A Multi-product EPQ Model for Defective Production and Inspection with Single Machine, and Operational Constraints: Stochastic Programming Approach

• Abu-Al-Nadi, D.I., Alsmadi, O.M., Abo-Hammour, Z.S., Hawa, M.F., Rahhal, J.S.: Invasive weed optimization for model order reduction of linear MIMO systems. Appl. Math. Model. 37(6), 4570–4577 (2013)

  Article  MathSciNet  Google Scholar 

• Alamri, A.A., Harris, I., Syntetos, A.A.: Efficient inventory control for imperfect quality items. Eur. J. Oper. Res. 254(1), 92–104 (2016)

  Article  MathSciNet  Google Scholar 

• Axsäter, S.: Exact analysis of continuous review (R, Q) policies in two-echelon inventory systems with compound Poisson demand. Oper. Res. 48(5), 686–696 (2000)

  Article  MathSciNet  Google Scholar 

• Barzoki, M.R., Jahanbazi, M., Bijari, M.: Effects of imperfect products on lot sizing with work in process inventory. Appl. Math. Comput. 217(21), 8328–8336 (2011)

  MathSciNet  MATH  Google Scholar 

• Cárdenas-Barrón, L.E., Shaikh, A.A., Tiwari, S., Trevino-Garza, G.: An EOQ inventory model with nonlinear stock dependent holding cost, nonlinear stock dependent demand and trade credit. Comput. Ind. Eng. 139, 105557 (2020)

  Google Scholar 

• Chang, H.C.: An application of fuzzy sets theory to the EOQ model with imperfect quality items. Comput. Oper. Res. 31(12), 2079–2092 (2004)

  Article  MathSciNet  Google Scholar 

• Chiu, S.W., Wang, S.L., Chiu, Y.S.P.: Determining the optimal run time for EPQ model with scrap, rework, and stochastic breakdowns. Eur. J. Oper. Res. 180(2), 664–676 (2007)

  Article  MathSciNet  Google Scholar 

• Cunha, L.R.A., Delfino, A.P.S., dos Reis, K.A., Leiras, A.: Economic production quantity (EPQ) model with partial backordering and a discount for imperfect quality batches. Int. J. Prod. Res. 56(18), 6279–6293 (2018)

  Article  Google Scholar 

• Samuel, E.: Scheduling for batch production. Inst. Prod. Eng. J. 36(9), 549–570 (1957)

  Article  Google Scholar 

• Feng, Q., Kapur, K.C.: Economic design of specifications for 100% inspection with imperfect measurement systems. Qual. Technol. Quant. Manage. 3(2), 127–144 (2006)

  Article  MathSciNet  Google Scholar 

• Gharaei, A., Hoseini Shekarabi, S.A., Karimi, M., Pourjavad, E., Amjadian, A.: An integrated stochastic EPQ model under quality and green policies: generalised cross decomposition under the separability approach. Int. J. Syst. Sci. Oper. Logist. 8, 1–13 (2019)

  Google Scholar 

• Gharaei, A., Hoseini Shekarabi, S.A., Karimi, M.: Modelling and optimal lot-sizing of the replenishments in constrained, multi-product and bi-objective EPQ models with defective products: generalised cross decomposition. Int. J. Syst. Sci. Oper. Logist. 7(3), 262–274 (2020)

  Google Scholar 

• 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)

  Article  Google Scholar 

• Karimi, M., Pasandideh, S.H.R., Niknamfar, A.H.: A newsboy problem for an inventory system under an emergency order: a modified invasive weed optimization algorithm. Int. J. Manage. Sci. Eng. Manage. 12(2), 119–132 (2017)

  Google Scholar 

• Karimkashi, S., Kishk, A.A.: Invasive weed optimization and its features in electromagnetics. IEEE Trans. Antennas Propag. 58(4), 1269 (2010)

  Article  Google Scholar 

• Khalilpourazari, S., Pasandideh, S.H.R.: Multi-item EOQ model with nonlinear unit holding cost and partial backordering: moth-flame optimization algorithm. J. Ind. Prod. Eng. 34(1), 42–51 (2017)

