Skip to main content

Advertisement

Log in

Exact analysis of a push–pull system with multiple non identical retailers, a distribution center and multiple non identical unreliable suppliers with supply disruptions

  • Original Paper
  • Published:
Operational Research Aims and scope Submit manuscript

Abstract

In this paper, a push–pull system with K (\(K \ge 1\)) non identical suppliers with disruptions that send products to an intermediate distribution center which in turn serves M (\(M \ge 1\)) non identical retailers is analyzed. Each retailer satisfies a Poisson distributed external demand of one product unit.The flow of material at the upstream stages (suppliers) is push type. The flow of material at the downstream stages (retailers) is driven by a continuous review inventory control policy (s, S). The replenishment rate of suppliers and retailers is exponentially distributed. More over it is assumed that the suppliers may not be always operational. This is modelled using exponentially distributed failure and repair rates of the suppliers. The considered system is modelled as a continuous time Markov process with discrete states. The derivation of the transition probabilities among the various states of the system is given. Solving the corresponding transition equations system, the stationary probabilities of the system's states are computed and therefore using the stationary probabilities, performance measures of the considered system such as the Fill Rate and WIP are evaluated. Moreover the effect of the system parameters on its performance measures is thoroughly explored. Finally the proposed model is examined from an economic point of view, where the optimal parameter values for the (s, S) type policy are detected to minimize a total inventory cost function.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

References

  • Barron Y (2021) The continuous (S, s, ) inventory model with dual sourcing and emergency orders. Eur J Oper Res. https://doi.org/10.1016/j.ejor.2021.09.021

    Article  Google Scholar 

  • Barron Y, Baron O (2020) QMCD approach for perishability models: the (S, s) control policy with lead time. IISE Trans 52(2):133–150

    Article  Google Scholar 

  • Bashyam S, Fu MC (1998) Optimization of (s, S) inventory systems with random lead times and a service level constraint. Manage Sci 44:S243–S256

    Article  Google Scholar 

  • Castellano D, Gebennini E, Grassi A, Murino T, Rimini B (2018) Stochastic modeling of a single-vendor single-buyer supply chain with (s, S) inventory policy. IFAC Papers on Line 51(11):974–979

    Article  Google Scholar 

  • Chen H, Li P (2015) Optimization of (R, Q) policies for serial inventory systems using the guaranteed service approach. Comput Ind Eng 80:261–273

    Article  Google Scholar 

  • Chen H, Dai B, Li Y, Zhang Y, Wan X, Deng Y (2020) Stock allocation in a two-echelon distributionsystem controlled by (s, S) policies. Int J Product Res. https://doi.org/10.1080/00207543.2020.1845915

    Article  Google Scholar 

  • Diamantidis AC, Koukoumialos S, Vidalis M (2016) Performance evaluation of a push-pull merge system with multiple suppliers, an intermediate buffer and a distribution center with parallel machines/channels. Int J Prod Res 54(9):2628–2652

    Article  Google Scholar 

  • Diamantidis AC, Koukoumialos S, Vidalis M (2017) Markovian analysis of a push-pull merge system with two suppliers, an intermediate buffer and two retailers. Int J Oper Res Inf Syst 8(2):1–35

    Article  Google Scholar 

  • Diaz R, Ezell BC (2012) A simulation-based optimization approach to a lost sale stochastic inventory model. Int J Oper Res Inf Syst 3(2):46–63

    Article  Google Scholar 

  • Esmaili N, Norman BA, Rajgopal J (2019) Exact analysis of (R, s, S) inventory control systems with lost sales and zero lead time. Nav Res Logist 66(2):123–132

    Article  Google Scholar 

  • Gershwin SB (1994) Manufacturing Systems Engineering. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Hollier RH, Mak KL, Yin KFC (2005) Optimal inventory control of lumpy demand items using (s, S) policies with a maximum issue quantity restriction and opportunistic replenishments. Int J Prod Res 43(23):4929–4944

    Article  Google Scholar 

  • Li J, Meerkov SM (2009) Production Systems Engineering. Springer, New York

    Book  Google Scholar 

  • Liu Y, Dehghanib E, Jabalamelib MS, Diabat A, Lu CC (2020) A coordinated location-inventory problem with supply disruptions: a two phase queuing theory–optimization model approach. Comput Ind Eng 142:106326

    Article  Google Scholar 

  • Movahed KK, Zhang Z-H (2015) Robust design of (s, S) inventory policy parameters in supply chains with demand and lead time uncertainties. Int J Syst Sci 46(12):2258–2268

    Article  Google Scholar 

  • Muhittin O, Malouin L, Hobbs JB (2007) An inventory control policy of the (Q, S, R) type for manufacturing industries: simulation analysis approach, IIE Trans 345–353

  • Nasr W, Maddah B (2015) Continuous policy with correlated demand. Eur J Oper Res 246:874–885

    Article  Google Scholar 

  • Noblesse A, Boute R, Lambrecht M, Van Houdt B (2014) Characterizing order processes of continuous review (s, S) and (r, nQ) policies. Eur J Oper Res 236(2):534–547

    Article  Google Scholar 

  • Papadopoulos HT, Heavey C, Browne J (1993) Queueing Theory in Manufacturing Systems Analysis and Design. Chapman & Hall, London

    Google Scholar 

  • Papadopoulos CT, O’Kelly MEJ, Vidalis MJ, Spinellis D (2009) Analysis and Design of Discrete Part Production Lines. Springer, New York

    Google Scholar 

  • Perera S, Janakiraman G, Niu S-C (2018) Optimality of (s, S) inventory policies under renewal demand and general cost structures. Prod Oper Manag 27(2):368–383

    Article  Google Scholar 

  • Vidalis MI, Koukoumialos St, Geranios M (2014) Performance evaluation of a merge supply network: a distribution center with multiple reliable random suppliers. Comput Ind Eng 70:43–58

    Article  Google Scholar 

  • Vidalis MI, Koukoumialos S, Diamantidis AC, Blanas G (2015) Performance evaluation of a merge supply network: A production center with multiple different reliable suppliers. In: 10th Conference on stochastic models of manufacturing and service operations (SMMSO),Volos, Greece June 1–6, 2015, pp.255–263.

  • Visentin A, Prestwich S, Rossi R, Tarim SA (2021) Computing optimal (R, s, S) policy parameters by a hybrid of branch-and-bound and stochastic dynamic programming. European Journal of Operations Research 294:91–99. https://doi.org/10.1016/j.ejor.2021.01.012

    Article  Google Scholar 

Download references

Acknowledgements

This research is co-financed by Greece and the European Union (European Social Fund-ESF) through the Operational Programme «Human Resources Development, Education and Lifelong Learning» in the context of the project “Strengthening Human Resources Research Potential via Doctorate Research” (MIS-5000432), implemented by the State Scholarships Foundation (ΙΚΥ).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alexandros Diamantidis.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kourepis, A., Diamantidis, A. & Koukoumialos, S. Exact analysis of a push–pull system with multiple non identical retailers, a distribution center and multiple non identical unreliable suppliers with supply disruptions. Oper Res Int J 22, 4801–4827 (2022). https://doi.org/10.1007/s12351-022-00722-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12351-022-00722-0

Keywords

Navigation