Docstoc

TWO-MACHINE

Document Sample
TWO-MACHINE Powered By Docstoc
					  INTERNATIONAL JOURNAL ISSN 0976 – 6502(Print), ISSN 0976
 International Journal of Management (IJM), OF MANAGEMENT (IJM) –
 6510(Online), Volume 3, Issue 2, May-August (2012)

ISSN 0976 – 6367(Print)
ISSN 0976 – 6375(Online)
Volume 3, Issue 2, May- August (2012), pp. 54-58                         IJM
© IAEME: www.iaeme.com/ijm.html
Journal Impact Factor (2011): 1.5030 (Calculated by GISI)          ©IAEME
www.jifactor.com




   TWO-MACHINE NO-WAIT FLOWSHOP SCHEDULING- A NEW
                     APPROACH
                                   Dr. Sunita Gupta
             Galaxy global Group of Institutions Ambala (Haryana) – INDIA
                                sunigupt@yahoo.co.in

 ABSTRACT

 No-wait scheduling problem is one of the classical scheduling problem that exist on
 many kinds of industries with no-wait constraint, such as metal working, plastic,
 chemical and food industries. In the two-machine no-wait flowshop problem, each job
 has to be processed on both the machines subject to the constraint that the processing on
 2nd machine follows the processing on machine 1 without waiting. In this paper the two-
 machine no-wait flowshop scheduling problem in which each machine may have an
 availability constraint is considered and the objective is to find an optimal sequence in
 which the jobs will not wait for second machine after the process on first machine.

 Key words: flowshop scheduling, idle time of machines, No-wait scheduling, optimized
 sequence.

 1. INTRODUCTION

 Scheduling tasks are applied in many fields of industrial production as they intend to
 optimally utilize the resources while meeting the customer requirements. Scheduling is
 considered for the allocation of available resources to a set of operations or tasks over a
 planning horizon, the objective being to best satisfy one or more performance criteria e.g.
 minimum make span, idle time or mean completion time etc.
         In a flow shop, the scheduling problem can be classified into two categories
 namely with and without an operation interval waiting time. In a flow shop system with
 waiting times, the jobs are processed from one machine to the next one allowing waiting
 time in between, whereas, in a no-wait flow shop system, the jobs are processed from one
 machine to the next machine without waiting time. Therefore, in the classical flow shop
 sequencing problem with waiting time jobs may be queued in front of each machine. In
 such a case, an unlimited buffer is considered at the front of each machine (Grabowski

                                             54
International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –
6510(Online), Volume 3, Issue 2, May-August (2012)

and Pempera, 2000 [4]).Johnson 1954 [6] has developed an algorithm to minimize the
makespane in such type of situation. In contrast, in a no-wait flowshop, jobs are
processed from one machine to the next without waiting time. There are two main
reasons for having a no-wait scheduling environment: either initiated from the nature of
production or the lack of intermediate buffers. In some industries, due to the temperature
or other attributes of the materials it is required that each operation follow the previous
one immediately. This means, when necessary, the start of a job on a given machine is
delayed in order that the operation’s completion coincides with the start of the next
operation on the subsequent machine. Similarly, a no-wait flow shop aims at minimizing
the in process buffer to obtain ‘Just In Time’ production. Applications of a no-wait flow
shop can be found in many industries such as plastic production processes that require a
series of processes to immediately follow one after another in order to prevent material
degradation during production. Similar situations also arise in the chemical and
pharmaceutical industries. Aldowaisan and Allahverdi, 2004 [1]; Candar, O. (1999) [2];
Grabowski and Pempera, 2000 [4]; Hall and Sriskandarajah, 1996 [5]; Raaymakers and
Hoogeveen, 2000 [7] have studied the no-wait problem extensively in the scheduling
literature. Hall and Sriskandarajah (1996) [5] reviewed the literature on this subject.
Reddi and Ramamurthy (1972) [8] proposed the Travelling Salesman Problem technique
to solve the flow shop scheduling problem. Gilmore and Gomory (1964) [3] also studied
a two stage, single processor no-wait flow shop problem using the Travelling Salesman
Problem techniques. The results of the investigation revealed that a Travelling Salesman
Problem based branch and bound algorithm obtained optimal solutions.
         In this paper, a no-wait two stage flow shop scheduling problem with minimum
flow time is investigated. The aim of this paper is to investigate the performance of the
proposed heuristic algorithms to solve a no-wait two stage flow shop scheduling problem
with minimum flow time. The remainder of this paper is organized as follows.
Assumptions and the notations used in the paper are denoted in section 2. In Section 3,
the problem studied in this research is described in detail. In Section 4, the structure of
the proposed algorithms is explained. Then numerical tests are established to solve the
problems in section 5. This is followed by a demonstration of the simulation results.
Finally Section 6 presents a summary of the research with concluding remarks and
recommendations for further research.

2. ASSUMPTION & NOTATIONS

        Consider an n job 2 machine no-wait flowshop scheduling problem where the
machines are ceaselessly ready to be used from time zero onwards. At any time, every
job can be processed at most one machine and every machine can process at most one
job. Preemption is not permitted; i.e., once an operation is started, it must be completed
without interruption

M1     1st Machine
M2     2nd Machine
Ji     ith job
S      optimal sequence
πi     ith position of the job in optimal sequence

                                            55
International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –
6510(Online), Volume 3, Issue 2, May-August (2012)

3. PROBLEM DESCRIPTION

        The problem studied in this paper is a no-wait two stage flow shop scheduling
problem. The performance of the proposed heuristic algorithm is studied in terms of the
Minimization of flow time. The structure of the problems studied is as follows. A set of n
jobs J = j1, j2, · · ·, jn are to be processed in a shop. Each job consists of two operations to
be processed in two subsequent stages namely S1 and S2. No-waiting time is allowed
between the two subsequent operations. Stages S1 and S2 have M1 and M2 machines,
respectively. The processing times of job i is Pi1 and Pi2 on machines M1 and M2
respectively. Hence, n jobs have n! possible schedules and in this paper an heuristic
algorithm for the above problem is proposed. The framework of this algorithm is
described in the next section.

