Abstract
In this paper, a production inventory model is studied considering imperfect production and deterioration of item, simultaneously. Both the serviceable and reworkable items are assumed to deteriorate with time. A cost-minimizing model is developed incorporating both Type I and Type II inspection errors. Shortages are allowed that are completely backlogged. All the screened items are reworked at the end of the production process. To encounter a more practical situation, the deterioration rate is considered to be a type-2 fuzzy number. Such a situation arises when the vendor assigns, with similar priority, a number of experts to determine the rate of deterioration and the decision given by each expert is in linguistic term, which may be replaced by a fuzzy number. The aim of the proposed model is to calculate the maximum back-order quantity allowed and the optimal lot size that must be produced in order to minimize the overall inventory cost. The problem is solved for both the crisp and fuzzy models and a numerical example with practical application is also presented to exemplify the procedure. A novel method for solving a type-2 fuzzy optimization problem is developed which results in a set of Pareto optimal solutions for the proposed problem. It is followed by presenting a sensitivity analysis of various parameters involved on the decision variables and the cost function for a better illustration of the model.
Similar content being viewed by others
References
Bhuiya, S.K., Chakraborty, D.: A fuzzy random EPQ model with fuzzy defective rates and fuzzy inspection errors. J. Intell. Fuzzy Syst. 30(6), 3527–3541 (2016)
Cardenas-Barron, L.E.: Economic production quantity with rework process at a single-stage manufacturing system with planned backorders. Comput. Ind. Eng. 57(3), 1105–1113 (2009)
Chen, X., Benjaafar, S., Elomri, A.: The carbon-constrained EOQ. Oper. Res. Lett. 41(2), 172–179 (2013)
Chiu, S.W.: Robust planning in optimization for production system subject to random machine breakdown and failure in rework. Comput. Oper. Res. 37(5), 899–908 (2010)
Chiu, S.W., Ting, C.-K., Chiu, Y.-S.P.: Optimal production lot sizing with rework, scrap rate, and service level constraint. Math. Comput. Model. 46(3), 535–549 (2007)
Chiu, Y.P.: Determining the optimal lot size for the finite production model with random defective rate, the rework process, and backlogging. Eng. Optim. 35(4), 427–437 (2003)
Chung, K.-J., Her, C.-C., Lin, S.-D.: A two-warehouse inventory model with imperfect quality production processes. Comput. Ind. Eng. 56(1), 193–197 (2009)
Flapper, S.D.P., Teunter, R.H.: Logistic planning of rework with deteriorating work-in-process. Int. J. Prod. Econ. 88(1), 51–59 (2004)
Ghosh, S.K., Khanra, S., Chaudhuri, K.S.: Optimal price and lot size determination for a perishable product under conditions of finite production, partial backordering and lost sale. Appl. Math. Comput. 217(13), 6047–6053 (2011)
Hamrawi, H., Coupland, S., John, R.: Type-2 fuzzy alpha-cuts. IEEE Trans. Fuzzy Syst. 25(3), 682–692 (2017)
Hayek, P.A., Salameh, M.K.: Production lot sizing with the reworking of imperfect quality items produced. Prod. Plan. Control 12(6), 584–590 (2001)
Hovelaque, V., Bironneau, L.: The carbon-constrained EOQ model with carbon emission dependent demand. Int. J. Prod. Econ. 164, 285–291 (2015)
Hsu, J.-T., Hsu, L.-F.: Two EPQ models with imperfect production processes, inspection errors, planned backorders, and sales returns. Comput. Ind. Eng. 64(1), 389–402 (2013)
Karnik, N.N., Mendel, J.M.: Centroid of a type-2 fuzzy set. Inf. Sci. 132(1), 195–220 (2001)
Khan, M., Jaber, M.Y., Bonney, M.: An economic order quantity (EOQ) for items with imperfect quality and inspection errors. Int. J. Prod. Econ. 133(1), 113–118 (2011)
Khanna, A., Kishore, A., Jaggi, C.: Strategic production modeling for defective items with imperfect inspection process, rework, and sales return under two-level trade credit. Int. J. Ind. Eng. Comput. 8(1), 85–118 (2017)
Krishnamoorthi, C., Panayappan, S.: An EPQ model for an imperfect production system with rework and shortages. Int. J. Oper. Res. 17(1), 104–124 (2013)
Liu, N., Kim, Y., Hwang, H.: An optimal operating policy for the production system with rework. Comput. Ind. Eng. 56(3), 874–887 (2009)
Mizumoto, M., Tanaka, K.: Fuzzy sets and type 2 under algebraic product and algebraic sum. Fuzzy Sets Syst. 5(3), 277–290 (1981)
Pal, S., Mahapatra, G.S.: A manufacturing-oriented supply chain model for imperfect quality with inspection errors, stochastic demand under rework and shortages. Comput. Ind. Eng. 106, 299–314 (2017)
Porteus, E.L.: Optimal lot sizing, process quality improvement and setup cost reduction. Oper. Res. 34(1), 137–144 (1986)
Raouf, A., Jain, J.K., Sathe, P.T.: A cost-minimization model for multicharacteristic component inspection. AIIE Trans. 15(3), 187–194 (1983)
Rommelfanger, H.: Fuzzy linear programming and applications. Eur. J. Oper. Res. 92(3), 512–527 (1996)
Rosenblatt, M.J., Lee, H.L.: Economic production cycles with imperfect production processes. IIE Trans. 18(1), 48–55 (1986)
Salameh, M.K., Jaber, M.Y.: Economic production quantity model for items with imperfect quality. Int. J. Prod. Econ. 64(1), 59–64 (2000)
Sarkar, B., Cardenas-Barron, L.E., Sarkar, M., Singgih, M.L.: An economic production quantity model with random defective rate, rework process and backorders for a single stage production system. J. Manuf. Syst. 33(3), 423–435 (2014)
Schrady, D.A.: A deterministic inventory model for reparable items. Nav. Res. Logist. 14(3), 391–398 (1967)
Shekarian, E., Kazemi, N., Abdul-Rashid, S.H., Olugu, E.U.: Fuzzy inventory models: a comprehensive review. Appl. Soft Comput. 55, 588–621 (2017)
Shih, W.: Optimal inventory policies when stockouts result from defective products. Int. J. Prod. Res. 18(6), 677–686 (1980)
Tai, A.H.: Economic production quantity models for deteriorating/imperfect products and service with rework. Comput. Ind. Eng. 66(4), 879–888 (2013)
Widyadana, G.A., Wee, H.M.: An economic production quantity model for deteriorating items with multiple production setups and rework. Int. J. Prod. Econ. 138(1), 62–67 (2012)
Yoo, S.H., Kim, D., Park, M.-S.: Economic production quantity model with imperfect-quality items, two-way imperfect inspection and sales return. Int. J. Prod. Econ. 121(1), 255–265 (2009)
Zhou, Y., Chen, C., Li, C., Zhong, Y.: A synergic economic order quantity model with trade credit, shortages, imperfect quality and inspection errors. Appl. Math. Model. 40(2), 1012–1028 (2016)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Rout, C., Kumar, R.S., Chakraborty, D. et al. An EPQ model for deteriorating items with imperfect production, inspection errors, rework and shortages : a type-2 fuzzy approach. OPSEARCH 56, 657–688 (2019). https://doi.org/10.1007/s12597-019-00390-3
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12597-019-00390-3