Integrated production-Inventory model with price-dependent demand, imperfect quality, and investment in quality and inspection

Document Type : Research Article


Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran


In practice, manufacturing systems are never perfect and may have low quality outputs. Therefore, different decisions such as reprocessing, sale at lower prices or diminishing are made according to industry and market. This paper investigates the importance of supply chain coordination through developing two models in centralized decision-making for an imperfect quality manufacturing system with probabilistic defect rate. Moreover, two types of errors in inspection process are considered: Type I error (classifying perfect products as defective ones) and Type II error (classifying defective products as perfect ones). Moreover, a cost function for investment on products quality as well as selling price is considered. The algorithms to find the optimal solution for both models are suggested. Numerical results show that even by less consumer prices; more profit, more satisfied customer, and improved quality can be achieved through coordination in supply chain.


[1]Dehghanbaghi N., 2014, Joint Optimization of Vendor & Buyer Policies in Production- Inventory system, Master thesis, Industrial Engineering Dept., Amirkabir University of Technology.
[2]Goyal S., An integrated inventory model for a single supplier-single customer problem, International Journal of Production Research, 14 (1976) 107–111.
[3] Glock C., The joint economic lot size problem: A review , International Journal of Production Economics, 135 (2012) 671–686.
[4] Goyal S., A joint economic-lot-size model for purchaser and vendor: a comment, Decision Sciences, 19 (1988) 236–241.
[5] Huang C., An integrated vendor–buyer cooperative inventory model for items with imperfect quality, Production Planning & Control, 13 (2002) 355–361.
[6] Affisco J., Paknejad M. & Nasri, F., A comparison of alternative joint vendor–purchaser lot-sizing models, International Journal of Production Research, 31 (1993) 2661–2676.
[7] Goyal S., Huang C. & Chen K., A simple integrated production policy of an imperfect item for vendor and buyer, Production Planning & Control: The Management of Operations, 14 (2003) 596-602.
[8] Liu X. & Cetinkaya S., A note on “quality improvement and setup reduction in the joint economic lot size model”, European Journal of Operational Research, 182 (2007) 194–204.
[9] Lin T., Optimal Policy For A Simple Supply Chain System With Defective Items And Returned Cost Under Screening Errors, Journal of the Operations Research Society of Japan, 52 (2009) 307-320.
[10] Hsu J. & Hsu L., An integrated single-vendor single-buyer production-inventory model for items with imperfect quality and inspection errors, International Journal of Industrial Engineering Computations, 3 (2012) 703–720.
[11] Lin H., An Integrated Supply Chain Inventory Model With Imperfect-Quality Items, Controllable Lead Time And Distribution-Free Demand, Yugoslav Journal of Operations Research, 23 (2013) 87-109.
[12] Li Y. & Chen Z., Optimal Integrated Production-inventory System for Defective Items, in: 20th International Conference on Management Science & Engineering, IEEE, Harbin, P.R.China, 2013, pp. 640-649.
[13] Chuang C., Ho C., Ouyang L. & Wu C., An integrated inventory model with order-size-dependent trade credit and quality improvement, Procedia Computer Science, 17 (2013) 365-372.
[14] Ahmadi Rad M., Khoshalhan F. & Setak M., Optimal Pricing and Ordering Policies for a Two-Layer Supply Chain with Imperfect Quality Items under Two Inspection Scenarios, Caspian Journal of Applied Sciences Research, 1 (2012) 133-144.
[15] Hsu J. & Hsu L., An integrated vendor–buyer inventory model with imperfect items and planned back orders, The International Journal of Advanced Manufacturing Technology, 68 (2013) 2121-2132.
[16] Khan M., Jaber M. & Ahmad A., An integrated supply chain model with errors in quality inspection and learning in production, Omega, 42 (2014) 16–24.
[17] Khan M., Jaber M. & Bonney M., An economic order quantity (EOQ) for items with imperfect quality and inspection errors, International Journal of Production Economics, 133 (2011) 113–118.
[18] Hsu L., A note on “An economic order quantity (EOQ) for items with imperfect quality and inspection errors”, International Journal of Industrial Engineering Computations, 3 (2012) 695–702.
[19] InTouch Manufacturing Services. Inspection Level And Selecting An AQL. Retrieved from InTouch: http://www.
[20] Wright M., The interior-point revolution in optimization: history, recent developments, and lasting consequences, Bulletin of the American Mathematical Society, 42 (2005) 39–56.
[21] Sajadieh M. & Jokar M., Optimizing shipment, ordering and pricing policies in a two-stage supply chain with price-sensitive demand, Transportation Research Part E, 45 (2009) 564–571.