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Minimising total tardiness for the worker assignment scheduling problem in identical parallel-machine models

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Abstract

The worker assignment scheduling problem involves both the decisions of job scheduling and worker assignment. In this research, only the performance measure of total tardiness is investigated in the model of identical parallel machines with nonpreemptive jobs. Since the worker assignment scheduling problem in the selected model can be shown to be NP-complete, heuristics have been developed for minimising the total tardiness. The worker assignment scheduling problem is solved in two phases of job scheduling and worker assignment. The SES (SPT, EDD, SLACK) heuristic is used for the phase of job scheduling. For the phase of worker assignment, the largest marginal contribution (LMC) procedure is used to minimise the total tardiness. From the simulation conducted, 88 out of 100 simulated problems yielded optimal solutions while the others also obtained very good results. In conclusion, the heuristics developed have shown very impressive results in both effectiveness and efficiency aspects.

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Abbreviations

n :

Total number of jobs waiting to be processed

m :

Total number of machines available to process the above jobs

J i :

A set of n jobs are to be processed, i=1, ..., n

M j :

A set of m machines are used to process these n jobs, j=1, ..., m

t i (W j ):

The processing time needed for job J i processed on machine M j , where W j workers have been assigned to M j

t j,[k](W j ):

The processing time function of the k th job assigned to machine M j , where W j workers have been assigned to M j

d i :

The due date of job J i

d j,[k] :

The due date of the k th job assigned to machine M j

r i :

the ready time of job J i

C i :

The completion time of job J i

C j,[k](W j ):

The completion time function of the k th job assigned to machine M j , where W j workers have been assigned to M j ; \({C_{{j,{\left[ k \right]}}} {\left( {W_{j} } \right)} = {\sum\limits_{p = 1}^k {t_{{j,{\left[ p \right]}}} {\left( {W_{j} } \right)}} }}\)

F i :

The flow time of job J i , F i =C i − r i

L i :

The lateness of job J i , L i =C i − d i

T i :

The tardiness of job J i , T i =max{0, L i }

T j,[k] :

The tardiness of the k th job assigned to machine M j , T j,[k]=max{0, C j,[k](W j )−d j,[k]}

N j :

The number of jobs assigned to machine M j

W j :

The number of workers assigned to machine M j

W :

The total number of workers

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Authors and Affiliations

  1. Department of Industrial Management, National Huwei Institute of Technology, 632, Yunlin, Taiwan, R.O.C.

    Po-Chieng Hu

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  1. Po-Chieng Hu
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Correspondence to Po-Chieng Hu.

Appendix A

Appendix A

Table 4 summarizes the data from one of the 100 simulated problems. The final sequence and worker assignment for this problem is given in Table 5.

Table 4. Data of one of the 100 simulated problems; t i (W j )=A i +B i / (E i× W j )
Full size table
Table 5. Final sequence and worker assignment for the problem data in Table 4
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Hu, PC. Minimising total tardiness for the worker assignment scheduling problem in identical parallel-machine models. Int J Adv Manuf Technol 23, 383–388 (2004). https://doi.org/10.1007/s00170-003-1716-9

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