New Approaches in Meta-heuristics to Schedule Purposeful Inspections of Workshops in Manufacturing Supply Chains

Document Type : Original Article


1 Department of Industrial Engineering, University of Science and Technology of Mazandaran, Behshahr, Iran

2 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran


Nowadays, with the growth of technology and the industrialization of societies, work-related accidents, and consequently the threat of human capital and material resources are among the problems of the countries of the world. The most important legal solution in most countries to control occupational accidents and illnesses is to conduct periodic site visits and identify hazardous sites. To the best of our knowledge, no study from the supply chain point of view has been reported to model and address this kind of problem. Thus, this paper is to select the best route that reduces the time elapsed between the workshops and the visit time of the inspectors by using two-tier supply chain simulation coupled with the vehicle routing problem (VRP) to give them more opportunity to visit more workshops. In this study, by considering the number of workshops, the limitation of the number of the existing inspectors and the priority of inspecting the workshops, a bi-objective mathematical model is presented. The main aims are to maximize the number of visited workshops and minimize travel times and workshops visit times. In this study, three meta-heuristics (i.e., SA, SEO and RDA) and two hybrid algorithms are used to address the model. Then, the quality of the meta-heuristics and hybrid algorithms are evaluated and compared by using four metrics. The SEO algorithm provides the best performance; however, in a long time, the hybrid GASA algorithm provides the worst performance. Finally, a real-case study is used to validate the presented model.


we can see that the less the number of first inspectors in 
comparision to the other two inspectors, the time taken to
do so is much more greater.

