The Learning and Forgetting Effects of Dynamic Workers on the Performance of

Dispatching Rules in Flow Shops

Horng-Chyi HORNGand

Shu-Pei HUDepartment of Industrial Engineering and Management, Chaoyang University of Technology

Wufong Township, Taichung County 41349, Taiwan

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Presentation Outline

qIntroductionqLearning and ForgettingqSimulation ConstructionqExperimental DesignqResults and AnalysisqConclusions

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Introduction

q The problem of worker shortage comes along with the decreasing birth rate for the recent decade in Taiwan.

q One possible solution is training workers to become so-called multitasking workers.

q The flexibility of production scheduling increases when adopting multitasking workers, however, so does the complexity.

q The purpose of this study is to evaluate how the performance of dispatching rules affected by the learning and forgetting effects of workers.

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Commonly used dispatching rules

q Flow shops

min. Zij = PijSPTmin. Zij = Pij / ( t-ri )PT/TISmin. Zij = rijFIFOmin. Zij = ri - rkiAT-RPTmin. Zij = riAT

DefinitionsDispatching Rules

q Reference: C. Rajendran and O. Holthaus, “A Comparative Study of Dispatching Rules in Dynamic Flow Shops and Job Shops,” European Journal of Operational Research, Vol. 116, 1999, pp. 156-170.

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Worker assignment rules

qTwo categories: “when” and “where”.qAdopting CEN (centralized): the most flexible

“when” rule that move away a worker whenever he/she completed the current job.qAdopting FCFS (first come first serve): a “where”

rule that prevents jobs waiting in a queue for too long.

q Reference: H.V. Kher, 2000, “Examination of Worker Assignment and Dispatching Rules for Managing Vital Customer Priorities in Dual Resource Constrained Job Shop Environments,” Computer and Operations Research, Vol. 27, 2000, pp. 525-537.

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Learning and Forgetting

qLearning effectsqThe efficiency of a worker in processing jobs at a

certain station shall improve as the number of jobs he/she continuously completed increases.

qForgetting effectsqThe deteriorating of a worker’s efficiency in processing

jobs at a certain station as he/she, for some reasons was removed away from that station, stopped processing the same jobs for a period of time.

q Reference: J.C. Fisk and D.P. Ballou, “Production Lot Sizing under a Learning Effect,” IIE Transactions, Vol. 14, No. 4, 1982, pp. 257-264.S. Globerson, and N. Levin, “Incorporating Forgetting into Learning Curves,” International Journal of Operations and Production Management, Vol. 7, No. 4, 1987, pp. 80-92.

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Models for learning and forgetting

qLearning model – Mazur and Hastie (1978)

qAdding forgetting effects – Nembhard and Uzumeri (2000)

xx rpxpx

ky ε+

++

+=

xx

xx

rpxR

pxRky εα

α+

++

+=

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Simulation Construction

q A hypothetical multi-station, single-server flow shop.

q Performance measurements:q mean flowtime of jobsq maximum flowtime of jobs, and q work-in-process (WIP).

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Experimental Factors

q number of stations: 10, 20, and 30;q number of multitasking workers: 10, 20, and

30;q processing time: Normal(3,12), Uniform(1, 5),

and Exponential(3) for coefficient of variation(CV) equals to 33.33%, 38.49%, and 100%, respectively; and

q utilization rate: 75%, 82.5%, and 90%.

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Experimental Design (I)

Learning effects with random forgetting rate5th stage

Learning effects with constant forgetting rate4th stage

Learning effects with complete forgotten3rd stage

Only learning effects 2nd stage

No learning nor forgetting effects1st stage

DescriptionsStages

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The 2nd stage learning model

Pro

duct

ion

Rat

e

0Time

k

Worker assigned to other station

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The 3rd stage learning and forgetting model

Pro

duct

ion

Rat

e

0Time

k

Worker assigned to other station

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The 4th stage learning and forgetting model

Pro

duct

ion

Rat

e

0 Time

k

Worker assigned to other station

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The 5th stage learning and forgetting model

Pro

duct

ion

Rat

e

0Time

k

Worker assigned to other station

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Experimental Design (II)

qAt each stage, a 22 factorial design with nc = 3 center points is adopted as guideline for performing simulation experiments. qTwo major factors are number of station and

utilization rate. qAt each simulation run, there are 30 replications

for statistical comparison purposes. Replication length is set to be 12,500 minutes in which the first 2,500 minutes is the system warm-up period.

