Inventory Model For Deteriorating Items With Variable Hosting Cost And Shortage

Nowadays, the social development focuses on how to do inventory management in a scientific way, thus, leading the inventory theory the important branch of the study of operational research. The traditional models incorporating inventory usually assume that the holding cost and shortage cost is constant for the entire inventory cycle. However, in fact, According to the changing time, stock and shortage level, holding and shortage cost can be changed. This paper considers the various conditions of variable holding and shortage cost in the models foundation process of deteriorating items, expanding the previous study.First, the paper study respectively the deteriorating immediately items when the holding cost has a function to time or holding quantity. Second, for the non-instantaneous deteriorating items, we assume that the holding cost periodically change during the period of guarantee and deterioration, studying the inventory model to acquire the optimal quantity and the retail price.Third, we develop the inventory model of deteriorating items taking account of the time-value of costs in the finite planning horizon in the direction of the variable holding costs. Then, we continue expanding the model on the assumption that both the holding and shortage cost have a function to the time or the inventory level (shortage level).In addition, we consider the change of shortage costs by the finite customer service level, and found another model on the assumption that backlogging ratio decreases with the shortage time or quantity respectively. In summary, several inventory models are founded in this paper. The existence and uniqueness of optimal solution, and optimality conditions or optimization algorithms are also studied in every model, illustrating the influence on optimal ordering policies in inventory system with the nonlinear cost. Finally, some numerical examples are showed to demonstrate the effectiveness and feasibility of these models, indicating some practical meaning of the study.