backlogging

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.

In this paper we developed an inventory model in mixed imprecise and uncertain environment. Presented model is developed form of (r,Q) and is a multi-items model with two objectives as minimizing costs (holding & shortage) and risk level under constraints including available budgetary, the least service level, storage spaces & allowable quantities of shortage. Demand distribution functions are assumed to be exponential and extra demands are supposed in two situations as lost sales and backlogging. At first we develop crisp model then fuzzy stochastic model with fuzzy budgetary, allowable quantities of shortage and shortage spaces (i.e. stochastic with normal distribution function) parameter. All of fuzzy numbers are triangular type. In methodology of solution we change model to a crisp multiobjectiveby using difuzzification of fuzzy constraints and fuzzy chance-constrained programming methods, and then solve it by fuzzy logic method. Finally an illustrated example is taken and solved using LINGO package.