Joint determination of order quantity and reorder point of continuous review model under quantity and freight rate discounts

The increased emphasis on transportation costs has enhanced the need to develop models with transportation consideration explicitly. However, in stochastic inventory models, the transportation cost is considered implicitly as part of fixed ordering cost and thus is assumed to be independent of the size of the shipment. As such, the effect of the transportation and purchasing costs are not adequately reflected in final planning decisions. In this paper, transportation and purchasing considerations are integrated with continuous review inventory model. The objective is to view the system as an integrated whole and determine the lot size and reorder point which minimize the expected total cost per unit time. In addition, procedures are developed to solve the proposed models. Numerical experiments are also performed to explore the effect of key parameters on lot size, reorder point and expected total cost. The new models have a significant impact on lot size, reorder point and expected total cost. Savings up to 17.15% of the expected total cost are realized when using the proposed models.