Some single machine scheduling problems with a learning effect

crazymeasleAI and Robotics

Oct 15, 2013 (3 years and 11 months ago)

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1

Some s
ingle

machine scheduling
problems
with a learning effect


Dar
-
Li Yang

(
楊達立
)

Department of Information Management

(
資管系
)

National
Formosa

University

(
虎尾科技大學
)

Yun
-
Lin, Taiwan 632, R.O.C.

E
-
mail:

dlyang@nfu.edu.tw



Abstract


In classical scheduling prob
lem
s
, the processing times of jobs are assumed to be
constant values. However, this assumption is not
appropriate
for the modeling of
many modern industrial processes where very often a job, executed in the same or
almost the same conditions, has a vari
ed

processing time. For example, a worker has
to assemble a large number of similar products. The processing time for the worker to
assemble one product depends on his knowledge, skills, organization of the working
place, and other

aspects
.
With repetition t
h
e worker learns how to

produce

the product
more efficiently
.
Consequently, h
e is better skilled, his knowledge has increased, and
the working place is better organized.
As a result
, the processing time for the worker
to assemble one product decreases. This

phenomenon is known as the “learning
effect” in
the
literature.

T
he learning effect was first applied to
the
industry more than
60 years ago (Wright [1]).
Since t
hen it has been studied extensively in a number of
areas (Nadler and Smith [2], Yelle [3]). H
owever, the learning effect has not been
studied in the context of scheduling until recently.

Biskup [4] was the first to investigate the learning effect in scheduling problems.
He assumed a learning process that reflects a decrease in the process time as
a
function of the number of repetitions i.e. as a function of the job position in the
sequence. Later, Mosheiov [5
-
6
] continued to study Biskup’s model

and

considered
the scheduling problem of minimizing flow time on parallel identical machines. He
showed
that the problem has a solution which is polynomial in the number of jobs.
T
he assumption of these papers is that the learning effect is
jo
b
-
independent
, i.e.
a
common
learning curve for all the jobs is assumed. However, in many realistic
situations, learn
ing of some jobs may be better than th
at

of others. Therefore,
M
osheiov and Sidney [
7
] further considered learning in the production process of
some jobs to be faster than th
at

of others, i.e. the learning
is

job
-
dependent
. They
showed that
the scheduling
problems of

makespan and total flow time minimization

on a single
-
machine, a due
-
date assignment problem, and total flow time
2

minimization on unrelated parallel machines remain polynomial
ly

solvable.

However, it still can not clearly describe
time
-
dependen
t

learning situations. That
is, the more time you practice, the better learning performance you will obtain. In this
discussion [8
-
9]
, we will introduce a time
-
dependent learning effect and incorporate it
into
some
single

machine scheduling problems i.e.

a

makespan minimization problem
,

and
a
total completion time minimization problem.


Keywords:
Scheduling, Time
-
dependent, Learning effect



References


[1] Wright TP. Factors affecting the cost of airplanes.
Journal of Aeronautical
Sciences

1936;
3:

122
-
128
.

[2]
Nadler

G,

Smith

WD.
Manufacturing progress functions for types of processes
.
International Journal of Production Research

1963;
2
:

115
-
135.

[3]
Yelle
LE.
The learning curve: historical review and comprehensive survey.
Decision Science

1979;
10
:

302
-
328
.


[4] Biskup D. Single
-
machine scheduling with learning considerations.
European
Journal of Operational Research

1999;
115:

173
-
178.

[5] Mosheiov G.

Scheduling problems with learning effect.
European Journal of
Operational Research

2001a;132:

687
-
693.

[6] Mosheiov G.

Parallel machine scheduling with learning effect.
Journal of the
Operational Research Society

2001b;
52:

1
-
5.

[7]
Mosheiov G, Sidney

JB. Scheduling with general job
-
dependent learning curves.
European Journal of Operational Research

2003;
1
47 :

665
-
670.

[8]
Kuo

WH,
Yang

DL.
Single
-
machine group scheduling with a time
-
dependent
learning effect.

Computers & Operations Research

2
005a;

(i
n press)
.

[9]
Kuo

WH,
Yang

DL.
Minimizing the
total completion time

in a single machine
scheduling problem wi
th a time
-
dependent learning effect.
European Journal of
Operational Research

2005b;
(under
the 2
nd

revision)
.