Malaya Journal of Matematik, Vol. S, No. 1, 75-78, 2018

https://doi.org/10.26637/MJM0S01/14

Recent trends in sequencing and schedulingManisha Sharma1*, Himansha Sharma2 and Meenakshi Sharma3

AbstractIn the present paper an overview has been demonstrated, on recent developments in the literature of sequencingand scheduling. These strategies are very useful in the academic literature and very important tools in the areaof operational research. Sequencing has given a remarkable attention in research since the improvement ofacademic publications. In this paper, various tools and techniques of sequencing, has been studied that areused in the scheduling of process. Scheduling comes in branch of mathematical modeling in which the problemsare pre defined, and there are common characteristics that are translated into similar types of constraints. Herevarious categories of scheduling and sequencing models are identified. Directions for future research are alsoprovided in present paper scenario along with objective of creating bridge between theory and practical use ofdifferent types of sequencing and scheduling in the field of operations research.

KeywordsSequencing, Scheduling.

1,3Department of Mathematics, Panjab University, Chandigarh-160014, India.2Rajiv Gandhi Proudyogiki Vishwavidyalaya, Bhopal-462036, Madhya Pradesh, India.*Corresponding author: 1manishatewaripu@gmail.comArticle History: Received 24 December 2017 ; Accepted 21 January 2018 c©2018 MJM.

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

2 Literature Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3 Objective of Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4 Types of Scheduling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76

5 Types of Scheduling Problems . . . . . . . . . . . . . . . . . . . . 77

6 Types of Scheduling Approach . . . . . . . . . . . . . . . . . . . . 77

7 Sequencing Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

8 Sequencing Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

9 Applications Of Scheduling & Sequencing . . . . . . . .78

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

1. IntroductionIn the recent time Scheduling had very important role in

many areas. It has practical importance in many challengingsituations of real world. Scheduling is basically the advance-ment of real life word schedule. In other words we can say,scheduling is allocation of available resources over a particulartime to perform a number of jobs.

There are various types of scheduling in different fields.Some types of scheduling involves Exams schedule in vari-ous institutes, bus time table schedule, car service schedule

etc. Whereas sequencing is the order in which the jobs areprocessed. It is the selection of an appropriate order in whicha number of operations can be assigned to a finite number ofmachines, so as to optimize the outputs in terms of time, costor profit.

There are many types of sequencing problems:

(1) n jobs through one machine.

(2) n jobs through two machines.

(3) n jobs through three machines.

2. Literature SurveyScheduling and Sequencing is one of the most important

researched areas of operational research. Classical flow shopscheduling problems are those which mainly focuses on com-pletion time related objectives. Best scheduling system resultsin significant impact on cost reduction, increased productivity,customer satisfaction and overall competitive advantage.

In addition, nowadays in production and manufacturingunits increase in demand of consumers for different high qual-ity products has resulted in increase of production complexitythat further emphasizes the need for improved scheduling.

Improved scheduling leads to increase in Utilization ca-pacity and hence thereby reduction in the time required tocomplete jobs and consequently increasing the profitability

Recent trends in sequencing and scheduling — 76/78

of an organization in present competitive environment. Intrendy producing and operations management, on time deliv-ery with minimum potential price may be an important issueas for the explanation of upward stress of competition on themarkets. Trade has got to supply a good type of completelydifferent and individual merchandise whereas customers pre-dict ordered product to be delivered on time. Hence, there’s ademand of multi-objective planning system through that allthe objectives will be achieved at the same time.

Johnson’s (1954) provided the place to begin to planningbeing considered a freelance space at intervals operationalanalysis. Johnson thought of the assembly

model that’s currently known as the flow look.Ignall & Scharge (1965) have introduced branch and bound

technique for minimizing the total flow time of jobs in n jobstwo machines flow shop.

Bomberger (1966) has given Dynamic programming ap-proach to turn planning downside. Main emphasis was put onthe scheduling of production of several different items oversimilar facility on a repetitive basis. The power within thesismodel is that just one item may be made by method at a time.

