Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A single-supplier, multi-buyer, multi-product VMI production-inventory system under partial backordering

  • 222 Accesses

  • 2 Citations

Abstract

The vendor managed inventory (VMI) is an efficient coordination policy in supply chain management, in which supplier is responsible to manage inventory at the buyer and decides on replenishment policies. This paper presents a VMI model for a supply chain problem with a single supplier, multi-buyer and multi-product, via a production-inventory system in which shortage is allowed and partially backordered. In order to take into account the concern about environmental issues, the total green house gas emission is also considered as a green constraint. The aim is to find the appropriate values of production quantity and the maximum shortage level for all products of all buyers in such a way that the total cost of supply chain is minimized under VMI. The problem is formulated as a non-linear programming model and then a decomposition based analytical approach is proposed to solve it optimally. At the end, a numerical example is discussed to illustrate the proposed approach.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

References

  1. Abad PL (2000) Optimal lot size for a perishable good under conditions of finite production and partial backordering and lost sale. Comput Ind Eng 38:457–465

  2. Arkan A, Rezvan T, Hejazi SR (2011) Supply chain coordination for minimisation of total cost with credit period approach. Int J Oper Res 10(3):290–306

  3. Braglia M, Zavanella L (2003) Modelling an industrial strategy for inventory management in supply chains: the ‘consignment stock’ case. Int J Prod Res 41(16):3793–3808

  4. Cárdenas-Barrón LE, Trevi˜no-Garza G, Wee HM (2012) A simple and better algorithm to solve the vendor managed inventory control system of multi-product multi-constraint economic order quantity model. Expert Syst Appl 39:3888–3895

  5. Chang W, Ellinger AE, Kim KK, Franke GR (2016) Supply chain integration and firm financial performance: a meta-analysis of positional advantage mediation and moderating factors. Eur Manag J 34(3):282–295

  6. Darwish MA, Odah OM (2010) Vendor managed inventory model for single-vendor multi-retailer supply chains. Eur J Oper Res 204:473–484

  7. Disney SM, Towill DR (2002) A procedure for the optimization of the dynamic response of a vendor managed inventory system. Comput Ind Eng 43:27–58

  8. Disney SM, Towill DR (2003) The effect of vendor managed inventory (VMI) dynamics on the bullwhip effect in supply chains. Int J Prod Econ 85:199–215

  9. Dong Y, Xu K (2002) A supply chain model of vendor managed inventory. Transp Res Part E: Logist Transp Rev 38:75–95

  10. Govindan K, Sivakumar R (2016) Green supplier selection and order allocation in a low-carbon paper industry: integrated multi-criteria heterogeneous decision-making and multi-objective linear programming approaches. Ann Oper Res 238:243–276

  11. Guillen-Gosalbez G, Grossmann IE (2009) Optimal design and planning of sustain- able chemical supply chains under uncertainty. AIChE J 55(1):99–121

  12. Hariga M, Gumus M, Daghfous A, Goyal SK (2013) A vendor managed inventory model under contractual storage agreement. Comput Oper Res 40:2138–2144

  13. Hill RM (1999) The optimal production and shipment policy for the single-vendor single-buyer integrated production-inventory model. Int J Prod Res 37:2463–2475

  14. Hill RM, Omar M (2006) Another look at the single-vendor single-buyer integrated production-inventory problem. Int J Prod Res 44(4):791–800

  15. Ivanov D, Dolgui A, Sokolovc B (2016) Robust dynamic schedule coordination control in the supply chain. Comput Ind Eng 94:18–31

  16. Kristianto Y, Helo P, Jiao J, Sandhu M (2012) Adaptive fuzzy vendor managed inventory control for mitigating the Bullwhip effect in supply chains. Eur J Oper Res 216:346–355

  17. Lee CC, Chu W, Hung J (2005) Who should control inventory in a supply chain? Eur J Oper Res 164:158–172

  18. Lin K, Chang P, Hung K, Pai P (2010) A simulation of vendor managed inventory dynamics using fuzzy arithmetic operations with genetic algorithms. Expert Syst Appl 37(3):2571–2579

  19. Linton J, Klassen R, Jayaraman V (2007) Sustainable supply chains: an introduction. J Oper Manag 25:1075–1082

  20. Magee JF (1958) Production planning and inventory control. McGraw-Hill Book Company, New York

  21. Mak KL (1987) Determining optimal production-inventory control policies for an inventory system with partial backlogging. Comput Oper Res 14:299–304

  22. Marque‘s G, Thierry C, Lamothe J, Gourc D (2010) A review of vendor managed inventory (VMI): from concept to processes. Prod Plan Control 21:547–561

