Sequential Models - Meaning, assumptions, Types and Problems

Sequencing Problems
Sequencing problems are quite common in real life.
They arise whenever there is a choice of determining the order in which
a number of jobs can be performed.
These problems play a very important role in manufacturing set-ups for
the optimal use of resources and/or the customer’s satisfaction.
Many-a-times, manufacturing firms produce goods made up of several
components, which are sourced from other manufacturing firms.
The final product undergoes many processes before it is taken to the
market for sale.
Since several machines are used in the production process, it is
important to sequence the production process optimally so that the
performance measures of the firm are satisfied.

Which occur commonly in our real life whenever n number of tasks
are to be performed in a predefined time schedule.
The aim is to determine the best available possible sequences of
jobs.
A sequencing problem is the determination of the best sequence
among all possible sequences.
Here ‘best’ may be defined with respect to set objectives or
performance measure for the concerned problem.
Sequencing Problems

Let us consider a common experience that most grown-up men face
everyday: whether to shave first and then take a bath, or to shave
after taking bath.
Clearly, the problem is to decide on the sequence (or order) of the two
tasks: shaving and bathing.
Now the choice lies between two alternative sequences, i.e.,
(1. Shaving, 2. Bathing) and (1. Bathing, 2. Shaving).
The first option ensures more cleanliness, whereas the second one gives
rise to ease in shaving.
The solution to the problem depends on the objective or performance
measure, i.e., cleanliness or ease in shaving, of the concerned
person.
Once the performance measure is specified, the solution is easy.
Example

What is??????
In sequencing problems, there are two or more customers (jobs) to
be served and one or more facilities (machines) available for this
purpose. We wish to know when each job is to begin and what its
due date or time is. We also wish to know which facilities are
required to do each job, in which order these facilities are required
and how long each operation is to take.
1
The selection of the appropriate order in
which a number of jobs (customers) are
to be performed (served) is called
sequencing.
2

An operation must be
completed before its
succeeding operation
can start.
Each operation, once
started, must be
completed
Assumptions we use while dealing
with sequencing problems:
Only one machine of
each type is available
No passing rule is followed
strictly, i.e., the same
order of jobs is
maintained over each
machine
Only one operation is
carried out on a
machine at a time
Processing times are
independent of the order
of processing the jobs.
A job is processed as
soon as possible, but
only in the order
specified
Processing times are
known and do not
change
The time involved in
moving jobs from one
machine to another is
negligible.

Types of Sequencing Models
Scheduling of n
jobs on m
machines
Scheduling of 2
jobs on m
machines
Scheduling of n
jobs on 2
machines
Scheduling of n
jobs on 3
machines
04
02
03
01

Let there be n jobs (1, 2, 3, . . . , n), each of which has to be
processed, one at a time, on each of m machines (A, B, C, …).
The time required for processing each job on each machine is
also given.
The order of processing each job through these machines may be
any of the (n!)ᴹpossible sequences.
But, we are interested in finding that technologically feasible
sequence for processing the jobs which gives the minimum
total elapsed time for all the jobs.
A general sequencing problem may
be defined as follows:

The possible sequences for processing of the jobs will be (2!)²= 4, which
are:
i) First process J1 , J2 in this order on machines A and B, respectively;
ii) First process J1 , J2 in this order on machines B and A, respectively;
iii) First process J2 , J1 in this order on machines A and B, respectively;
iv) First process J2 , J1 in this order on machines B and A, respectively.
For example, suppose we have a problem of 2 jobs (J1, J2) and 2
machines (A, B) with the following processing times (in hours)

For the first sequence, the various times can be calculated as in the following table:
Here, the total elapsed time is 12 hours.
The idle time for machine A = Total elapsed time - Time when the last job is out of the machine A,
= 12 – 6 = 6 hrs
The idle time for machine B = Time of starting the first job at B + (Time of starting the second job at
B – time of finishing the first job at B)
= 2 + (6 – 5) = 3 hrs
i) First process J1 , J2 in this order on machines A & B,
Jobs
Machine A Machine B
Time in Time Out Time in Time Out
J₁ 0 2 2 2+3=5
J₂ 2 2+4=6 6 6+6=12

For the second sequence , the various times can be calculated as in the following table:
The idle time for machine B
= Total elapsed time - Time when the last job is out of machine B
= 13 – 9 = 4 hrs
The idle time for machine A
= Time of starting the first job at A + (Time of starting the second job at A – time of finishing the first
job at A)
= 3 + (9 – 5) = 7 hrs
ii) First process J1 , J2 in this order on machines B and A
Jobs
Machine B Machine A
J₁ 0 3 3 3+2=5
J₂ 3 3+6=9 9 9+4=13

For the third sequence, the various times can be calculated as in the following table:
= Total elapsed time - Time when the last job is out of machine A
= 13 – 6 = 7 hrs
= Time of starting the first job at B + (Time of starting the second job at B – time of finishing the first
job at B)
= 4 + (10 – 10) = 4 hrs
iii) First process J2 , J1 in this order on machines A and B
Jobs
Machine A Machine B
J₂ 0 4 4 4+6=10
J₁ 4 4+2=6 10 10+3=13

For the fourth sequence , the various times can be calculated as in the following table:
= Total elapsed time - Time when the last job is out of machine B
= 12 – 9 = 3 hrs
= Time of starting the first job at A + (Time of starting the second job at A – time of finishing the first
job at A)
= 6 + (10 – 10) = 6 hrs
iv) First process J2 , J1 in this order on machines B and A
Jobs
Machine B Machine A
J₂ 0 6 6 6+4=10
J₁ 6 6+3=9 10 10+2=12

So, in the above example, the technologically feasible
sequence for processing the jobs, which gives the
minimum total elapsed time for all the jobs is either the
first sequence or the fourth sequence. Idle times of the
machines are also less for these sequences.
The processing, therefore, should be done adopting either
the first or the fourth sequence.

Sequential Models - Meaning, assumptions, Types and Problems

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Sequential Models - Meaning, assumptions, Types and Problems