Crowin and Esogbue (1974) thought of the 2 totally dif-ferent flow search planning issues. His research work focusedon minimization of total completion time with processing ofone machine is based on sequence dependent setup time.

Genetic Algorithm is based on Darwin’s theory of selec-tion and survival of the fittest. European country (1975), haspopularized these algorithms. Panwalkar et al., (1977) ordersan in depth clarification of a number of these dispatchingrules.

Gupta, (1982) introduced problem of sequence dependentsetup time, using the branch and bound techniques to resolvestatic planning issues involving n jobs and m machines forminimizing the value of Machine setting. The rule was basi-cally developed to solve small scale issues.

Hundal et al., (1988) given heuristic rule for the flowsearch planning downside. Beck et al., (1991) Berry et al.,(1993) used knowledge based or AI-based systems techniques.

Taillard, (1993) used Ant Colony Optimization Algo-rithms (ACOA) to evaluate upper bound values for makespan factor.

Engin and Doyen, (2004) studied problems related tohybrid flow shop scheduling problems. AIS based heuristicalgorithm was applied to the benchmark problems for hybridflow shops. This algorithm out performs results given byBranch and Bound algorithms.

Eren, (2010) used a bi-criteria m-machine flow shop schedul-ing problem with sequence dependent setup times with min-imization of the weighted sum of total completion time andmakespan. He used the special heuristics algorithm for fitnessfunction considered. He proved that the special heuristic forall number of jobs and machines was more effective.

3. Objective of StudyScheduling model concerns with the determination of an

optimal sequence to service customers, to perform a set of jobsetc. in order to minimize total elapsed time or some anothersuitable measure of performance. Scheduling problems areused in the production concerns where the production of someitems is made into distinct but successive stages. At eachstage there is a machine to perform the required set of jobs.The main objectives of the present study are as follows:

(1) To develop an algorithm minimizing the rental cost ofthe machines taken on rent under a restrictive rental pol-icy in two stage flow shop scheduling, the processingtime of jobs on machines are associated with proba-bilities including break-down intervals and job blockcriteria.

(2) To develop a new heuristic algorithm minimizing thetotal elapsed time for n jobs, 3 machines flow shopscheduling problem involving processing times, trans-portation time and breakdown interval, whenever meanweighted flow time is taken into consideration.

(3) To study bi-criteria in two stages, three stage and multistage flow shop scheduling to minimize the rental costof machines taken on rent under a specified rental policywith minimum make span.

(4) To study bi-criteria in flow shop scheduling with se-quence dependent set up time.

(5) To widen flow shop scheduling models with jobs in astring of disjoint job block.

(6) To study flow shop scheduling on two machines withsetup time and single transport facility in fuzzy environ-ment.

(7) To develop fuzzy flow shop model with single transportfacility with job block criteria.

(8) To introduce the concept of fuzziness in parallel ma-chine scheduling to optimize the criteria: Number ofTardy jobs and Maximum Tardiness; Total Tardinessand Weighted Flow time.

4. Types of Scheduling

(1) Demand Scheduling – In this scheduling customers areassigned to a definite time for order fulfilment.

(2) Workforce Scheduling – This is type of scheduling thatdetermines when employees work.

(3) Operations Scheduling – A type of scheduling in whichjobs are assigned to workstations or employees are as-signed to job for specified time periods.

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Figure 1. Process of Scheduling

5. Types of Scheduling Problems(1) STATIC vs. DYNAMIC PROBLEMS - In static prob-

lems, all the production orders and their arrival timesare known beforehand in dynamic problems, new pro-duction orders can arrive at unexpected times while theschedule is being executed.

(2) FLOW SHOP vs. JOB SHOP PROBLEMS - Assumethat the jobs require to perform multiple operations ondifferent machines.

• Flow shop: Every job consists of the same setof tasks to be performed in the same order. Theunits are accordingly arranged in production linesto minimize the movement of materials and man-power (multiproduct plant).

• Compound Flow shop: Each unit in the series maybe replaced by a set of parallel equipment itemswhich may be identical or very different. Eachjob goes to one unit in the first stage, then it istransferred to one in the second stage and so on.

