ESCAPE 18

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• Batch Scheduling with Intermediate Due Dates
  Using Timed Automata Models
• Subanatarajan Subbiah, Thomas Tometzki, Sebastian
  Engell
• Process Dynamics and Operations Group TU
  Dortmund, Germany

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Outline

• Introduction Batch scheduling problems
• Timed Automata based approach
• Modeling technique
• Solution technique
• Case study
• Numerical results
• Summary Outlook

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Introduction Batch Scheduling

• Multiproduct and multipurpose batch plants
• Production of high valued materials in low volume
• Flexibility
• Product variety
• Production quantity
• Scheduling problem - Decision making process
• Allocation of scarce resources to operations
• Meet the constraints
• Optimize one or more objective function(s)
• Multiple release dates for raw materials
• Intermediate due dates for demanded products
• Penalty
• Delay cost
• Storage or inventory cost

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Introduction Optimization Techniques

• Exact methods
• Mathematical programming - MI(N)LP
• Constraint programming (CP)
• Heuristics and meta-heuristics
• Evolutionary algorithm, Simulated annealing, Tabu
  search, ...
• Hybrid approach
• MI(N)LP CP Exact methods Heuristics
• New approach Timed automata Reachability
  analysis
• Approach to model real time discrete event
  systems
• Modeling approach transparent, relatively easy,
  
• Efficient solution techniques
• Pruning Reachability algorithms (Panek et.al.
  2004, 2005) (Abdeddaim et.al. 2004)
• Guidance Graph search algorithms

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TA Based Modeling Approach

• Illustrative example
• 2 recipes J1 , J2
• Recipe J1 - ( op1 , p1 , R1 ) -gt ( op2 , p2 ,
  R2 )
• Recipe J2 - ( op3 , p3 , R1 ) -gt ( op4 , p4 ,
  R2 )

a2
a1
f1
f2
c10
c1 p1
c10
c1 p2
c1 p1
c1 p2
a4
a3
f3
f4
c20
c20
c2 p3
c2 p4
c2 p3
c2 p4
a1
a2
a4
a3
f1
f2
f3
f4
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Modeling Release dates and Due dates

• Extension of the recipe J1 with,
• release date - r1
• due date - d1
• penalty - storage cost and delay cost

• Recipe automaton J1 with extensions

d
c1 r1
d
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TA Based Optimization Approach

• Parallel composition - J1

J2
R1
R2
J2
wop3
a3
eop3
R1
f3
wop4
a4
eop4
R2
f4
finishJ2
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Global Automaton

• Global automaton A

J1
due date automaton J1
J2 R1 R2
J1
due date automaton
wop1
eop1
wop2
eop2
earlyJ1
finishJ1
wdd
a2
a1
f2
f1
d
tardyJ1

d
finishJ1
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Reachability Graph
Initial state -
Global Automaton - A
finshJ1 finshJ1 wop3
Target state -
tardyJ1
d

• Each valid schedule is a path from the initial
  state to the final state

wdd
d

• The path with lowest cost corresponds to the
  optimal schedule

d

• Efficient search
• Search strategies
• guides
• Reduction techniques prunes
• Sub-optimal traces
• Identical traces

d
finshJ1 finshJ1 finishJ2
d
(Panek et.al. 2004, 2006)
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Case Study Batch Plant Demonstrator

• Process topology
• multistage, flexible flow shop structure
• Red White Blue
• Yellow White Green
• Constraints
• resource capacity and utilization
• timing constraint
• Discrete decision variables
• Objective function
• minimization of makespan
• minimization of lateness

• Multiple release dates
• Intermediate due dates

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Numerical Results

• Objective Minimization of delay cost ( optimal
  solution tardiness 0 )
• TA based optimization tool TAOpt (Panek et. al
  2004)
• Search strategy - depth first best first search
• Termination criteria - 2.6 mio. nodes explored
  (or) opt. sol. reached
• Comparison with continuous time MILP formulation
  with opt. gap 1
• GAMS 22.5 / CPLEX 10.2 (Ierapetritou et. al.
  99)

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Summary Outlook

• TA based modeling approach is transparent and
  intuitive
• TA based approach allows possible problem
  extensions
• Feasible solutions are computed faster
• Computation of lower cost bounds is under
  investigation
• Decomposition techniques to handle large scale
  problems will also be considered for future work

Thank you very much for your kind
attention Queries, comments ?
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