Skip to main content
SpringerLink
Log in

Effect of inspection and rework of probabilistic defective production on two-layer supply chain incorporating deterioration and reliability dependent demand

  • Original article
  • Published:
International Journal of System Assurance Engineering and Management Aims and scope Submit manuscript

Abstract

This paper develops a two-layer supply chain for defective and non-defective types of items produced by manufacturer and retailer. The manufacturer produces items on the condition that the faulty items will return to the manufacturer after inspecting without financial liability of the retailer. The damaged items are identified subsequent of the conducted full screening process and reworked by the retailer. Hence, the retailer sells the non-defective item to the customer. Effect of deterioration estimates to make this research a more realistic one for the manufacturer and retailer. This study discusses the impact of several business strategies such as production rate, unit production cost, idle time costs in a collaborative marketing system, reliability dependent demand, etc., to determine the optimum average profit of the integrated model. The selling price of the retailer, the purchase cost of the manufacturer, and holding cost has the potential to be a significant breakthrough. Numerical and managerial implications are demonstrated along with sensitivity analysis of different parameters for the proposed two-layer supply chain.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Adak S, Mahapatra GS (2020) Effect of reliability on multi-item inventory system with shortages and partial backlog incorporating time dependent demand and deterioration. Ann Oper Res. https://doi.org/10.1007/s10479-020-03694-6

    Article  MATH  Google Scholar 

  • Adak S, Mahapatra GS (2020) Effect of reliability dependent varying demand and holding cost on inventory system incorporating probabilistic deterioration. J Ind Manag Optim. https://doi.org/10.3934/jimo.2020148

    Article  Google Scholar 

  • Ahmad B, Benkherouf L (2018) Economic-order-type inventory models for non-instantaneous deteriorating items and backlogging. RAIRO Oper Res 52:895–901

    MathSciNet  MATH  Google Scholar 

  • AlDurgam M, Adegbola K, Glock CH (2017) A single-vendor single-manufacturer integrated inventory model with stochastic demand and variable production rate. Int J Prod Econ 191:335–350

    Google Scholar 

  • Ben-Daya M, Hassini E, Hariga M, Al Durgama M (2013) Consignment and vendor managed inventory in single-vendor multiple buyers supply chains. Int J Prod Res 51:1347–1365

    Google Scholar 

  • Bottani E, Montanari R (2010) Supply chain design and cost analysis through simulation. Int J Prod Res 48:2859–2886

    MATH  Google Scholar 

  • Boyaci T, Gallego G (2002) Coordinating pricing and inventory replenishment policies for one wholesaler and one or more geographically dispersed retailers. Int J Prod Econ 77:95–111

    Google Scholar 

  • Cannella S, Dominguez R, Ponte B, Framinan JM (2018) Capacity restrictions and supply chain performance: modelling and analysing load-dependent lead times. Int J Prod Econ 204:264–277

    Google Scholar 

  • Chan CK, Wong WH, Langevin A, Lee YCE (2017) An integrated production-inventory model for deteriorating items with consideration of optimal production rate and deterioration during delivery. Int J Prod Econ 189:1–13

    Google Scholar 

  • Chiu SW, Gong DC, Wee HM (2004) The effects of the random defective rate and the imperfect rework process on the economic production quantity model. Jpn J Ind Appl Math 21:375–389

    MathSciNet  MATH  Google Scholar 

  • Chung KJ, Cárdenas-Barrón LE (2013) The simplified solution procedure for deteriorating items under stock-dependent demand and two-level trade credit in the supply chain management. Appl Math Model 37:4653–4660

    MathSciNet  MATH  Google Scholar 

  • Chung KJ, Liao JJ, Ting PS, Lin SD, Srivastava HM (2015) The algorithm for the optimal cycle time and pricing decisions for an integrated inventory system with order-size dependent trade credit in supply chain management. Appl Math Comput 268:322–333

    MathSciNet  MATH  Google Scholar 

  • Costantino N, Dotoli M, Falagario M, Fanti MP, Mangini AM (2012) A model for supply management of agile manufacturing supply chains. Int J Prod Econ 135:451–457

    Google Scholar 

  • Dolgui A, Tiwari MK, Sinjana Y, Kumar SK, Son YJ (2018) Optimising integrated inventory policy for perishable items in a multi-stage supply chain. Int J Prod Econ 56:902–925

