Optimal Selling Price, Marketing Expenditure and Order Quantity with Backordering

Demand is assumed constant in the classical economic order quantity (EOQ) model. However, in the real world, the demand is dependent on many factors such as the selling price, warranty of product and marketing effort. In addition pricing and ordering quantity decisions are interdependent for a seller when demand for the product is price sensitive in the inventory models. These types of models are very popular in the literature as joint pricing and order quantity models. Many researchers consider these models under some conditions such as quantity discount, trade credit and marketing effort. In this paper, we propose a new inventory model for the seller who conducts marketing effort. The marketing effort is the process of performing market research, selling products and/or services to customers and promoting them via advertising to further enhance sales. It is used to identify the customer, to satisfy the customer, and to keep the customer. This process will happen during the planning horizon; therefore the product will be demanded increasingly as time passes. This increasing in the demand leads to the backorder condition in the model. Since the marketing effort as a decision variable is dependent of the time, in this paper, the marketing effort is assumed a linear function of time which has an effect on the demand in addition of price in our model. The model would be included the backorder cost due to raising the shortage of inventory in addition, the purchasing, ordering and holding costs. An algorithm for finding the optimal solution for the selling price, marketing expenditure and the time length of positive stock are obtained when the seller’s pro?t is maximized. To clarify the model more, numerical examples presented in this paper, including sensitivity analysis of some key parameter- the cost parameters and non-cost parameters- that will compare the obtained results of proposed model.