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Results and Analysis

qSimulation results from the 1st stage and 2nd stage serve as fundamental basis for comparison with subsequent stages one by one.qThe 1st stage simulation results are validated and

compared to those mentioned in the literature. qMean flowtime ~ SPT and PT/TISqWIP ~ SPT and PT/TISqMaximum flowtime ~ AT, FIFO, and AT-RPT

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ATFIFO

AT-RPT

SPTPT/TISFIFO

1st

Stage

SPT

FIFOAT

AT-RPTSPTPT/TIS

SPTPT/TIS

AT-RPTFIFOAT

SPTPT/TIS

SPTPT/TISFIFO

AT-RPTFIFOAT

SPTPT/TIS

2nd

Stage

WIPFmaxWIPFmaxWIPFmax

EXPOUNIFNORM

Best rule(s) from the 2nd stage experiment for large system with high utilization rate

FFF

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ATFIFOSPT

ATAT-RPT

SPTAT

FIFO AT-RPT

1st

Stage

SPTPT/TIS

FIFOSPTATSPT

PT/TISSPT

PT/TIS

AT-RPTAT

SPTPT/TIS

SPTPT/TIS

2nd

Stage

SPTAT

FIFOSPT

SPTSPTAT

AT-RPTSPT

SPTPT/TIS

ATAT-RPT

FIFO

SPT3rd

Stage

WIPFmaxWIPFmaxWIPFmax

EXPOUNIFNORM

Best rule(s) from the 3rd stage experiment for small system with low utilization rate

FFF

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1st

Stage

SPTPT/TIS

AT-RPT AT

FIFO

SPTPT/TIS

SPTPT/TIS

SPTPT/TIS

SPTPT/TIS

AT-RPTAT

SPTPT/TIS

2nd

Stage

SPTAT-RPT

FIFOAT

SPTSPT

AT-RPTAT

SPTSPTAT-RPT

AT FIFO

SPT4th

Stage

WIPFmaxWIPFmaxWIPFmax

EXPOUNIFNORM

Best rule(s) from the 4th stage experiment for medium-size system with medium utilization rate

FFF

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1st

Stage

ATAT-RPT

FIFO

SPTPT/TISFIFO

AT-RPTAT

FIFO

SPTPT/TISFIFO

SPTPT/TISFIFO

AT-RPTAT

FIFO

SPTPT/TISFIFO

2nd

Stage

SPTPT/TIS

ATFIFO

AT-RPTSPT

PT/TIS

SPTPT/TIS

AT-RPTAT

SPTPT/TIS

SPTPT/TIS

ATAT-RPT

SPTPT/TIS

5th

Stage

WIPFmaxWIPFmaxWIPFmax

EXPOUNIFNORM

Best rule(s) from the 5th stage experiment for small system with high utilization rate

FFF

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Conclusionsq In general, SPT is the best dispatching rule for the mean

flowtime and WIP criteria. On the other hand, AT and AT-RPT perform better than others in the maximum flowtime criterion.

q Only when the system is relatively small with lower utilization rate, does the learning effect without forgetting effect produces different ranking of best rules than that of no learning effect case.

q The rule PT/TIS is a good candidate for the mean flowtime and WIP criteria. However, it is significantly influenced by the models for the forgetting effects of workers.

q The incorporation of the forgetting effects of workers to the system actually changes the rankings of best rules in statistical sense.

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Research Directions

q Considering the effects caused by the shortage of workers;

q Incorporating more worker assignment rules; andq Examining the effects of learning and forgetting effects

on other production systems, such as job shops.

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Thanks for listening!