    Google Scholar 

  • Dominguez R, Cannella S, Framinan JM (2014) The impact of the supply chain structure on bullwhip effect. Appl Math Model 39:7309–7325

    MathSciNet  MATH  Google Scholar 

  • Ganesh MK, Uthayakumar R (2019) A two-echelon integrated inventory model under generalized lead time distribution with variable backordering rate. Int J Syst Assur Eng Manag 10:552–562

    Google Scholar 

  • Ghiami Y, Williams T (2015) A two-echelon production-inventory model for deteriorating items with multiple buyers. Int J Prod Econ 159:233–240

    Google Scholar 

  • Ghosh PK, Hazari S, Dey JK, Kar S (2018) Three-layer supply chain production/by-production inventory model under fuzzy rough environment. J Adv Manuf Syst 17:61–88

    Google Scholar 

  • Giri BC, Chakraborty A, Maiti T (2015) Quality and pricing decisions in a two-echelon supply chain under multi-manufacturer competition. Int J Adv Manuf Technol 78:1927–1941

    Google Scholar 

  • Goyal SK (1976) An integrated inventory model for a single supplier-single customer problem. Int J Prod Res 15:107–111

    Google Scholar 

  • Goyal SK, Huang CK, Chen HK (2003) A simple integrated production policy of an imperfect item for vendor and buyer. Prod Plan Control 14:596–602

    Google Scholar 

  • Gumte KM, Mitra K (2019) Bio-supply chain network design to tackle ethanol deficiency in India: a mathematical framework. J Clean Prod 234:208–224

    Google Scholar 

  • Hsu JT, Hsu LF (2013) An integrated vendor buyer cooperative inventory model in an imperfect production process with shortage backordering. Int J Adv Manuf Technol 65:493–505

    MathSciNet  Google Scholar 

  • Ivanov D, Dolgui A, Sokolov B (2018) Scheduling of recovery actions in the supply chain with resilience analysis considerations. Int J Prod Res 56:6473–6490

    Google Scholar 

  • Jalbar BA, Gutiérrez JM, Sicilia J (2008) Policies for a single-vendor multi-buyer system with finite production rate. Decis Support Syst 46:84–100

    Google Scholar 

  • Kerkkamp RBO, van den Heuvel W, Wagelmans APM (2018) Two-echelon supply chain coordination under information asymmetry with multiple types. Omega 76:137–159

    Google Scholar 

  • Kuiti MR, Ghosh D, Basu P, Bisi A (2020) Do cap-and-trade policies drive environmental and social goals in supply chains: strategic decisions, collaboration, and contract choices. Int J Prod Econ 223:107537

    Google Scholar 

  • Kumar RS, Tiwari MK, Goswami A (2016) Two-echelon fuzzy stochastic supply chain for the manufacturer-buyer integrated production-inventory system. J Intell Manuf 27:875–888

    Google Scholar 

  • Kundu A, Guchhait P, Panigrahi G, Maiti M (2019) An EOQ model for deteriorating item with promotional effort and credit linked demand. Eur J Ind Eng 13:368–399

    Google Scholar 

  • Lee S, Kim D (2014) An optimal policy for a single-vendor single-buyer integrated production-distribution model with both deteriorating and defective items. Int J Prod Econ 147:161–170

    Google Scholar 

  • Li J, Wang S, Cheng TCE (2010) Competition and cooperation in a single retailer two-supplier supply chain with supply disruption. Int J Prod Econ 124:137–150

    Google Scholar 

  • Liao JJ, Huang KN, Chung KJ (2012) Lot-sizing decisions for deteriorating items with two warehouses under an order-size dependent trade credit. Int J Prod Econ 137:102–115

    Google Scholar 

  • Mahapatra GS, Adak S, Mandal TK, Pal S (2017) Inventory model for deteriorating items with time and reliability dependent demand and partial backorder. Int J Oper Res 29:344–359

    MathSciNet  Google Scholar 

  • Mahapatra GS, Adak S, Kaladhar K (2019) A fuzzy inventory model with three parameter Weibull deterioration with reliant holding cost and demand incorporating reliability. J Intell Fuzzy Syst 36:5731–5744

    Google Scholar 

  • Mahata P, Mahata GC, De SK (2020) An economic order quantity model under two-level partial trade credit for time varying deteriorating items. Int J Syst Sci Oper Logist 7:1–17