4. PROPOSED ALGORITHM

       To find an optimal sequence S of the jobs processing on two the machines we will
follow the following steps:-

1. Select a job having maximum processing time on machine M1 and put it at the first
   position of the sequence S. Let it be π1.
2. Now to select the 2nd job π2 of the optimal sequence S, consider all the jobs whose
   processing time on M1 is greater than the processing time of π1 on M2 and among
   them the one whose processing time is maximum on M2 is considered as 2nd job of
   the optimal sequence. It is denoted by π2.
3. For the next selection of jobs in the sequence, again consider the jobs whose
   processing time on M1 is greater than the processing time of π2 on M2 and among
   them the one whose processing time is maximum on M2 is considered as 3rd job as
   π3. Continue this process till the jobs are available.
4. If no such job is available whose processing time on M1 is greater than the
   processing time of its previous job on M2 then go to step 1 again till all the jobs are
   considered.
5. If there are more than one jobs having same maximum processing time on machine1
   during the selection of jobs for the optimal sequence, than consider the one whose
   processing time on machine 2 is maximum.

5. COMPUTATIONAL EXPERIMENTS

        In this study, a test problem is used to evaluate the performance of the proposed
algorithm. The data sets used in this research are created in various sizes in terms of
seven jobs processing on two machines. Tab. 1 demonstrates the processing time of jobs
on machines M1 and M2 in the problem.




                                              56
International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –
6510(Online), Volume 3, Issue 2, May-August (2012)


                  Job      J1        J2    J3       J4        J5       J6   J7
                  M1       8        21     14       10        15       16   21
                  M2       15       12     18       13        20       9    15

                                                Table 1
5.1 Solution for the optimal sequence
     To find the optimal sequence the steps of proposed algorithm are as follows
     1.                             There are two jobs J2 & J7 having maximum processing time
        i.e. 21 on machine M1 but job J7 has the greater processing time 15 on M2. So π1
        = J7
     2.                            Now for the selection of 2nd job , there are three jobs J2 J5& J6
        but the processing time of J5 on M2 is maximum. So π2 = J5
     3.                            Following the next steps of the algorithm, the sequence S= {
        J7, J5, J3, J2, J1, J6,J4 } is an optimal sequence

5.2 Optimal Makespane and the idle time of the machines


jobs 7             5            2          3              6        4          1       Idle
                                                                                      time
M1        0-21     21-36        36-57      57-71          73-89    89-99      104-112 7 units
M2        21-36    36-56        57-69      71-89          89-98    99-112     112-127 4 units



6. CONCLUSION & FURTHER RESEARCH

    In this paper, a new algorithm is developed to solve the no-wait two stage flow shop
scheduling problem. For this purpose, a numerical experiment is established to evaluate
the performance of the proposed algorithm. In general the results revealed that the
proposed outperforms gives an optimal sequence which minimizes the flow time and the
machines’ idle time of the problem. So in case of finding hiring time of the machines or
the machine utility cost, this algorithm is very useful. Therefore the proposed algorithm
can be considered as an efficient algorithm for a no-wait two stage flow shop with
minimum flow time. For further research, it is recommended that the performance of the
proposed algorithm with respect to other performance measures such as due time,
lateness and tardiness of the jobs be investigated and even on three or more machines. In
addition, the performance of the proposed algorithms for a problem with a sequence
dependent set up time, transportation time, job blocking concept are also worth studying.




                                                  57
International Journal of Management (IJM), ISSN 0976 – 6502(Print), ISSN 0976 –
6510(Online), Volume 3, Issue 2, May-August (2012)


REFERENCES

[1] Aldowaisan, T. and Allahverdi, A. (2004). A New heuristics for m-machine no-wait
flow shop to minimize total completion time. Omega, 32:345–352.

[2] Candar, O. (1999). Machine scheduling problems with blocking and no-wait in
process. Department of Industrial Engineering. Research Report, Bilkunt University.

[3] Gilmore, P. and Gomory, E. (1964). Sequencing a one statevariable machine: A
solvable case of the traveling salesman problem. Operations Research, 12(5):655–679.

[4] Grabowski, J. and Pempera, J. (2000). Sequencing of jobs in some production system.
European Journal of Operational Research, 125:535–550.

[5] Hall, N. and Sriskandarayah, C. (1996). A survey of machine scheduling problems
with blocking and no-wait in process. Operations Research, 44:510–525.

[6] Johnson, S.M (1954), optimal two and three stage production scheduling with set up
times included , Nav Res Log Quart, Vol1 pp 61-88.

[7] Raaymakers, W. and Hoogeveen, J. (2000). Scheduling multipurpose batch process
industries with no-wait restrictions by simulated annealing. European Journal of
Operational Research, 126: 131–151.

[8] Reddi, S. and Ramamoorthy, C. (1972). On the flow shop sequencing problem with
no-wait in process. Operational Research Quarterly, 23(3):323–331.




                                          58

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:7
posted:11/17/2012
language:
pages:5