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 decisionsare interdependent for a seller when demand for the product is price sensitive in the inventorymodels. These types of models are very popular in the literature as joint pricing and orderquantity models. Many researchers consider these models under some conditions such asquantity discount, trade credit and marketing effort. In this paper, we propose a new inventorymodel for the seller who conducts marketing effort. The marketing effort is the process ofperforming market research, selling products and/or services to customers and promoting themvia advertising to further enhance sales. It is used to identify the customer, to satisfy thecustomer, 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 thedemand leads to the backorder condition in the model. Since the marketing effort as a decisionvariable is dependent of the time, in this paper, the marketing effort is assumed a linearfunction of time which has an effect on the demand in addition of price in our model. Themodel would be included the backorder cost due to raising the shortage of inventory inaddition, the purchasing, ordering and holding costs. An algorithm for finding the optimalsolution for the selling price, marketing expenditure and the time length of positive stock areobtained when the seller’s profit is maximized. To clarify the model more, numerical examplespresented in this paper, including sensitivity analysis of some key parameter- the costparameters and non-cost parameters- that will compare the obtained results of proposed model.