1. Murthy, D.N.P. and Blischke, W.R. Strategic warranty management: a life-cycle approach", IEEE T. Eng. Manage., 47(1), pp. 40{54 (2000). 2. Nguyen, D. and Murthy, D.P. Optimal burn-in time to minimize cost for products sold under warranty", AIIE. Trans., 14(3), pp. 167{174 (1982). 3. Murthy, D.N.P. Product warranty and reliability", Ann. Oper. Res., 143(1), pp. 133{146 (2006). 4. Zhou, Z., Li, Y., and Tang, K. Dynamic pricing and warranty policies for products with _xed lifetime", Eur. J. Oper. Res., 196(3), pp. 940{948 (2009). 5. Lin, P.-C., Wang, J., and Chin, S.-S. Dynamic optimisation of price, warranty length and production rate", Int. J. Syst. Sci., 40(4), pp. 411{420 (2009). 6. Wu, C.-C., Lin, P.-C., and Chou, C.-Y. Determination of price and warranty length for a Gamma lifetime distributed product", J. of Inf. and Opt. Sci., 28(3), pp. 335{355 (2007). 7. Wu, C.-C., Lin, P.-C., and Chou, C.-Y. Determination of price and warranty length for a normal lifetime distributed product", Int. J. Prod. Econ., 102(1), pp. 95{107 (2006). 8. Glickman, T.S. and Berger, P.D. Optimal price and protection period decisions for a product under warranty", Manage. Sci., 22(12), pp. 1381{1390 (1976). 9. Nasrollahi, M. and Asgharizadeh, E. Pro-rata warranty pricing model with risk-averse buyers", The Modares. J. of Manage. Res. in Iran, 20(1), pp. 131{ 154 (2016). 10. Lin, P.-C. and Shue, L.-Y. Application of optimal control theory to product pricing and warranty with free replacement under the inuence of basic lifetime distributions", Comput. Ind. Eng., 48(1), pp. 69{82 (2005). 11. Huang, H.-Z., Liu, Z.-J., and Murthy, D. Optimal reliability, warranty and price for new products", Iie. Trans., 39(8), pp. 819{827 (2007). 12. Manna, D.K. Price-warranty length decision with Glickman-Berger model", Int. J. of Rel. and Saf., 2(3), pp. 221{233 (2008). 13. Wu, C.-C., Chou, C.-Y., and Huang, C. Optimal price, warranty length and production rate for free replacement policy in the static demand market", Omega, 37(1), pp. 29{39 (2009). 14. Fang, C.-C. and Huang, Y.-S. A study on decisions of warranty, pricing, and production with insu_cient information", Comput. Ind. Eng., 59(2), pp. 241{250 (2010). 15. Sha_ee, M. and Chukova, S. Optimal upgrade strategy, warranty policy and sale price for second-hand products", Appl. Stoch. Model. Bus., 29(2), pp. 157{ 169 (2013). 16. Faridimehr, S. and Niaki, S. Optimal strategies for price, warranty length, and production rate of a new product with learning production cost", Scientia Iranica, Transactions E, Industrial Engineering, 20(6), pp. 2247{2258 (2013). 17. Mahmoudi, A. and Shavandi, H. Analyzing price, warranty length, and service capacity under a fuzzy environment: Genetic algorithm and fuzzy system", Scientia Iranica, 20(3), pp. 975{982 (2013). 18. Tsao, Y.C., Teng, W.G., Chen, R.S., and Chou, W.Y. Pricing and inventory policies for hi-tech products under replacement warranty", INT. J. Sysy. Sci., 45(6), pp. 1255{1267 (2014). 19. Wei, J., Zhao, J., and Li, Y. Price and warranty period decisions for complementary products with horizontal _rms' cooperation/noncooperation strategies", J. Clean. Prod., 105, pp. 86{102 (2015). 20. Yazdian, S.A., Shahanaghi, K., and Makui, A. Joint optimisation of price, warranty and recovery planning in remanufacturing of used products under linear and non-linear demand, return and cost functions", Int. J. Syst. Sci., 47(5), pp. 1155{1175 (2016). 21. Murthy, D., Solem, O., and Roren, T. Product warranty logistics: Issues and challenges", Eur. J. Oper. Res., 156(1), pp. 110{126 (2004). 514 M. Afsahi et al./Scientia Iranica, Transactions E: Industrial Engineering 27 (2020) 494{515 22. Gallagher, T., Mitchke, M.D., and Rogers, M.C. Pro_ting from spare parts", The McKinsey Quarterly, 2, pp. 1{4 (2005). 23. Kim, B. and Park, S. Optimal pricing, EOL (end of life) warranty, and spare parts manufacturing strategy amid product transition", Eur. J. Oper. Res., 188(3), pp. 723{745 (2008). 24. Chari, N., Diallo, C., Venkatadri, U., and Khatab, A. Modeling and analysis of a warranty policy using new and reconditioned parts", Appl. Stoch. Model. Bus., 32(4), pp. 539{553 (2016). 