    Google Scholar 

  • Manna AK, Dey JK, Mondal SK (2018) Two layers supply chain in an imperfect production inventory model with two storage facilities under reliability consideration. J Ind Prod Eng 35:57–73

    Google Scholar 

  • Mukhopadhyay S, Mukherjee RN, Chaudhuri KS (2005) An EOQ model with two parameter Weibull distribution deterioration and price-dependent demand. Int J Math Educ Sci Technol 36:25–33

    MathSciNet  Google Scholar 

  • Pal S, Mahapatra GS (2017) A manufacturing-oriented supply chain model for imperfect quality with inspection errors, stochastic demand under rework and shortages. Comput Ind Eng 106:299–314

    Google Scholar 

  • Palanivel M, Priyan S, Uthayakumar R (2015) An inventory model with finite replenishment, probabilistic deterioration and permissible delay in payments. J Manag Anal 2:254–279

    Google Scholar 

  • Panda S, Modak NM, Basu M, Goyal SK (2015) Channel coordination and profit distribution in a social responsible three-layer supply chain. Int J Prod Econ 168:224–233

    Google Scholar 

  • Panicker VV, Vamshidhar Reddy M, Sridharan R (2018) Development of an ant colony optimisation-based heuristic for a location-routing problem in a two-stage supply chain. Int J Value Chain Manag 9:38–69

    Google Scholar 

  • Panja S, Mondal SK (2020) Exploring a two-layer green supply chain game theoretic model with credit linked demand and mark-up under revenue sharing contract. J Clean Prod 250:119491

    Google Scholar 

  • Patel RD, Patel J (2019) Different deterioration rates two storage facilities deteriorating items inventory model under time and price dependent demand for single buyer single vendor. Int J Sci Technol Res 8:1824–1829

    Google Scholar 

  • Saha S, Chakrabarti T (2018) Two-echelon supply chain model for deteriorating items in an imperfect production system with advertisement and stock dependent demand under trade credit. Int J Supply Oper Manag 5:207–217

    Google Scholar 

  • Salameh MK, Jaber MY (2010) Economic production quantity model for items with imperfect quality. Int J Prod Econ 64:59–64

    Google Scholar 

  • Singh SR, Sharma S (2019) A partially backlogged supply chain model for deteriorating items under reverse logistics, imperfect production/remanufacturing and inflation. Int J Logist Syst Manag 33:221–255

    Google Scholar 

  • Taleizadeh AA, Noori-daryan M (2014) Pricing, manufacturing and inventory policies for raw material in a three-level supply chain. Int J Syst Sci 47:919–931

    MathSciNet  MATH  Google Scholar 

  • Taleizadeh AA, Noori-daryan M, Tavakkoli-Moghaddam R (2015) Pricing and ordering decisions in a supply chain with imperfect quality items and inspection under a buyback contract. Int J Prod Res 53:4553–4582

    Google Scholar 

  • Tiwari S, Jaggi CK, Gupta M, Cardenas-Barron LE (2018) Optimal pricing and lot-sizing policy for supply chain system with deteriorating items under limited storage capacity. Int J Prod Econ 200:278–290

    Google Scholar 

  • Woo YY, Hsu SL, Wu S (2001) An integrated inventory model for a single vendor and multiple buyers with ordering cost reduction. Int J Prod Econ 73:203–215

    Google Scholar 

  • Wu KS, Ouyang LY (2003) An integrated single-vendor single-buyer inventory system with shortage derived algebraically. Prod Plan Control 14:551–561

    Google Scholar 

Download references

Acknowledgements

We are grateful to Editors, and anonymous referees for their valuable comments and helpful suggestions, which have helped us to improve this work significantly.

Author information

Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Puducherry, Karaikal, 609609, India

    Sudip Adak & G. S. Mahapatra

Authors
  1. Sudip Adak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. S. Mahapatra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. S. Mahapatra.

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

Adak, S., Mahapatra, G.S. Effect of inspection and rework of probabilistic defective production on two-layer supply chain incorporating deterioration and reliability dependent demand. Int J Syst Assur Eng Manag 12, 565–578 (2021). https://doi.org/10.1007/s13198-021-01119-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13198-021-01119-6

Keywords

Search

Navigation