  Google Scholar 

• Khalilpourazari, S., Pasandideh, S.H.R.: Modeling and optimization of multi-item multi-constrained EOQ model for growing items. Knowl.-Based Syst. 164, 150–162 (2019)

  Article  Google Scholar 

• Khan, M., Hussain, M., Cárdenas-Barrón, L.E.: Learning and screening errors in an EPQ inventory model for supply chains with stochastic lead time demands. Int. J. Prod. Res. 55(16), 4816–4832 (2017)

  Article  Google Scholar 

• Kwon, D., Lippman, S.A., McCardle, K., Tang, C.S.: Time-based contracts with delayed payments. Working paper. UCLA Anderson School, Los Angeles (2009)

  Google Scholar 

• Liao, H., Li, L.: Environmental sustainability EOQ model for closed-loop supply chain under market uncertainty: a case study of printer remanufacturing. Comput. Ind. Eng. 151, 106525 (2021)

  Google Scholar 

• Mehrabian, A.R., Lucas, C.: A novel numerical optimization algorithm inspired from weed colonization. Ecol. Inform. 1(4), 355–366 (2006)

  Article  Google Scholar 

• Mehrabian, A.R., Yousefi-Koma, A.: Optimal positioning of piezoelectric actuators on a smart fin using bio-inspired algorithms. Aerosp. Sci. Technol. 11(2–3), 174–182 (2007)

  Article  Google Scholar 

• Moinzadeh, K.: A multi-echelon inventory system with information exchange. Manage. Sci. 48(3), 414–426 (2002)

  Article  Google Scholar 

• Mondal, S., Maiti, M.: Multi-item fuzzy EOQ models using genetic algorithm. Comput. Ind. Eng. 44(1), 105–117 (2003)

  Article  Google Scholar 

• Nia, A.R., Far, M.H., Niaki, S.T.A.: A hybrid genetic and imperialist competitive algorithm for green vendor managed inventory of multi-item multi-constraint EOQ model under shortage. Appl. Soft Comput. 30, 353–364 (2015)

  Google Scholar 

• Nobil, A.H., Sedigh, A.H.A., Cárdenas-Barrón, L.E.: A multiproduct single machine economic production quantity (EPQ) inventory model with discrete delivery order, joint production policy and budget constraints. Ann. Oper. Res. 286(1–2), 265–301 (2020). https://doi.org/10.1007/s10479-017-2650-9

  Article  MathSciNet  MATH  Google Scholar 

• Ojha, A.K., RamuNaidu, Y.: Hybridizing particle swarm optimization with invasive weed optimization for solving nonlinear constrained optimization problems. In: Das, K.N., Deep, K., Pant, M., Bansal, J.C., Nagar, A. (eds.) Proceedings of Fourth International Conference on Soft Computing for Problem Solving. AISC, vol. 336, pp. 599–610. Springer, New Delhi (2015). https://doi.org/10.1007/978-81-322-2220-0_49

  Chapter  Google Scholar 

• Pal, B., Sana, S.S., Chaudhuri, K.: A mathematical model on EPQ for stochastic demand in an imperfect production system. J. Manuf. Syst. 32(1), 260–270 (2013)

  Article  Google Scholar 

• Pasandideh, S.H.R., Niaki, S.T.A.: A genetic algorithm approach to optimize a multi-products EPQ model with discrete delivery orders and constrained space. Appl. Math. Comput. 195(2), 506–514 (2008)

  MathSciNet  MATH  Google Scholar 

• Pasandideh, S.H.R., Niaki, S.T.A., Nia, A.R.: A genetic algorithm for vendor managed inventory control system of multi-product multi-constraint economic order quantity model. Expert Syst. Appl. 38(3), 2708–2716 (2011)

  Article  Google Scholar 

• Pourjafari, E., Mojallali, H.: Solving nonlinear equations systems with a new approach based on invasive weed optimization algorithm and clustering. Swarm Evol. Comput. 4, 33–43 (2012)