25. Agrawal, S., Singh, R.K., and Murtaza, Q. A literature review and perspectives in reverse logistics", Resour. Conserv. Recy., 97, pp. 76{92 (2015). 26. Pokharel, S. and Mutha, A. Perspectives in reverse logistics: a review", Resour. Conserv. Recy., 53(4), pp. 175{182 (2009). 27. Wang, K.-H. and Tung, C.-T. Construction of a model towards EOQ and pricing strategy for gradually obsolescent products", Appl. Math. Comput., 217(16), pp. 6926{6933 (2011). 28. Fulkerson, D.R. An out-of-kilter method for minimalcost ow problems", J. of the Soc. for Ind. and Ap. Math., 9(1), pp. 18{27 (1961). 29. Kashan, A.H. A new metaheuristic for optimization: optics inspired optimization (OIO)", Comput. Oper. Res., 55, pp. 99{125 (2015). 30. Jalili, S. and Husseinzadeh Kashan, A. Optimum discrete design of steel tower structures using optics inspired optimization method", The Str. Des. of Tall and Spe. Build., 27(9), p. e1466 (2018). 31. Ozdemir, M.T. and Ozturk, D. Comparative performance analysis of optimal PID parameters tuning based on the optics inspired optimization methods for automatic generation control", Energies, 10(12), p. 2134 (2017). 32. Ozdemir, M.T. and Ozturk, D., Optimal PID Tuning for Load Frequency Control Using Optics Inspired Optimization Algorithm, ICNES (2016). 33. Husseinzadeh Kashan, A. An e_ective algorithm for constrained optimization based on optics inspired optimization (OIO)", Comput. Aided Design., 63, pp. 52{ 71 (2015). 34. Mohammadi, M. and Musa, S.N. Bahreininejad, optimization of economic lot scheduling problem with backordering and shelf-life considerations using calibrated metaheuristic algorithms", Comput. Aided. Design., 251(Supplement C), pp. 404{422 (2015). 35. Kuo, R.J., Lee, Y.H., Zulvia, F.E., and Tien, F.C. Solving bi-level linear programming problem through hybrid of immune genetic algorithm and particle swarm optimization algorithm", Appl. Math. Comput., 266(Supplement C), pp. 1013{1026 (2015). 36. Yang, M.-F. and Lin, Y. Applying the linear particle swarm optimization to a serial multi-echelon inventory model", Expert. Syst. Appl., 37(3), pp. 2599{2608 (2010). 37. Mousavi, S.M., Bahreininejad, A., Musa, S.N., and Yusof, F. A modi_ed particle swarm optimization for solving the integrated location and inventory control problems in a two-echelon supply chain network", J. Intell. Manuf., 28(1), pp. 191{206 (2017). 38. Majumder, P., Bera, U.K., and Maiti, M. An EPQ model for two-warehouse in unremitting release pattern with two-level trade credit period concerning both supplier and retailer", Appl. Math. Comput., 274(Supplement C), pp. 430{458 (2016). 39. Bhunia, A.K. and Shaikh, A.A. An application of PSO in a two-warehouse inventory model for deteriorating item under permissible delay in payment with di_erent inventory policies", Appl. Math. Comput., 256(Supplement C), pp. 831{850 (2015). 40. Jiang, Y., Hu, T., Huang, C., and Wu, X. An improved particle swarm optimization algorithm", Appl. Math. Comput., 193(1), pp. 231{239 (2007). 41. Kennedy, J. and Eberhart, R. Particle Swarm Optimization (PSO)", In Proc. IEEE International Conference on Neural Networks, Perth, Australia (1995). 42. Huang, W., Kulkarni, V., and Swaminathan, J.M. Coordinated inventory planning for new and old products under warranty", Probab. Eng. Inform. SC., 21(02), pp. 261{287 (2007). 43. Yeo, W.M. and Yuan, X.-M. Optimal Inventory Policy For Products With Warranty Agreements. in Industrial Electronics", ISIE 2007. IEEE International Symposium on, IEEE (2007). 44. Khawam, J., Hausman, W.H., and Cheng, D.W. Warranty inventory optimization for Hitachi global storage technologies", Inc. Interfaces, 37(5), pp. 455{ 471 (2007). 45. Darghouth, M.N., Ait-kadi, D., and Chelbi, A. Joint optimization of design, warranty and price for products sold with maintenance service contracts", Reliab. Eng. Syst. Safe., 165, pp. 197{208 (2017). 46. Shi, Y. and Eberhart, R.C. Empirical study of particle swarm optimization", In evolutionary computation", CEC 99. Proceedings of the 1999 Congress on, IEEE (1999).