Proposing a Fuzzy Multi Product Production- Inventory Model with Backlogging, Rework, Constraints Production Rate Limits, Storage Space and Capital And Solving It By Meta-Heuristic Methods

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.