S-graph F ramework in B atch P rocess S cheduling

1. S-graph Framework in Batch Process Scheduling T. Holczinger1, R. Adonyi1, G. Biros1, J. Romero2, L. Puigjaner2, F. Friedler1 1Department of Computer Science, University of Veszprém, Veszprém, Egyetem u. 10., H-8200, Hungary 2Department of Chemical Engineering, Universitat Politècnica de Catalunya, Barcelona, Av. Diagonal 647, E-08028 CAPE Forum 2004 Veszprem

2. Problem definition Given: • The order of the tasks (recipe) • The set of plausible equipment units for each task (with operation times) • Necessary amount of products • Storage policy • Timing data Aim: • The optimal order of the tasks • Using the given resources

3. Conventional representation Notations PT: processing time Eq.: equipment unit

4. Product A Product B Product C Graph representation

5. Recipe • Directed graph Products: A, B, and C

6. 2 S-graph representation • Directed graph • The changeovers are denoted by arcs

7. 6 1 2 E1 E2 3 7 4 E2 E1 6 1 2 E2 E1 3 7 4 E2 E1 NIS vs. UIS Unlimited Intermediate Storage Non Intermediate Storage

8. 1 2 3 10 A E1 E3 E2 4 5 6 11 B E2 E3 E1 7 9 8 12 C E1 E2 E3 Schedule-graph • AnS-graph is a schedule-graph, if • the equipment-task assignment and • the operation order of the tasks are given (schedule-arc)

9. Basic algorithm • Branch and bound framework • Extension of the recipe-graph with schedule-arcs according to the rules • Introduction of schedule-arcs • Identical set of nodes • The weight of the recipe-arcs can be changed • The number of the possible extensions are finitethe algorithm is finite

10. Product A Product B More than one batch per product • Considering each batch as an individual productis not efficient enough

11. Single equipment unit for a task

12. Optional equipment units for a task with identical processing time

13. Acceleration tools • Cycle prediction • To predict that a subgraph has no feasible solution • Based on the cycle search algorithm • It can reduce the size of the search tree • LP model for sharpening the lower bound

14. 1 2 7 E1 E2 3 4 8 E1 E2 5 6 9 1 1 1 E1 E2 2 4 3 3 1 2 1 1 2 2 7 7 7 E1 E2 E1 E1 E2 E2 3 4 8 E1 E2 3 3 4 4 8 8 E1 E1 E2 E2 5 6 9 E2 E1 5 5 6 6 9 9 E2 E2 E1 E1 Illustrative example S-graph Search tree S-graph Search tree 1 2 4 3 2

15. 1 1 2 2 7 7 E1 E1 E2 E2 3 3 4 4 8 8 E1 E1 E2 E2 5 5 6 6 9 9 E2 E2 E1 E1 Illustrative example S-graph Search tree 1 3 4 2 5 1 3 4 2 6 6 5

16. 1 2 7 E1 E2 3 4 8 E1 E2 5 6 9 E2 E1 Illustrative example: search tree 1 3 4 2 6 5 1 1 7 3 4 2 3 4 2 6 5 6 8 7 9 5 10 7 11 12 13 With cycle prediction Without cycle prediction

17. Industrial size scheduling problem • 123 products • 31 different base products • 13 possible pack sizes from 5 to 20000 liters • Necessary amount is from 5 to 12000 tons for a year (solved the production of a week) • Batch size is 6 tons for each mixer • Two types of tank • T901 – T922 (8 tons) • T951 – T968 (15 tons) • 120 minutes minimum residence time for intermediate products in a tank (bubbling)

18. Parameters of the problem Number of products: 123 Total number of batches: 389 Number of equipment units Mixer: 5 (batch type equipment unit) Tank: 40 Packing line: 26 (continuous type equipment unit) Running time on PC (1 GHz) is less than 4 minutes and the optimality gap is 2.6%

19. Further information • Publications • E. Sanmartí, F. Friedler, and L. Puigjaner, Combinatorial technique for short term scheduling of multipurpose batch plants based on schedule-graph representation, Comput. Chem. Engng.22 (1998) • E. Sanmartí, L. Puigjaner, T. Holczinger, and F. Friedler, Combinatorial framework for effective scheduling of multipurpose batch plants, AIChE J.48 (2002) • Holczinger, T., J. Romero, L. Puigjaner, and F. Friedler, Scheduling of Multipurpose Batch Processes with Multiple Batches of the Products, Hung. J. Ind. Chem., 30, 305-312 (2002) • Demonstration programs • http://www.dcs.vein.hu/CAPO/demo/sch/