Ind. Eng. Chem. Res. 2005, 44, 1985-1986
1985
CORRESPONDENCE Comments on “New General Continuous-Time State-Task Network Formulation for Short-Term Scheduling of Multipurpose Batch Plants” by Christos T. Maravelias and Ignacio E. Grossmann and on “Enhanced Continuous-Time Unit-Specific Event-Based Formulation for Short-Term Scheduling of Multipurpose Batch Processes: Resource Constraints and Mixed Storage Policies” by Stacy L. Janak, Xiaoxia Lin, and Christodoulos A. Floudas Christodoulos A. Floudas* and Stacy L. Janak Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544-5263
Sir: Our recent work1 extended the continuous-time unit-specific event-based formulation of Floudas and coworkers2-6 to address short-term scheduling problems of multipurpose batch processes that have mixed storage policies and resource constraints. The computational results in the work by Janak et al.1 were compared with our implementation of the global event-based model of Maravelias and Grossmann,7 which used time points that are common to all units, and a number of points of their paper7 were also addressed. We were not aware of the errata published as an Additions and Corrections paper.8 Therefore, all of the reported results in the paper by Janak et al.1 were based upon the original data in the paper by Maravelias and Grossmann.7 We implemented the model M* of Maravelias and Grossmann7 according to the description in their paper that consists of constraints (1)-(36). Extra constraints were added to model M* to account for the additional features specified in some problems. Constraint (37) was added to model M* for the case of sequence-dependent setup times, constraints (38)-(40) were added to model M* for the case of shared storage tanks, and constraints (11′) and (41) were added to model M* when the objective function was the minimization of the makespan. All of our reported results for the model M* were based on the hypothesis that no additional constraints (not reported by Maravelias and Grossmann7) were included. We have re-solved the examples presented in the work of Janak et al.1 with the errata reported by Grossmann.8 For example 1 in our paper1 or example 2 in their paper,7 we found that the new data reported in the errata8 addressed most of the issues in the work of Maravelias and Grossmann.7 The model and solution statistics for both formulations can be found in Tables 1 and 2. Note that the number of event points, binary variables, continuous variables, and objective function values match those reported in their paper.7 The number of constraints is consistently lower in our implementation of their model M*1 than the number of constraints reported in their paper.7 For this example, two different schedules in their paper,7 found in Figures 13 and 15, contain mass balances that are not satisfied. * To whom correspondence should be addressed. E-mail:
[email protected].
Table 1. Model and Solution Statistics for Example 1 (Janak et al.1 Formulation) with the Corrected Data of Maravelias and Grossmann8 max sales event points binary variables continuous variables constraints LP relaxation objective nodes CPU time (s)
min makespan
case 1
case 2
case 1
case 2
6 57 453 1528 10981.82 $5904.00 111 0.39
5 45 380 1238 6414.71 $5227.7778 12 0.13
7 69 526 1870 7.00 8.50 h 834 3.78
6 57 453 1568 7.00 9.025 h 22 0.35
Table 2. Model and Solution Statistics for Example 1 (Our Implementation of the Maravelias and Grossmann7 Formulation) with the Corrected Data8 max sales case 1 event points binary variables continuous variables constraintsa LP relaxation objective nodesa CPU time (s)
case 2
min makespan case 1
case 2
7 84 661
6 72 567
8 96 755
7 84 661
1145 (1335) 8870.47 $5904.00 882 (1173) 1.57
981 (11460 7267.08 $5227.7778 127 (117) 0.20
1310 (1528) 5.47 8.50 h 3589 (3411) 9.64
1146 (1339) 5.83 9.025 h 300 (509) 0.88
a Numbers in parentheses represent values reported by Maravelias and Grossmann.7
Table 3. New Corrected Data for Example 3a unit capmax capmin R β a
T11
T21
T12
T22
T13
T23
U1 5 2 0.5 0.4
U1 5 2 0.75 0.6
U2 3 1.2 1 1.333
U2 3 1.2 1 1.333
U1 5 2 0.5 0.4
U1 5 2 0.5 0.4
capmax/capmin in tons, R in h, β in h/tons batch.
Note that the violations of these mass balances in their paper7 are due to typographical errors. For example 3 in our paper1 or example 4 in the work of Maravelias and Grossmann,7 we found that the new data reported in their errata8 results in different schedules compared to the schedules reported in their paper.7 By analyzing parts a and b of Figure 20 in their paper,7 we were able to determine the correct set of data for this example, which can be found in Table 3. These data yield the objective function value of 5.019 reported in their original paper.7 The model and solution statis-
10.1021/ie050135j CCC: $30.25 © 2005 American Chemical Society Published on Web 02/19/2005
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Ind. Eng. Chem. Res., Vol. 44, No. 6, 2005
Table 4. Model and Solution Statistics for Example 3 with the New Corrected Data
event points binary variables continuous variables constraintsa LP relaxation objective nodesa CPU time (s)
Lin and Floudas6 formulation
our implementation of the Maravelias and Grossmann7 formulation
5 26 257 571 9.0 5.019 35 0.06
9 144 732 1411 (1627) 7.1307 5.019 2259 (3117) 5.93
a Numbers in parentheses represent values reported by Maravelias and Grossmann.7
tics for both formulations with the new corrected data can be found in Table 4. Literature Cited (1) Janak, S. L.; Lin, X.; Floudas, C. A. Enhanced ContinuousTime Unit-Specific Event-Based Formulation for Short-Term Scheduling of Multipurpose Batch Processes: Resource Constraints and Mixed Storage Policies. Ind. Eng. Chem. Res. 2004, 43, 2516.
(2) Ierapetritou, M. G.; Floudas, C. A. Effective ContinuousTime Formulation for Short-Term Scheduling. 1. Multipurpose Batch Processes. Ind. Eng. Chem. Res. 1998, 37, 4341. (3) Ierapetritou, M. G.; Floudas, C. A. Effective ContinuousTime Formulation for Short-Term Scheduling. 2. Continuous and Semicontinuous Processes. Ind. Eng. Chem. Res. 1998, 37, 4360. (4) 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. (5) Ierapetritou, M. G.; Hene´, T. S.; Floudas, C. A. Effective Continuous-Time Formulation for Short-Term Scheduling. 3. Multiple Intermediate Due Dates. Ind. Eng. Chem. Res. 1999, 38, 3446. (6) Lin, X.; Floudas, C. A. Design, Synthesis and Scheduling of Multipurpose Batch Plants via an Effective Continuous-Time Formulation. Comput. Chem. Eng. 2001, 25, 665. (7) Maravelias, C. T.; Grossmann, I. E. New General Continuous-Time State-Task Network Formulation for Short-Term Scheduling of Multipurpose Batch Plants. Ind. Eng. Chem. Res. 2003, 42, 3056. (8) Maravelias, C. T.; Grossmann, I. E. Additions/Corrections: New General Continuous-Time State-Task Network Formulation for Short-Term Scheduling of Multipurpose Batch Plants. Ind. Eng. Chem. Res. 2003, 42, 4422.
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