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A vendor–buyer JELS model with stock-dependent demand and consigned inventory under buyer’s space constraint

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Abstract

In this article, we consider a single-vendor single-buyer supply chain model in which the vendor produces a single product at a constant rate and delivers to the buyer following a consignment stock policy. The customers’ demand is assumed to be dependent on the on-hand stock displayed at the buyer. An integrated vendor–buyer model is developed and solved for optimal delivery batch size and number of shipments, aiming at minimizing the average cost of the system. The model is further generalized considering the space limitation at the buyer’s end. As coordination mechanism, a contract which distributes the total cost between the vendor and the buyer in an arbitrary ratio is suggested. The proposed model is numerically illustrated and the effects of the buyer’s space constraint on the optimal number of shipments, delivery batch size and overall cost are studied. The outcome of the proposed model is also compared with that of the model under lot-for-lot policy to conclude which of the policies should be preferred to the other and under what conditions.

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References

  • Baker RC, Urban TL (1988) A deterministic inventory system with an inventory-level-dependent demand rate. J Oper Res Soc 39:923–931

    Article  Google Scholar 

  • Ben-Daya M, As’ad R, Seliaman M (2013) An integrated production inventory model with raw material replenishment considerations in a three layer supply chain. Int J Prod Econ 143:53–61

    Article  Google Scholar 

  • Bolan WH (1988) Contemporary retailing, 3rd edn. Prentice-Hall, New Jersey

    Google Scholar 

  • Braglia M, Zavanella L (2003) Modeling an industrial strategy for inventory management in supply chains: the ‘Consignment Stock’ case. Int J Prod Res 41:3793–3808

    Article  Google Scholar 

  • Cárdenas-Barrón LE, Wee HM, Blos MF (2011) Solving the vendor–buyer integrated inventory system with arithmetic–geometric inequality. Math Comput Model 53(5–6):991–997

    Article  Google Scholar 

  • Cárdenas-Barrón LE, Trevi\({\ddot{\hbox {n}}}\)o-Garza G, Wee HM (2012a) 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(3):3888–3895

  • Cárdenas-Barrón LE, Teng JT, Trevi\({\ddot{\hbox {n}}}\)o-Garza G, Wee HM, Lou KR (2012b) An improved algorithm and solution on an integrated production-inventory model in a three-layer supply chain. Int J Prod Econ 136(2):384–388

  • Cárdenas-Barrón LE, Taleizadeh AA, Trevi\({\ddot{\hbox {n}}}\)o-Garza G (2012c) An improved solution to replenishment lot size problem with discontinuous issuing policy and rework, and the multi-delivery policy into economic production lot size problem with partial rework. Expert Syst Appl 39(18):13540–13546

  • Coughlan AT, Anderson E, Stern LW, El-Ansary AI (2001) Marketing channels. Prentice-Hall, New Jersey

    Google Scholar 

  • Giri BC, Bardhan S (2012) Supply chain coordination for a deteriorating item with stock and price-dependent demand under revenue sharing contract. Int Trans Oper Res 19:753–768

    Article  Google Scholar 

  • Gümüş M, Jewkes EM, Bookbinder JH (2008) Impact of consignment inventory and vendor-managed inventory for a two-party supply chain. Int J Prod Econ 113:502–517

    Article  Google Scholar 

  • Huang QY, Chen JF (2009) A note on: modeling an industrial strategy for inventory management in supply chains: the ‘Consignment Stock’ case. Int J Prod Res 47(22):6469–6475

    Article  Google Scholar 

  • Lee W, Wang SP (2008) Managing level of consigned inventory with buyer’s warehouse capacity constraint. Prod Plan Control 19(7):677–685

    Article  Google Scholar 

  • Levin RI, McLaughlin CP, Lamone RP, Kottas JF (1972) Production/operations management: contemporary policy for managing operating systems. McGraw-Hill, New York

    Google Scholar 

  • Ong HL, Ang BW, Goh TN, Deng CC (1996) A model for vending machine services in the soft drink industry. Asia Pac J Oper Res 13(2):209–224

