Scheduling and Scheduling Philosophies

1
Scheduling and Scheduling Philosophies

• By
• Nilesh
• Sivaramakrishnan
• For
• IEM 5303

2
Overview

• Introduction
• Definitions and measures
• Classification of Scheduling
• Classification of scheduling approaches
• Drawbacks of traditional approaches
• Conclusion

3
Introduction (1)

• Scheduling
• Is a form of decision making
• It is the efficient allocation of resources
• The objective is to find a way to assign and
  sequence shared resources to
• Minimizing production costs and satisfying all
  production constraints

4
Definitions and Measures (1)

• Scheduling is the process of organizing
  choosing and timing resource usage to carry out
  all the activities necessary to produce the
  desired outputs at desired times, while
  satisfying a large number of time an relationship
  constraints among the activities and resources
• Morton and Pentico (1993)3

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Definitions and Measures(2)

• Jobs
• Machines
• Measures
• Maximizing profit and minimizing costs
• Proxy objectives
• Functions of completion time
• Objective is to minimize this function

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Definition and Measures(3)

• n Number of jobs to process
• m Number of jobs to process
• pik the time to process job ? on machine k (pi
  if m 1)
• ri the release time for job ?
• di the due time for job ?
• wi the weight of job ? relative to other jobs

• Ci the completion time for job ?
• Fi Ci - ri, the flow time of job ? (Fi gt 0)
• Li Ci - di, the lateness of job ? (Li lt 0
  denotes earliness)
• Ti Max 0, Li , is the tardiness of job ?
• Ei max 0, - Li , the earliness of job ?

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Definition and Measures(4)

• nmAB
• n is the number of jobs
• m is the number of machines
• A describes the flow pattern
• B describes the performance measure

• Assumptions
• Data are known with certainty
• Set up times are independent of order of
  processing
• All jobs are immediately available
• No precedence exists between jobs
• Once jobs starts processing it cannot be
  interrupted

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Classification of production scheduling (1)

• Requirement generation
• Open shop
• Closed shop
• Processing complexity
• One-stage, one processor (facility)
• One stage, parallel processors (facilities)
• Multistage, flow shop
• Multistage, job shop

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Classification of production scheduling (2)

• Scheduling criteria
• Schedule cost
• Schedule performance
• Requirements specifications
• Deterministic scheduling
• Stochastic scheduling
• Scheduling environment
• Dynamic scheduling
• Static scheduling

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Classification of scheduling approaches (1)

• Scheduling approach
• Conventional
• Knowledge based
• Distributed solving
• Conventional scheduling approaches
• Algorithmic solutions
• Enumeration methods
• Scheduling heuristics
• Discrete event simulation

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Classification of scheduling approaches (2)

• Algorithmic solutions
• Algorithm is a recipe for obtaining a solution to
  a model
• Johnsons algorithm (n2FFmax )
• Start processing with the job having the shortest
  processing time on machine 1
• Finish processing with the job having the
  shortest processing time on machine 2
•   

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Classification of scheduling approaches (3)

• Enumeration methods
• Objective is to eliminate large groups of
  non-optimal solutions
• Lists or enumerates all possible schedules and
  then eliminates the non-optimal possibilities
  from the list
• Dynamic programming
• Branch and bound method

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Classification of scheduling approaches (4)

• Scheduling heuristics
• Rules involving processing time
• Dynamic scheduling rules
• Rules involving due dates
• Simple rules

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Classification of scheduling approaches (5)

• Discrete event simulation
• Approach for implementing scheduling forecasting
  system
• Problem analysis
• Model development
• Experimentation, Integration, prototype
  development
• Implementation, Installation, and training

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Drawback of traditional approach

• Failed to bridge the gap between theory and
  practice
• Assumed idealized conditions in the problem
  formulation
• Optimization algorithms
• Heuristic solutions
• Enumeration methods
• Discrete event simulation

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Conclusion

• No single approach offers a unified theory of
  production scheduling
• Reduce the gap between theory and practice
• Combine traditional approach with knowledge based
  approach
• Essential characteristics of a good scheduling
  system

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References1

• 1 Rodammer, F.A., and White, K.P., A Recent
  Survey Of Production Scheduling, IEEE Trans.,
  1988, SMC-18, (6), pp.841-851
• 2 Michael Pinedo, Scheduling Theory,
  Algorithms, And Systems, New Jersey, Prentice
  Hill (1995).
• 3 Morton, T.E., and Pentico, D.W., Heuristics
  Scheduling Systems, New York, John Wiley Sons
  (1993).
• 4 Sipper, D. and Bulfin, R.L., Production
  Planning, Control, and Integration, New York,
  McGraw Hill (1997).

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References 2

• 5 Baver, A., Bowden, R., Browne, J., Duggan,
  J., and Lyons, G., Shop Floor Control Systems
  From Design To Implementation, New York, Chapman
  Hill (1991).
• 6 Graves, S.C., A Review Of Production
  Scheduling, Operat. Res., 1981, 29, (4), pp.
  646-675
• 7 Suresh, V., and Chaudhuri, D., Dynamic
  Scheduling A Survey Of Research, International
  Journal Of Production Economics, 1993, 32, pp.
  53-63.

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References 3

• 8 Cunningham, P. and Browne, J., A LISP-
  Based Heuristic Scheduler For Automatic Insertion
  In Electronics Assembly, International Journal
  Of Production Research, 1986, 24, (6), pp.
  1395-1408.
• 9 Bellman, R., Dynamic Programming, New York,
  Princeton University Press (1957).
• 10 French, S., Sequencing and Scheduling An
  Introduction To The Mathematics Of The Job Shop,
  West Sussex, Ellis Harwood Ltd., (1982).
• 11 Barr, A., Feigenbaum (eds), The Handbook of
  Artificial Intelligence, Vol1. MA,
  Addison-Welsey,(1981).

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References 4

• 12 Blackstone, J.H., Phillips, D.T, Hogg, G.L.
  A State-Of-The-Art Survey Of Dispatching Rules
  For Manufacturing Job Shop Operation,
  International Journal of Production Research,
  1982, 20, (1), pp. 27-45.
• 13 Conway, R.W., Maxwell, W.L., Miller, L.W.,
  Theory of Scheduling, Mass, Addison-Wesley,
  (1967)