• Job shop: Production orders have different routes(require different sequences of tasks) and someorders ma y even visit a given unit several times(multipurpose plants).

6. Types of Scheduling Approach(1) Heuristic Methods

• Basic Dispatching Rules

• Composite Dispatching Rules

(2) Algorithms of The Improvement Type

• Simulated Annealing

• Genetic Algorithms

• Tabu Search

(3) Optimization Approaches

• Discrete Time Models

• Continuous Time Models

• Network-oriented Formulations

• Batch-oriented Formulations

7. Sequencing Rule(1) FCFS – Jobs processed in the order they come to the

shop.

(2) SPT – Jobs with the shortest processing time are sched-uled first.

(3) EDD – Jobs are sequenced according to their due dates.

(4) CR – Compute the ratio of processing time of the joband remaining time until the due date. Schedule the jobwith the largest CR value next.

Figure 2. Job Shop Sequencing

8. Sequencing Problems(1) One machines, many jobs.

• Total time is independent of sequence.

• Sequencing minimizes idle time.

• Sequence dependent total time

• No wait sequencing

(2) Two machines, many jobs.

• All jobs follow same sequence. (Johnson’s Rule)

• Jobs have different sequence. (Jackson’ Rule)

• Johnson’s three machine rule.

(3) Three machines, many jobs.

(4) Many machines, many jobs.

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9. Applications Of Scheduling &Sequencing

Sequencing and scheduling is important in real worldsituations. Some of these are given below:

• Production and manufacturing fields

• Material handling decision.

• Military and defence services.

• In planning strategy.

• Field of construction.

• In resource allocation for Operating System scenario.

• In air craft for landing clearance.

• In operational research problems to optimize the use ofavailable facilities to effectively process the item or thejobs.

• In service industries to observe the various dispatchingrules.

• In algorithms to find computational complexity.

• In CPU scheduling and DISK scheduling in operatingsystem.

• In fuzzy logic with the aim to satisfy a set of constraintsas much as possible, and optimize a set of objectives.

• In artificial Intelligence systems.

• In Ant Colony Optimization Techniques.

References• K.R. Baker and Dan Trietsch, Principles of sequencing and

scheduling, 1943.• E. Ignall and L. E. Schrage, Application of branch and

bound techniques to some flow shop problems, OperationResearch, 13(1965), 400–412.

• E.E. Bomberger, A Dynamic Programming Approach toa Lot Size Scheduling Problem, JSTOR: Management Sci-ence, 12(11)(1966), 778–784.

• B.D. Corwin and A.O. Esogbue, Two machine flow shopscheduling problems with sequence dependent setup times:A dynamic programming approach, Naval Research Logis-tics Quarterly, 21(1974), 515–524.

• J.H. Holland, Genetic algorithms and the optimal allocationof trials, SIAM Journal on Computing, 2(2)(1973), 88–105.

• S.S. Panwalkar and W. Iskander, A Survey of SchedulingRules, Operations Research, 125(1)(1977), 45–62.

• S.K. Gupta, N jobs and m machines job shop problem withsequence dependent setup times, International Journal ofProduction Research, 20(1982), 643–656.

• T.S. Hundal and J. Rajgopal, An extension of palmer’sheuristic for the flow-shop scheduling problem, Interna-tional Journal of Production Research, 26(1988), 1119–1124.

• H. Beck, B. Drabblc and R. Kirby, Course Notes on Plan-ning and Scheduling, Artificial Intelligence ApplicationsInstitute, University of Bdinburgh, 1991.

• E. Taillard, Benchmarks of basic scheduling problems, Eu-ropean Journal of Operation Research, 64(1993), 278–285.

• T. Eren, A bicriteria m-machine flowshop scheduling withsequence-dependent setup times, Applied MathematicalModelling, 34(2)(2010), 284–293.

• S. Gill and R. Kumar, Literature review for scheduling prob-lems, International Journal of Latest Research in Scienceand Technology, 1(1)(2012), 98–100.

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