Ordering cost reductions in joint inventory systems with time discounted

This paper investigates the impact of ordering cost reduction on joint inventory systems for a single vendor and a single buyer with time discounted. In this model, two types of expenditure are considered for reducing the ordering cost. One is the one-time capital expenditure spent at the time of decision to establish the new ordering process. The other is an operating cost incurred continuously to keep the ordering process effective. Both expenditures assumed to be proportional to the amount of reduction in buyer's ordering cost. Since a capital expenditure is involved at the time of decision and the time value of money considered, the cost components of each production cycle are continuously discounted throughout the entire planning horizon. The decision for the system is to determine the buyer's planned ordering cost, order quantity, and the vendor's production lot size such that the present worth of total joint vendor and buyer cost over the entire planning horizon is minimized. A numerical example along with sensitivity analysis is presented to illustrate the application of the model.