Abstract
In this paper, based on the group technology and the just-in-time manufacturing concepts, two loading models for optimal utilisation of the processing capabilities of an integrated manufacturing system consisting of a set of heterogeneous workstations are developed. These loading models are developed to integrate and utilise the available information from both the bill of materials and the process plans. The objective functions for these models are: the maximum tardiness and the makespan. In these models, the production quantity of each customer order for any part or product always equals its corresponding demand quantity; each part requires a finite number of aggregated stages of operation; job splitting is allowed; and the processing priorities of all the jobs during the planning time horizon are specified based on a desirable dispatching rule. The proposed mathematical programming models are fixed charge problems which are solved by compatible mixed integer programming algorithms. Finally, to provide additional decision-making capabilities, based on these models and their corresponding solution algorithms, a compatible decision support system is suggested.
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Abbreviations
- l(1 toL):
-
the product index
- t(1 toN):
-
the component (e.g., job type) index
- i(1 toN):
-
the job type priority index
- j(1 toM):
-
the workstation index
- r(1 toR):
-
the processing stage priority index
- k(1 toK):
-
the due date priority index
- J i,j,r,k :
-
the job with the job type priority indexi of the customer with the processing stage priority indexr and the due date priority indexk which has to be processed at the workstationj
- L i,r,k :
-
the number of units of the job with the job type priority indexi of the customer with processing stage priority indexr and the due date priority indexk (e.g. demand quantities)
- t i,j,r :
-
the required time to perform the processing stage priority indexr of each unit of the job with the job type priority indexi at the workstationj
- D i,r,k :
-
the due date of the job with the job type priority indexi of the customer with the processing stage priority indexr and the due date priority indexk
- s i,j,r :
-
the required time for setting up the workstationj for processing the job with the processing stage priority indexr, and the job type priority indexi
- X i,j,r,k :
-
the number of units of the job with job type priority indexi of the customer with the processing stage priority indexr, and the due date priority indexk to be produced at the workstationj
- l i,j,r,k :
-
the idle time at the workstationj prior to processing the job with the job type priority indexi and the processing stage priority indexr with the due date priority indexk
- V :
-
the maximum tardiness
- W :
-
the makespan of the operation
- Y i,j,r,k=1:
-
ifX i,j,r,k>0
- Y i,j,r,k=0:
-
ifX i,j,r,k=0
- α i,j,r,k :
-
a sufficiently large constant (e.g.α i,j,r,k≥L i,r,k)
References
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IBM Mixed Integer Programming/370 (MIP/370) Program Reference Manual, Form number SH19-1099, IBM Corporation, 1975.
IBM Mathematical Programming System Extended/370 (MPSX/370) Program Reference Manual, form number SH19-1095, IBM Corporation, 1979.
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Pourbabai, B. Loading strategies for a class of just-in-time manufacturing system. Int J Adv Manuf Technol 10, 46–51 (1995). https://doi.org/10.1007/BF01184277
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DOI: https://doi.org/10.1007/BF01184277