    Google Scholar 

  • Sajadieh MS, Thorstenson A, Jokar MRK (2010) An integrated vendor–buyer model with stock-dependent demand. Trans Res Part E 46(6):963–974

    Article  Google Scholar 

  • Sarker BR (2014) Consignment stocking policy models for supply chain systems: a critical review and comparative perspectives. Int J Prod Econ 155:52–67

    Article  Google Scholar 

  • Silver EA, Peterson R (1985) Decision systems for inventory management and production planning. Wiley, New York

    Google Scholar 

  • Teng JT, Cárdenas-Barrón LE, Lou KR (2011) The economic lot size of the integrated vendor–buyer inventory system derived without derivatives: a simple derivation. Appl Math Comput 217(12):5972–5977

    Article  Google Scholar 

  • Teng JT, Cárdenas-Barrón LE, Lou KR, Wee HM (2013) Optimal economic order quantity for buyer–distributor–vendor supply chain with backlogging derived without derivatives. Int J Syst Sci 44(5):986–994

    Article  Google Scholar 

  • Trevi\({\ddot{\hbox {n}}}\)o-Garza G, Castillo-Villar KK, Cárdenas-Barrón LE (2014) Joint determination of the lot size and number of shipments for a family of integrated vendor-buyer systems considering defective products. Int J Syst Sci. doi:10.1080/00207721.2014.886750

  • Valentini G, Zavanella L (2003) The consignment stock of inventories: industrial case and performance analysis. Int J Prod Econ 81–82:215–224

    Article  Google Scholar 

  • Wang SP, Lee W, Chang CY (2012) Modeling the consignment inventory for a deteriorating item while the buyer has warehouse capacity constraint. Int J Prod Econ 138:284–292

    Article  Google Scholar 

  • Wang Y, Jiang L, Shen ZJ (2004) Channel performance under consignment contract with revenue sharing. Manag Sci 50(1):34–47

    Article  Google Scholar 

  • Wu KS, Ouyang LY, Yang CT (2006) An optimal replenishment policy for non- instantaneous deteriorating items with stock-dependent demand and partial backlogging. Int J Prod Econ 101(2):369–384

    Article  Google Scholar 

  • Yang S, Hong K, Lee C (2014) Supply chain coordination with stock-dependent demand rate and credit incentives. Int J Prod Econ 157:105–111

    Article  Google Scholar 

  • Yi H, Sarker BR (2013) An operational policy for an integrated inventory system under consignment stock policy with controllable lead time and buyer’s space limitation. Comput Oper Res 40:2632–2645

    Article  Google Scholar 

  • 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

    Article  Google Scholar 

  • Zanoni S, Grubbström RW (2004) A note on an industrial strategy for stock management in supply chains: modeling and performance evaluation. Int J Prod Res 42:4421–4426

    Article  Google Scholar 

  • Zanoni S, Jaber MY, Zavanella L (2012) Vendor managed inventory (VMI) with consignment considering learning and forgetting effects. Int J Prod Econ 140(2):721–730

    Article  Google Scholar 

  • Zhou YW, Yang SL (2005) A two-warehouse inventory model for items with stock-level-dependent demand rate. Int J Prod Econ 95:215–228

    Article  Google Scholar 

  • Zhou YW, Zhong Y, Li J (2012) An uncooperative order model for items with trade credit, inventory-dependent demand and limited displayed shelf-space. Eur J Oper Res 223:76–85

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Jadavpur University, Kolkata, 700032, India

    B. C. Giri & S. Bardhan

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  1. B. C. Giri
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  2. S. Bardhan
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Correspondence to S. Bardhan.

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Giri, B.C., Bardhan, S. A vendor–buyer JELS model with stock-dependent demand and consigned inventory under buyer’s space constraint. Oper Res Int J 15, 79–93 (2015). https://doi.org/10.1007/s12351-015-0167-z

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  • DOI: https://doi.org/10.1007/s12351-015-0167-z

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Mathematics Subject Classification