The lot size-reorder level inventory system with customers impatience functions

In this paper, we study a continuous review inventory model with deterministic demand. The model allows shortages, which are partially backlogged. The backlogging is characterized using an approach in which customers are considered impatient. Total profit function is developed using three general costs: holding cost, order cost and shortage cost. Holding cost is based on average stocks and order cost is fixed per replenishment. In shortage cost, we include three significant costs: the unit backorder cost (depending on the shortage time), the goodwill cost (constant) and the opportunity cost. A general approach is presented to determine the economic lot size, the reorder level and the minimum total inventory cost. We consider two customers impatience functions to illustrate the application of the procedure. This paper extends several models studied by other authors.