عنوان مقاله [English]
Inventory management and production planning are two of necessary tasks for each manufacturing organization. In this paper, a production-inventory model with backlogging is expanded to identify the optimal value of inventory in multi-product organizations when demand is uncertain. The purpose of this problem is maximizing the total company’s profit considering inventory costs such as storage of raw materials and finished goods, backlogging contains both back order and lost sale, and purchasing, which is resulted in a nonlinear model. Also in this paper reworking of defected items and constraints such as finite production rate, warehouse space and capital are considered. The fuzzy set theorem is used to cope with uncertain inputs. To solve the proposed model a combined Honey Bee, Pareto and VIKOR method is applied. Results show that in the similar situations, applying this methodology leads to a maximum profit and minimum cost for manufacturing organizations.
 Akbarzadeh, M., Esmaeily, M., Taleizadeh, A., Economic Production Quantity model with complete reworking of imperfect items considering Vendor Management Inventory Policy, 9th international conference on industrial engineering, 2013 (In Persian).
 Haji, B., Haji, R. and Haji, A. Optimal batch production with rework and non-zero setup cost for rework, International Conference on Computers and Industrial Engineering, Paris, France, 2009, pp. 857–862.
 Pal, Brojeswar, Sana, Shib Sankar, Chaudhuri, Kripasindhu, A mathematical model on EPQ for stochastic demand in an imperfect production system, Journal of Manufacturing Systems 32, 2013, 260– 270.
 Sarkara Biswajit, Eduardo Leopoldo, Barrón Cárdenas, Sarkar Mitali, Laksono Singgih Moses, An economic production quantity model with random defective rate rework process and backorders for a single stage production system. Journal of Manufacturing Systems 33 (3), 2014, 423–435.
 Chan, C.K., Wong, W.H., Langevin, A., Lee, Y.C.E., An integrated production-inventory model for deteriorating items with consideration of optimal production rate and deterioration during delivery. International Journal of Production Economics, 189, 2017, pp. 1–13.
 Azar, A., Kolyaei, M., Amini, M.R., Rajabzadeh Gatari, A.R., Design of integrated mathematical model for closed-loop supply chain. Management Researches in Iran 20 (1), 2016, pp. 1-32 (In Persian).
 Behzadian, M., Inventory control and planning, Shomal Paydar (Shomal University), 2005, pp. 106 (In Persian).
 Bjoِrk, K.-M., The economic production quantity problem with a finite production rate and fuzzy cycle time, in: Proceedings of the 41st Annual Hawaii International Conference on System Sciences, 2008, pp. 68–77.
 Mansoori, F., Abbasnejad, T., Askarpour, H.R., Designing an agile supply chain network in terms of demand dependence on price. Modern Researches in Decision Making, 2, (1), 2017, pp. 179-206 (In Persian).
 Bjork, K.-M.,Carlsson,C., The effect of flexible lead times on a paper producer. International Journal of Production Economics 107(1), 2007, 139–150.
 Kazemi, A., Malekian, M.R., Sarrafha, K., A new multi-product Economic Production Quantity (EPQ) model with stochastic fuzzy demand, Journal of Industrial Engineering 46 (1), 2012, 62-53 (In Persian).
 Sadeghi,J., Sadeghi,S., Akhavan Niaki,T., Optimizing a hybrid vendor-managed inventory and transportation problem with fuzzy demand: An improved particle swarm optimization algorithm, Information Sciences 272, 2014, 126-144.
 Bhunia, A.K., Shaikh, A.A., Cárdenas-Barrón, L.E., A partially integrated production-inventory model with interval valued inventory costs, variable demand and flexible reliability. Applied Soft Computing, 55, 2017, pp. 491–502.
 Kundu, A., Guchhait, P., Pramanik, P., Maiti, M.K., Maiti, M., A production inventory model with price discounted fuzzy demand using an interval compared hybrid algorithm. Swarm and Evolutionary Computation, 34, 2017, pp. 1–17.
 Akbari, M., A model for production and inventory control in crisis condition. Management Researches in Iran, 19, (4), 2016, pp. 45-70 (In Persian).
 Janson, S., Middendorf, M., Beekman M., Honybee swarm: How to scouts guide a swarm of uniformed bees.Animal behavior 70, 2005, 349-358.
 Shams kia, F., Application of Honey Bee Algorithm on mathematical optimization, Scientific and Information Technology and Communication group, Engineering department, Najaf Abad branch of Payam Noor university, 2012 (In Persian).
 Karaboga, D., Basturk, B., A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm, J Glob Optim 39, 2007, 459–471.
 Taleizadeh, A., Akhavan Niaki, T., Aryanezhad, M., A hybrid method of Pareto, TOPSIS and genetic algorithm to optimize multi-product multi-constraint inventory control systems with random fuzzy replenishments, Mathematical and Computer Modelling 49, 2009, 1044 -1057.
 Opricovic, S. Multi-criteria optimization of civil engineering systems, Belgrade: Faculty of Civil Engineering, 1998.
 Opricovic, S., Tzeng, G.H., Extended VIKOR method in comparison with outranking methods, European Journal of Operational Research 178 (2), 2007, 514–529.
 Taleizadeh, A.A., Jalali-Naini, S.Gh., Wee, H.M., Kuo, T.C., An imperfect multi-product production system with rework, Sharif University of Technology, Scientia Iranica Transactions E: Industrial Engineering, accepted 10 October 2012.
 Ghozati, H., Pasandideh, S.H.R., Optimization inventory model of combined production and purchase with backlogging and warehouse storage constraint, 2th national conference on Industrial and Systems Engineering, Industrial Engineering Group, Najaf Abad Branch of Islamic Azad university, 2014 (In Persian).