Introduction:
Sequencing model is the part of operation research which is not include in linear programming, used to minimise the production time and maximise the profit.
Sequencing model:
a) In sequencing model, the order or sequence in which the jobs are to be processed through machines so as to minimize the total processing time.
b) the total effectiveness, which may be the time or cost that is to be minimized is the function of the order of sequence. Such type of problem is known as SEQUENCING PROBLEM.
c) In case there are three or four jobs are to be processed on two machines, it may be done by trial and error method to decide the optimal sequence (i.e. by method of enumeration).
d) In the method of enumeration for each sequence, we calculate the total time or cost and search for that sequence, which consumes the minimum time and select that sequence.
e) This is possible when we have small number of jobs and machines. But if the number of jobs and machines increases, then the problem becomes complicated. It cannot be done by method of enumeration.
f) Consider a problem, where we have ‘machines and ‘m’ jobs then we have (n!)m theoretically possible sequences.
g) For example, we take n = 5 and m = 5, then we have (5!)5 sequences i.e. which works out to 25, 000,000,000 possible sequences. It is time consuming to find all the sequences and select optima among all the sequences.
h) Sequencing problem is basically a minimization problem or minimization model.
Definition:
A general sequencing problem may be defined as follows:
“ Let there be ‘n’ jobs (J1, J2, J3 ………Jn) which are to be processed on ‘m’ machines (A, B, C …), where the order of processing on machines i.e. for example, ABCmeans first on machine A, second on machine B and third on machine C or CBAmeans first on machine C, second on machine B and third on machine A etc. and the processing time of jobs on machines (actual or expected) is known to us, then our job is to find the optimal sequence of processing jobs that minimizes the total processing time or cost. Hence our job is to find that sequence out of (n!)m sequences, which minimizes the total elapsed time (i.e... time taken to process all the jobs).
The usual notations used in this problem are: Ai = Time taken by i th job on machine A where i = I, 2, 3…n. Similarly we can interpret for machine B and C i.e. Bi and Ci etc. T = Total elapsed time which includes the idle time of machines if any and set up time and transfer time”