To decrease occupational accidents, we proposed a
scheduled plan for inspection from workshops. In this
study, from another angle, the issue of routing within the
supply chain framework has been addressed. The
application of routing in this paper is to visit workshops
which were introduced and modeled. The objective
functions not only maximize the number of visited
workshops but also minimize travel times and workshops
visit times. The model is formulated as MILP alongside
with some assumptions that help to reach a real study. To
figure out the best outputs for the proposed model,
several hybrid and meta-heuristic algorithms containing
SEO, SA, RDA, GAKA, and GASA, have been utilized.
To compare the result of solution approaches, we needed
to tune factors of algorithm which were different and
various so the Taguchi method was used. Then, four
metrics alongside with the  GAP index were introduced
and applied to compute and measure the best suitable
algorithm. The proposed SEO demonstrated the best
outputs and stability among suggested meta-heuristic and
hybrid algorithms. The outcomes depicted when
inspectors wanted to gain better efficiency of managing
the plan from the daily operations, they could count on
the model stemmed from the supply chain. This model
was a practical appliance for the decision-makers in
making operational decisions. This technical planning
calculates the number of workshops assigned to each
inspector and the occupied time of inspectors as shown
in the case study to maximize the number of visits. 
For future studies, extending the mathematical model
by applying uncertainty and stochastic in the parameters
is suggested. Also, new hybrid and evolutionary
algorithms were utilized for evaluating and comparing
the outputs of the model. Some real constraints, such as
social and environmental aspects of Greenhouse Gas
(GHG) emission can be added to the suggested model for
the subsequent expansion of this model. 
1. Hämäläinen, P., Takala, J. and Kiat, T. B., “Global estimates of
occupational accidents and work-related illnesses”, In World
Congress on Safety and Health at Work, Singapore, (2017), 1–20.  
2. Ani, A.I.C., Sairi, A., Johar, S., Abd Razak, M.Z. and Tawil, N. .,
“The practice of building inspection in Malaysian total asset
management”, Jurnal Teknologi, Vol. 78, No. 1, (2016), 1–11.  
3. Arquillos, A.L., Romero, J.C.R. and Gibb, A., “Analysis of
construction accidents in Spain, 2003-2008”, Journal of Safety
Research, Vol. 43, No. 5–6, (2012), 381–388.  
4. Cheng, C.W., Yao, H.Q. and Wu, T. C., “Applying data mining
techniques to analyze the causes of major occupational accidents
in the petrochemical industry”, Journal of Loss Prevention in the
Process Industries, Vol. 26, No. 6, (2013), 1269–1278.  
5. Arntz-Gray, J., “Plan, Do, Check, Act: The need for independent
audit of the internal responsibility system in occupational health
and safety”, Safety Science, Vol. 84, (2016), 12–23.  
6. Awwad, R., El Souki, O. and Jabbour, M., “Construction safety
practices and challenges in a Middle Eastern developing country”,
Safety Science, Vol. 83, (2016), 1–11.  
7. Hajakbari, M.S. and Minaei-Bidgoli, B., “A new scoring system
for assessing the risk of occupational accidents: A case study
using data mining techniques with Iran’s Ministry of Labor data”,
Journal of Loss Prevention in the Process Industries, Vol. 32,
(2014), 443–453.  
8. Zhou, C. and Ding, L. Y., “Safety barrier warning system for
underground construction sites using Internet-of-Things
technologies”, Automation in Construction, Vol. 83, (2017),
9. Akbarpour, N., Kia, R. and Hajiaghaei-Keshteli, M., “A new biobjective
integrated vehicle transportation model considering
simultaneous pick-up and split delivery,” Scientia Iranica,
(2020). Articles in Press, doi:10.24200/SCI.2020.52996.2993. 
10. Amiri, S.A.H.S., Zahedi, A., Kazemi, M., Soroor, J. and
Hajiaghaei-Keshteli, M., “Determination of the optimal sales
level of perishable goods in a two-echelon supply chain network”,
Computers & Industrial Engineering, Vol. 139, (2020). 
11. Seyedi, I., Hamedi, M. and Tavakkoli-Moghaddam, R., “Truck
Scheduling in a Cross-Docking Terminal by Using Novel Robust
Heuristics”, International Journal of Engineering - Transaction
B: Applications, Vol. 32, No. 2, (2019), 296–305.  
12. Fallah, M., Tavakkoli-Moghaddam, R., Salamatbakhsh-Varjovi,
A. and Alinaghian, M., “A Green Competitive Vehicle Routing
Problem under Uncertainty Solved by an Improved Differential
Evolution Algorithm”, International Journal of Engineering -
Transaction A: Basics, Vol. 32, No. 7, (2019), 976–981.  
13. Ke, L., “A brain storm optimization approach for the cumulative
capacitated vehicle routing problem”, Memetic Computing, Vol.
10, No. 4, (2018), 411–421.  
14. Bula, G.A., Afsar, H.M., González, F.A., Prodhon, C. and
Velasco, N., “Bi-objective vehicle routing problem for hazardous
materials transportation”, Journal of Cleaner Production, Vol.
206, (2019), 976–986.  
15. Kirkpatrick, S., Gelatt, C.D. and Vecchi, M. P., “Optimization by
simulated annealing”, Science, Vol. 220, No. 4598, (1983), 671–
16. Fathollahi-Fard, A.M., Hajiaghaei-Keshteli, M. and TavakkoliMoghaddam,
R., “The social engineering optimizer (SEO)”,
Engineering Applications of Artificial Intelligence, Vol. 72,
(2018), 267–293.  
17. Hajiaghaei-Keshteli, M. and Fard, A. M. F., “Sustainable closedloop
supply chain network design with discount supposition”,
Neural Computing and Applications, Vol. 31, No. 9, (2019),
18. Hajiaghaei-Keshteli, M. and Aminnayeri, M. J. A. S. C., “Solving
the integrated scheduling of production and rail transportation
problem by Keshtel algorithm”, Applied Soft Computing, Vol.
25, (2014), 184–203.  
19. Abdi, A., Abdi, A., Akbarpour, N., Amiri, A.S. and HajiaghaeiKeshteli,
M., “Innovative approaches to design and address green supply chain network with simultaneous pick-up and split
delivery”, Journal of Cleaner Production, Vol. 250, (2020).