Sgraph Framework in Batch Process Scheduling

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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

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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

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Conventional representation

• Notations
• PT processing time
• Eq. equipment unit

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Graph representation
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Recipe

• Directed graph Products A, B, and C

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S-graph representation

• Directed graph
• The changeovers are denoted by arcs

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NIS vs. UIS
Unlimited Intermediate Storage
Non Intermediate Storage
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Schedule-graph

• An S-graph is a schedule-graph, if
• the equipment-task assignment and
• the operation order of the tasks are given
  (schedule-arc)

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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

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More than one batch per product

• Considering each batch as an individual product
  is not efficient enough

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Single equipment unit for a task
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Optional equipment units for a task with
identical processing time
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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

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Illustrative example
S-graph
Search tree
S-graph
Search tree
1
2
3
4
2
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Illustrative example
S-graph
Search tree
1
3
4
2
5
1
3
4
2
6
6
5
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Illustrative example search tree
1
3
4
2
6
5
1
1
7
3
4
2
2
3
4
5
6
5
6
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With cycle prediction
Without cycle prediction
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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)

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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

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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/