A multi-objective inventory model for deteriorating items with backorder and stock dependent demand.

Classical deterministic inventory models consider the demand rate to be either constant or time-dependent but independent from the stock status. However, for a certain type of inventory, the demand rate may be influenced by the stock level. Also in many real-life problems, some products such as fruits, vegetables, pharmaceuticals and volatile liquids continuously deteriorate to evaporation, obsolescence, spoilage, etc. In this paper, a multi-deteriorating inventory model with shortage in fuzzy form is formulated and solved where the demand’s pattern has a linear trend. In this paper, we present a multi-objective inventory model of deteriorating items in fuzzy environment with the consideration of shortage in the problem formulation. The demand here is assumed with a linear trend and the shortage is allowed for all items. The objectives of maximizing net profit of the inventory system and minimizing the total annual cost of deteriorated items are considered subject to the total cost and the storage area. The vagueness in the objectives is expressed by fuzzy linear membership functions and the resulted fuzzy models are transferred into a non-linear programming and solved using Fuzzy Non-Linear Programming (FNLP) method. The implementation of the model is presented with some numerical examples and finally the results of two fuzzy models are compared.