Scheduling and Scheduling Philosophies By Nilesh Sivaramakrishnan For IEM 5303

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

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

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]

Definitions and Measures(2) Jobs Machines Measures – Maximizing profit and minimizing costs –Proxy objectives Functions of completion time Objective is to minimize this function

Definition and Measures(3) n = Number of jobs to process m = Number of jobs to process p ik = the time to process job і on machine k (p i if m = 1) r i = the release time for job і d i = the due time for job і w i = the weight of job і relative to other jobs C i = the completion time for job і F i = C i - r i, the flow time of job і (F i > 0) L i = C i - d i, the lateness of job і (L i < 0 denotes earliness) T i = Max {0, L i }, is the tardiness of job і E i = max {0, - L i }, the earliness of job і

Definition and Measures(4) n|m|A|B –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

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

Classification of production scheduling (2) Scheduling criteria –Schedule cost –Schedule performance Requirements specifications –Deterministic scheduling –Stochastic scheduling Scheduling environment –Dynamic scheduling –Static scheduling

Classification of scheduling approaches (1) Scheduling approach –Conventional –Knowledge based –Distributed solving Conventional scheduling approaches –Algorithmic solutions –Enumeration methods –Scheduling heuristics –Discrete event simulation

Classification of scheduling approaches (2) Algorithmic solutions –Algorithm is a recipe for obtaining a solution to a model –Johnson’s algorithm (n|2|F|F max ) 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

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

Classification of scheduling approaches (4) Scheduling heuristics –Rules involving processing time –Dynamic scheduling rules –Rules involving due dates –Simple rules

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

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

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

References[1] [1] Rodammer, F.A., and White, K.P., ‘ A Recent Survey Of Production Scheduling’, IEEE Trans., 1988, SMC-18, (6), pp [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).

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 [7] Suresh, V., and Chaudhuri, D., ‘Dynamic Scheduling: A Survey Of Research’, International Journal Of Production Economics, 1993, 32, pp

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 [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).

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 [13] Conway, R.W., Maxwell, W.L., Miller, L.W., ‘Theory of Scheduling’, Mass, Addison- Wesley, (1967)