EPQ model with scrap and backordering under Vendor managed inventory policy

Document Type : Research Paper


1 Department of Industrial Engineering, Alzahra University, Tehran, Iran

2 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran


This paper presents the economic production quantity (EPQ) models for the imperfect quality items produced with/without the presence of shortage condition. The models are presented in a two-level supply chain composed of a single manufacturer and a single buyer to investigate the performance of vendormanaged inventory (VMI) policy. The total costs are minimized to obtain the optimal production lot size and the allowable backorder level before and after applying VMI policy. Numerical examples and sensitivity analysis based on certain parameters are performed to show the capability of the proposed supply chain model enhanced with VMI policy.


Bernstein, F., Chen, F., &Federgruen, A. (2006). Coordinating supply chains with simple pricing
schemes: the role of vendor managed inventories.Management Science, 52, 1483–1492.
Cárdenas-Barrón, L.E. (2000), Observation on: economic production quantity model for items
with imperfect quality, [International Journal of Production Economics, 64, 59–64],International
Journal of Production Economics, 67, 201.
Cárdenas-Barrón,L.E. (2008).Optimal manufacturing batch size with rework in a single-stage
production system - a simple derivation.Computers & Industrial Engineering, 55,758–765.
Cárdenas-Barrón, L.E., Taleizadeh, A.A., & Trevino-Garza, G. (2012). An improved solution to
replenishment lot size problem with discontinuous issuing policy and rework, and the multidelivery
policy into economic production lot size problem with partial rework. ExpSystAppl,
Cetinkaya, S., &Lee, C.Y. (2000). Stock replenishment and shipment scheduling for vendor
managed inventory systems.Management Science, 46, 217–232.
Darwish, M. A., &Odah, O. M. (2010). Vendor managed inventory model for single-vendor
multi-retailer supply chains. European Journal of Operational Research, 204(3),473-484.
Eroglu, A.,&Ozdemir,G. (2007).An economic order quantity model with defective items and
shortages.International Journal of Production Economics, 106,544–549.
Goyal, S.K., &Cardenas-Barron,L.E. (2002). Note on: economic production quantity model for
items with imperfect quality - a practical approach.International Journal of Production
Economics, 77,85–87.
Goyal, S.K., Huang, C.K., & Chen,H.K. (2003). A simple integrated production policy of an
imperfect item for vendor and buyer.Production Planning & Control,14,596–602.
Hariga, M., Gumus, M., &Daghfous, A. (2013a). Storage constrained vendor managed inventory
models with unequal shipment frequencies. Omega (Accepted).
Hariga, M., Gumus, M., Daghfous, A., &Goyal, S. K. (2013b). A vendor managed inventory
model under contractual storage agreement. Computers & Operations Research, 40(8), 2138-
Hsu, J.-T., & Hsu, L.-F.(2013). Two EPQ models with imperfect production processes,
inspection errors, planned backorders, and sales returns.Comput. Ind. Eng, 64 (1), 389–402.
Kannan, G., Grigore, M. C., Devika, K., &Senthilkumar, A. (2013).An analysis of the general
benefits of a centralised VMI system based on the EOQ model.International Journal of
Production Research, 51(1), 172-188.
Khan, M., Jaber, M.Y., Guiffrida, A.L.,&Zolfaghari, S. (2011). A review of the extensions of a
modified EOQ model for imperfect quality items.Int. J. Prod. Econ., 132 (1), 1–12.
Kleywegt, A.J., Nori, V.S.,&Savelsberg, M.W.P.(2002).The stochastic inventory routing problem
with direct deliveries.Transportation Science, 36,94–118.
Konstantaras, I., Goyal, S.K.,&Papachristos, S. (2007).Economic ordering policy for an item
with imperfect quality subject to the in-house inspection.International Journal of Systems
Science, 38,473–482.
Ma, S., Ying, D., Guan, X.,& Huang, K. (2013).Managing inventory through (Q, r) policy for a
VMI programme with freshness clause. International Journal of Applied Management Science,
5(2), 129 – 143.
Marquès, G., Thierry, C., Lamothe, J., &Gourc, D. (2010). A review of Vendor Managed
Inventory (VMI): from concept to processes. Production Planning & Control, 21(6), 547-
Nagarajan, M.,&Rajagopalan, S. (2008). Contracting under vendor managed inventory systems
using holding cost subsidies.Production and Operations Management, 17, 200–210.
Pal, B., Sana, S.S,&Chaudhuri, K.S. (2013).A mathematical model on EPQ for stochastic
demand in an imperfect production system. J ManufactSyst, 32, 260–270.
Pasandideh, S.H.R., AkhavanNiaki, S.T., &RoozbehNia, A. (2010). An investigation of vendormanaged
inventory application in supply chain: the EOQ model with shortage.The International
Journal of Advanced Manufacturing Technology ,49, 329–339.
Salameh, M.K.,&Jaber, M.Y. (2000).Economic production quantity model for items with
imperfect quality.International Journal of Production Economics, 64, 59–64.
Sarkar, B., & Moon, I. (2011).An EPQ model with inflation in an imperfect production
system.Appl. Math. Comput, 217 (13), 6159–6167.
Shah J.,&Goh M. (2006).Setting operating policies for supply hubs. International Journal of
Production Economics, 100, 239–252.
Taheri-Tolgari, J., Mirzazadeh, A.,&Jolai, F. (2012).An inventory model for imperfect items
under inflationary conditions with considering inspection errors.Comput.Math.Appl, 63 (6),
Valentini, G.,&Zavanella, L. (2003). The consignment stock of inventories: industrial case and
performance analysis. International Journal of Production Economics, 81–82,215–224.
Waller, M., Johnson, M.E. & Davis, T. (1999). Vendor-managed inventory in the retail supply
chain. Journal of Business Logistics, 20, 183–203.
Wee, H.M., Yu, J., & Chen,M.C. (2007).Optimal inventory model for items with imperfect
quality and shortage backordering.Omega, 35,7–11.
Woo, Y., Hsu, S.,& Wu, S. (2001). An integrated inventory model for a single vendor and
multiple buyers with ordering cost reduction.International Journal of Production Economics, 73,
Zhang, T., Liang L., Yu, Y., & Yu, Y. (2007). An integrated vendor-managed inventory model
for a two-echelon system with order cost reduction.International Journal of Production
Economics, 109, 241–253.
Volume 8, Issue 1 - Serial Number 1
February 2015
Pages 85-102
  • Receive Date: 12 November 2014
  • Revise Date: 16 January 2015
  • Accept Date: 12 March 2015
  • First Publish Date: 12 March 2015