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Scheduling of mobile robots for transportation and manufacturing tasks

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Abstract

Current manufacturing systems have a tendency to become more and more flexible to adapt to the needs of product diversification. Such a system, e.g. flexible manufacturing system, consists of a number of automatic machines, material handling devices such as automated guided vehicles (AGVs) or mobile robots, and a central control computer. Mobile robots, as well as AGVs, can move around in their working space to transport components among machines. The main novelty of this work is that mobile robots can also execute various value-added tasks without human intervention thanks to their manipulation arms which is not possible for AGVs. This new characteristic certainly makes the problem more complex and computationally expensive. To utilize these manufacturing systems in an efficient manner, it is necessary to schedule transportation of product components by mobile robots and to schedule processing of products on machines possibly by mobile robots. Consequently, the key innovation of this work lies in consideration of three interrelated sub-problems which must be solved. They include computing the sequence of operations on machines, the robot assignment for transportation, and the robot assignment for processing. To achieve this goal, a computationally efficient hybrid heuristic method combining genetic algorithm and tabu search is developed to solve the problem considering makespan minimization. A mixed-integer programming (MIP) model is formulated. Another combined method using results of the hybrid heuristic is proposed to speed up the solving of MIP model. The quality of hybrid heuristic’s solutions is compared and evaluated by using those of the MIP model as reference points.

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Notes

  1. We have also attempted to feed full solutions from the heuristic into CPLEX, the results are however quite close. This is because the branch-and-cut algorithm of CPLEX spends a large amount of time on the binary decisions variables, i.e. xijk, hijk, αijk, ωijk. Hence, feeding of full solutions is not considered in our paper.

  2. Instances are also available from https://sites.google.com/site/schedulingmobilerobots.

  3. “Appendices A and B” are also available from https://sites.google.com/site/schedulingmobilerobots.

  4. Detailed results for further comparisons between the hybrid heuristic and the other proposed approaches for the two groups of problems are presented in Tables 12.1 and 13.1, which are available from https://sites.google.com/site/schedulingmobilerobots.

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Author information

Authors and Affiliations

  1. Faculty of Informatics, Masaryk University, Botanická 68a, Brno, Czech Republic

    Quang-Vinh Dang & Hana Rudová

  2. Faculty of Engineering, Vietnamese-German University, Thu Dau Mot City, Binh Duong, Vietnam

    Cong Thanh Nguyen

Authors
  1. Quang-Vinh Dang
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  2. Cong Thanh Nguyen
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  3. Hana Rudová
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Corresponding author

Correspondence to Quang-Vinh Dang.

Appendices

Appendix A

1.1 Data for traveling times used in test problems

See Tables 14, 15, 16 and 17.

Table 14 Traveling time for layout 1
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Table 15 Traveling time for layout 2
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Table 16 Traveling time for layout 3
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Table 17 Traveling time for layout 4
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Appendix B

2.1 Data for the job sets used in test problems

The operations marked by underlines are assumed to need a robot for processing

  • Job Set 1

  • Job 1: M1(8); M2(16); M4(12)

  • Job 2: M1(20); M3(10); M2(18)

  • Job 3: M3(12); M4(8); M1(15)

  • Job 4: M4(14); M2(18)

  • Job 5: M3(10); M1(15)

  • Job Set 2

  • Job 1: M1(10); M4(18)

  • Job 2: M2(10); M4(18)

  • Job 3: M1(10); M3(20)

  • Job 4: M2(10); M3(15); M4(12)

  • Job 5: M1(10); M2(15); M4(12)

  • Job 6: M1(10); M2(15); M3(12)

  • Job Set 3

  • Job 1: M1(16); M3(15)

  • Job 2: M2(18); M4(15)

  • Job 3: M1(20); M2(10)

  • Job 4: M3(15); M4(10)

  • Job 5: M1(8); M2(10); M3(15); M4(17)

  • Job 6: M2(10); M3(15); M4(8); M1(15)

  • Job Set 4

  • Job 1: M4(11); M1(10); M2(7)

  • Job 2: M3(12); M2(10); M4(8)

  • Job 3: M2(7); M3(10); M1(9); M3(8)

  • Job 4: M2(7); M4(8); M1(12); M2(6)

  • Job 5: M1(9); M2(7); M4(8); M2(10); M3(8)

  • Job Set 5

  • Job 1: M1(6); M2(12); M4(9)

  • Job 2: M1(18); M3(6); M2(15)

  • Job 3: M3(9); M4(3); M1(12)

  • Job 4: M4(6); M2(15)

  • Job 5: M3(3); M1(9)

  • Job Set 6

  • Job 1: M1(9); M2(11); M4(7)

  • Job 2: M1(19); M2(20); M4(13)

  • Job 3: M2(14); M3(20); M4(9)

  • Job 4: M2(14); M3(20); M4(9)

  • Job 5: M1(11); M3(16); M4(8)

  • Job 6: M1(10); M3(12); M4(10)

  • Job Set 7

  • Job 1: M1(6); M4(6)

  • Job 2: M2(11); M4(9)

  • Job 3: M2(9); M4(7)

  • Job 4: M3(16); M4(7)

  • Job 5: M1(9); M3(18)

  • Job 6: M2(13); M3(19); M4(6)

  • Job 7: M1(10); M2(9); M3(13)

  • Job 8: M1(11); M2(9); M4(8)

  • Job Set 8

  • Job 1: M2(12); M3(21); M4(11)

  • Job 2: M2(12); M3(21); M4(11)

  • Job 3: M2(12); M3(21); M4(11)

  • Job 4: M2(12); M3(21); M4(11)

  • Job 5: M1(10); M2(14), M3(18); M4(9)

  • Job 6: M1(10); M2(14), M3(18); M4(9)

  • Job Set 9

  • Job 1: M3(9); M1(12); M2(9); M4(6)

  • Job 2: M3(16); M2(11); M4(9)

  • Job 3: M1(21); M2(18); M4(7)

  • Job 4: M2(20); M3(22); M4(11)

  • Job 5: M3(14); M1(16); M3(13); M4(9)

  • Job Set 10

  • Job 1: M1(11); M3(19); M2(16); M4(13)

  • Job 2: M2(21); M3(16); M4(14)

  • Job 3: M3(8); M2(10); M1(14); M4(9)

  • Job 4: M2(13); M3(20); M4(10)

  • Job 5: M1(9); M3(16); M4(18)

  • Job 6: M2(19); M1(21), M3(11); M4(15)

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Dang, QV., Nguyen, C.T. & Rudová, H. Scheduling of mobile robots for transportation and manufacturing tasks. J Heuristics 25, 175–213 (2019). https://doi.org/10.1007/s10732-018-9391-z

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  • DOI: https://doi.org/10.1007/s10732-018-9391-z

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