Joint production and transportation scheduling in flexible manufacturing systems

Abstract

This work proposes an integrated formulation for the joint production and transportation scheduling problem in flexible manufacturing environments. In this type of systems, parts (jobs) need to be moved around as the production operations required involve different machines. The transportation of the parts is typically done by a limited number of Automatic Guided Vehicles (AGVs). Therefore, machine scheduling and AGV scheduling are two interrelated problems that need to be addressed simultaneously. The joint production and transportation scheduling problem is formulated as a novel mixed integer linear programming model. The modeling approach proposed makes use of two sets of chained decisions, one for the machine and another for the AGVs, which are inter-connected through the completion time constraints both for machine operations and transportation tasks. The computational experiments on benchmark problem instances using a commercial software (Gurobi) show the efficiency of the modeling approach in finding optimal solutions.

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Fig. 1

Notes

  1. 1.

    Here and hereafter, unless specified otherwise, all computational experiments and results refer to these instances.

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Corresponding author

Correspondence to Dalila B. M. M. Fontes.

Additional information

We acknowledge the financial support of ERDF - European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia within projects POCI-01-0145-FEDER-031821 and PTDC/EEI-AUT/2933/2014 POCI-01-0145-FEDER-016858 and the Deputy Dean for Research & Technology of the Islamic Azad University, Lenjan Branch.

Appendices

Appendix A: Problem instances data

Job sets data used in the benchmark instance

Each job set requires a list of the jobs, as detailed in Table 7. For each of these jobs the machine processing each operation is specified and the number in brackets is the processing time. The order in which the machines, and respective processing times, are given corresponds to the order in which they must be processed.

Table 7 Job Sets: sequence – machines and processing times

Layouts data used in the benchmark instance

The configuration of the four layouts considered is depicted in Fig. 2 and the corresponding traveling times in Table 8.

Fig. 2
figure2

Layouts configuration: a Layout 1; b Layout 2; c Layout 3; d Layout 4

Appendix B: Results reported in [9, 21, 22, 24]

In Table 9 we provide the results reported in [9, 21, 22, 24]. Some of these results have been proved wrong before in [1, 28], in here however, some more can be shown to be wrong by comparing them to the optimal solution found. In the tables these wrong values are marked with \(^\ddag \).

Table 8 Workshop layouts travelling time
Table 9 Results reported in [9, 21, 22, 24]

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Fontes, D.B.M., Homayouni, S.M. Joint production and transportation scheduling in flexible manufacturing systems. J Glob Optim 74, 879–908 (2019). https://doi.org/10.1007/s10898-018-0681-7

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Keywords

  • Flexible manufacturing system
  • Integrated scheduling
  • Mixed integer linear programming model