  23. Mateen A, Chatterjee AK (2015) Vendor managed inventory for single-vendor multi-retailer supply chains. Decis Support Syst 70:31–41

  24. Nagurney A, Liu Z, Woolley T (2006) Optimal endogenous carbon taxes for electric power supply chains with power plants. Math Comput Model 44:899–916

  25. Park YB, Yoo JS, Park HS (2016) A genetic algorithm for the vendor-managed inventory routing problem with lost sales. Expert Syst Appl 53:149–159

  26. Pasandideh SHR, Niaki STA, Nia AR (2011) A genetic algorithm for vendor managed inventory control system of multi-product multi-constraint economic order quantity model. Expert Syst Appl 38:2708–2716

  27. Pasandideh SHR, Akhavan Niaki ST, Hemmati Far M (2014) Optimization of vendor managed inventory of multiproduct EPQ model with multiple constraints using genetic algorithm. Int J Adv Manuf Technol 71:365–376

  28. Pentico DW, Drake MJ (2009) The deterministic EOQ with partial backordering: a new approach. Eur J Oper Res 194:102–113

  29. Pentico DW, Drake MJ (2011) A survey of deterministic models for the EOQ and EPQ with partial backordering. Eur J Oper Res 214:179–198

  30. Ramudhin A, Chaabane A, Kharoune M, Paquet M (2008) Carbon market sensitive green supply chain network design. In: Proceedings of the 2008 IEEE IEEM, 1093–1097

  31. Roozbeh Nia A, Hemmati Far M, Niaki STA (2015) A hybrid genetic and imperialist competitive algorithm for green vendor managed inventory of multi-item multi-constraint EOQ model under shortage. Appl Soft Comput 30:353–364

  32. Sadeghi J, Sadeghi A, Saidi-Mehrabad M (2011) A parameter-tuned genetic algorithm for vendor managed inventory model for a case single-vendor single-retailer with multi-product and multi-constraint. Int J Optim Ind Eng 4:57–67

  33. Sadeghi J, Sadeghi S, Akhavan Niaki ST (2014a) A hybrid vendor managed inventory and redundancy allocation optimization problem in supply chain management: an NSGA-II with tuned parameters. Comput Oper Res 41:53–64

  34. Sadeghi J, Sadeghi S, Akhavan Niaki ST (2014b) Optimizing a hybrid vendor-managed inventory and transportation problem with fuzzy demand: an improved particle swarm optimization algorithm. Inf Sci 272:126–144

  35. San José LA, Sicilia J, García-Laguna J (2005) The lot size-reorder level inventory system with customers impatience functions. Comput Ind Eng 49:349–362

  36. San José LA, Sicilia J, García-Laguna J (2014) Optimal lot size for a production- inventory system with partial backlogging and mixture of dispatching policies. Int J Prod Econ 155:194–203

  37. Taleizadeh AA, Niaki STA, Aryanezhad MB, Fallah-Tafti A (2010) A genetic algorithm to optimize multi-product multi-constraint inventory control systems with stochastic replenishment intervals and discount. Int J Adv Manuf Technol 51:311–323

  38. Van der Vlist P, Kuik R, Verheijen B (2007) Note on supply chain integration in vendor-managed inventory. Decis Support Syst 44:360–365

  39. Vergin RC, Barr K (1999) Building competitiveness in grocery supply through continuous replenishment planning: insights from the field. Ind Mark Manag 28:145–153

  40. Waller M, Johnson ME, Davis T (1999) Vendor-managed inventory in the retail supply chain. J Bus Logist 20:183–203

  41. Yao Y, Evers PT, Dresner ME (2007) Supply chain integration in vendor-managed inventory. Decis Support Syst 43:663–674

  42. Yu Y, Wang Z, Liang L (2012) A vendor managed inventory supply chain with deteriorating raw materials and products. Int J Prod Econ 136:266–274

  43. Zavanella L, Zanoni S (2009) A one-vendor multi-buyer integrated production-inventory model: the consignment stock case. Int J Prod Econ 118:225–232

  44. Zhu QH, Sarkis J (2004) Relationships between operational practices and performance among early adopters of green supply chain management practices in Chinese manufacturing enterprises. J Oper Manag 22:265–289

Download references

Author information

Correspondence to Hadi Mokhtari.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mokhtari, H., Rezvan, M.T. A single-supplier, multi-buyer, multi-product VMI production-inventory system under partial backordering. Oper Res Int J 20, 37–57 (2020). https://doi.org/10.1007/s12351-017-0311-z

Download citation

Keywords

  • Vendor managed inventory
  • Green house gas
  • Green supply chain
  • Analytical approach