  Google Scholar 

• Rahim, M.A., Ben-Daya, M.: Joint determination of production quantity, inspection schedule, and quality control for an imperfect process with deteriorating products. J. Oper. Res. Soc. 52(12), 1370–1378 (2001)

  Article  Google Scholar 

• Ramezanian, R., Rahmani, D., Barzinpour, F.: An aggregate production planning model for two phase production systems: Solving with genetic algorithm and tabu search. Expert Syst. Appl. 39(1), 1256–1263 (2012)

  Google Scholar 

• Rezaei, J., Salimi, N.: Economic order quantity and purchasing price for items with imperfect quality when inspection shifts from buyer to supplier. Int. J. Prod. Econ. 137(1), 11–18 (2012)

  Article  Google Scholar 

• Rogers, J.: A computational approach to the economic lot scheduling problem. Manage. Sci. 4(3), 264–291 (1958)

  Article  Google Scholar 

• Sahinidis, N.V., Tawarmalani, M.: BARON 7.2. 5: Global optimization of mixed-integer nonlinear programs. User’s manual (2005)

  Google Scholar 

• Sahraei-Ardakani, M., Roshanaei, M., Rahimi-Kian, A., Lucas, C.: A study of electricity market dynamics using invasive weed colonization optimization. In: IEEE Symposium on Computational Intelligence and Games, CIG 2008, pp. 276–282. IEEE, December 2008

  Google Scholar 

• Sana, S.S., Goyal, S.K., Chaudhuri, K.: An imperfect production process in a volume flexible inventory model. Int. J. Prod. Econ. 105(2), 548–559 (2007)

  Article  Google Scholar 

• Sarkar, B., Saren, S.: Product inspection policy for an imperfect production system with inspection errors and warranty cost. Eur. J. Oper. Res. 248(1), 263–271 (2016)

  Article  Google Scholar 

• Shaikh, A.A., Khan, M.A.A., Panda, G.C., Konstantaras, I.: Price discount facility in an EOQ model for deteriorating items with stock-dependent demand and partial backlogging. Int. Trans. Oper. Res. 26(4), 1365–1395 (2019)

  Article  MathSciNet  Google Scholar 

• Taft, E.W.: The most economical production lot. Iron Age 101(18), 1410–1412 (1918)

  Google Scholar 

• Taleizadeh, A.A., Cárdenas-Barrón, L.E., Mohammadi, B.: A deterministic multi product single machine EPQ model with backordering, scraped products, rework and interruption in manufacturing process. Int. J. Prod. Econ. 150, 9–27 (2014)

  Google Scholar 

• Tawarmalani, M., Sahinidis, N. V.: A polyhedral branch-and-cut approach to global optimization. Math. Program. 103(2), 225–249 (2005)

  Google Scholar 

• Yokota, T., Gen, M., Li, Y.X.: Genetic algorithm for non-linear mixed integer programming problems and its applications. Comput. Ind. Eng. 30(4), 905–917 (1996)

  Article  Google Scholar 

• Yoo, S.H., Kim, D., Park, M.S.: Inventory models for imperfect production and inspection processes with various inspection options under one-time and continuous improvement investment. Comput. Oper. Res. 39(9), 2001–2015 (2012)

  Article  MathSciNet  Google Scholar 

• Yoon, K., Hwang, C.L.: TOPSIS (Technique for Order Preference by Similarity to Ideal Solution)–A Multiple Attribute Decision Making, W: Multiple Attribute Decision Making–Methods and Applications, a State-of-The-Art Survey. Springer, Berlin (1981)

  Google Scholar 

• Zhang, X., Wang, Y., Cui, G., Niu, Y., Xu, J.: Application of a novel IWO to the design of encoding sequences for DNA computing. Comput. Math. Appl. 57(11–12), 2001–2008 (2009)

  Article  Google Scholar 

• Zipkin, P.H.: Foundations of inventory management (2000)

  Google Scholar 

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