Modem information technologies have become important means for manufacturing and retailing firms to gain such competitive advantages as lower logistics costs and securer customers' loyalty. In this paper, we investigate a joint inventory system where the vendor produces a single item for its sole buyer and the buyer sells the item to consumers with backorders allowed. Each production lot is delivered to the buyer in a number of shipments and consecutive shipments will be increased by a fixed factor. Both vendor and buyer are willing to participate in order processing time reduction by applying information technologies in order to decrease their joint total cost. The order processing time can be reduced by certain expenditures and will affect the lot-size decisions. An analytical model is developed for determining the optimal expenditure in order processing time reduction and lot sizes for both vendor and buyer. The numerical experiment along with sensitivity analysis is also performed to obtain some insights of our model.