach is relatively inefficient. It should be noted that the statement “...our formulation gives rise to mathematical models that are solved faster” in ref 1 referred to a comparison between the two RTN formulations and not between our RTN formulation and the STN formulation of Ierapetritou and Floudas.3 Literature Cited (1) Castro, P.; Barbosa-Po´voa, A. P. F. D.; Matos, H. An Improved RTN Continuous-Time Formulation for the Short-term Scheduling of Multipurpose Batch Plants. Ind. Eng. Chem. Res. 2001, 40, 2059. (2) Ierapetritou, M. G.; Floudas, C. A. Comments on “An Improved RTN Continuous-Time Formulation for the Short-term Scheduling of Multipurpose Batch Plants”. Ind. Eng. Chem. Res. 2001, 40, 5040. (3) Ierapetritou, M. G.; Floudas, C. A. Effective ContinuousTime Formulation for Short-Term Scheduling. 1. Multipurpose Batch Processes. Ind. Eng. Chem. Res. 1998, 37, 4341.
IE010632+
10.1021/ie010632+ CCC: $20.00 © 2001 American Chemical Society Published on Web 10/04/2001
