A Mathematical Model and an Artificial Bee Colony Algorithm for In-Plant Milk-Run Design

  • Kadir Buyukozkan
  • Sule Itir SatogluEmail author
Conference paper
Part of the Lecture Notes in Management and Industrial Engineering book series (LNMIE)


As a result of the product diversification, many types of components are used in the products’ bill-of-materials. Consequently, smaller quantities of many different types of components are needed to be distributed. All these factors complicated the part-feeding to the assembly lines. In this study, a mathematical model is developed for an in-plant milk-run material supply system that periodically distributes multiple parts by using multiple vehicles to the stations of the assembly lines. This model is called the Multi-Vehicle Milk-Run Model. As the proposed mathematical model is NP-hard, an Artificial Bee Colony Algorithm is developed to solve the large instances. The proposed ABC Algorithm is tested based on the optimum solutions (where available) and the best-known feasible solutions of different sized instances of a real washing machine assembly plant. Hence, the performance of the ABC Algorithm is validated.


In-plant milk-run Part feeding Artificial Bee Colony Algorithm Mathematical model 



This study has been financially supported by the Turkish National Science Foundation (TUBITAK), through the 215M143 research project.


  1. Baudin M (2004) Lean logistics: the nuts and bolts of delivering materials and goods. Productivity Press, New YorkGoogle Scholar
  2. Boschetti MA, Maniezzo V, Roffilli M, Röhler AB (2009) Matheuristics: optimization, simulation and control. In: International workshop on hybrid metaheuristics. Springer, Heidelberg, pp 171–177CrossRefGoogle Scholar
  3. Buyukozkan K, Bal A, Oksuz MK, Kapukaya EN, Satoglu SI (2019) A mathematical model and a matheuristic for in-plant milk-run systems design and application in white goods industry. In: Calisir F, Cevikcan E, Camgoz Akdag H (eds) Industrial engineering in the big data era. Springer, Cham, pp 99–112CrossRefGoogle Scholar
  4. Buyukozkan K, Kucukkoc I, Satoglu SI, Zhang DZ (2016) Lexicographic bottleneck mixed-model assembly line balancing problem: artificial bee colony and tabu search approaches with optimised parameters. Expert Syst Appl 50:151–166CrossRefGoogle Scholar
  5. Caputo AC, Pelagagge PM, Salini P (2015) Planning models for continuous supply of parts in assembly systems. Assembly Autom 35(1):35–46CrossRefGoogle Scholar
  6. Emde S, Schneider M (2018) Just-in-time vehicle routing for in-house part feeding to assembly lines. Transp. Sci. 52:657–672CrossRefGoogle Scholar
  7. Emde S, Gendreau M (2017) Scheduling in-house transport vehicles to feed parts to automotive assembly lines. Eur J Oper Res 260(1):255–267MathSciNetCrossRefGoogle Scholar
  8. Emde S, Boysen N (2012) Optimally routing and scheduling tow trains for JIT-supply of mixed-model assembly lines. Eur J Oper Res 217:287–299MathSciNetzbMATHGoogle Scholar
  9. Fathi M, Rodríguez V, Fontes DBMM, Alvarez MJ (2015) A modified particle swarm optimization algorithm to solve the part feeding problem at assembly lines. Int J Prod Res 54(3):878–893CrossRefGoogle Scholar
  10. Golz J, Gujjula R, Günther HO, Rinderer S (2012) Part feeding at high-variant mixed-model assembly lines. Flex Serv Manufact J 24:119–141CrossRefGoogle Scholar
  11. Karaboga D, Akay B (2009) A comparative study of artificial bee colony algorithm. Appl Math Comput 214(1):108–132MathSciNetzbMATHGoogle Scholar
  12. Kilic HS, Durmusoglu MB (2013) A mathematical model and a heuristic approach for periodic material delivery in lean production environment. Int J Adv Manuf Technol 69(5–8):977–992CrossRefGoogle Scholar
  13. Limere V, Landeghem HV, Goetschalckx M, Aghezzaf EH, McGinnis LF (2012) Optimizing part feeding in the automotive assembly industry: deciding between kitting and line stocking. Int J Prod Res 50(15):4046–4060CrossRefGoogle Scholar
  14. Limere V, Van Landeghem H, Goetschalckx M (2015) A decision model for kitting and line stocking with variable operator walking distances. Assembly Autom 35(1):47–56CrossRefGoogle Scholar
  15. Osman IH, Kelly JP (1996) Meta-heuristics: an overview. In: Osman IH, Kelly JP (eds) Meta-heuristics. Springer, Boston, pp 1–21CrossRefGoogle Scholar
  16. Sali M, Sahin E, Patchong A (2015) An empirical assessment of the performances of three line-feeding modes used in the automotive sector: line stocking vs. kitting vs. sequencing. Int J Prod Res 53(5):1439–1459CrossRefGoogle Scholar
  17. Sali M, Sahin E (2016) Line feeding optimization for just in time assembly lines: an application to the automotive industry. Int J Prod Econ 174:54–67CrossRefGoogle Scholar
  18. Satoglu SI, Ucan K (2015) Redesigning the material supply system of the automotive suppliers based on lean principles and an application. In: 2015 international conference on industrial engineering and operations management (IEOM). IEEE, pp 1–6Google Scholar
  19. Satoglu SI, Sahin IE (2013) Design of a just-in-time periodic material supply system for the assembly lines and an application in electronics industry. Int J Adv Manuf Technol 65:319–332CrossRefGoogle Scholar
  20. Volling T, Grunewald M, Spengler TS (2013) An integrated inventory-transportation system with periodic pick-ups and leveled replenishment. Bus Res 6(2):173–194CrossRefGoogle Scholar
  21. Zhou B, Peng T (2017) Scheduling the in-house logistics distribution for automotive assembly lines with just-in-time principles. Assembly Autom 37(1):51–63CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Industrial Engineering Department, Faculty of ManagementIstanbul Technical UniversityIstanbulTurkey
  2. 2.Industrial Engineering Department, Faculty of EngineeringKaradeniz Technical UniversityTrabzonTurkey

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