In this paper a new analytical approach to safety stock management, within single buyer–single vendor framework under VMI with consignment agreement, is presented. In particular, the cost of the safety stock is evaluated adopting a logistic approximation of the standard normal cumulative distribution. The service level is put in relation to the dimension of the single shipment, to the average demand on the buyer and to the number of admissible stockouts. Once the mean joint total cost function is defined, on the basis of the model of Braglia and Zavanella, (2003. Int. J. Prod. Res. 41, 3793–3808) modified according to Braglia et al. (2014. Int. J. Logist. Syst. Manage. forthcoming 2014), a minimum cost solution (within a predefined domain) is derived. Moreover, a numerical study is carried out. First, a sensitivity analysis is shown. Then, the model of Braglia and Zavanella, (2003. Int. J. Prod. Res. 41, 3793–3808), in its original expression, is compared with both Hill (1997. Eur. J. Oper. Res. 97, 493–499), Hill (1999. Int. J. Prod. Res. 37, 2463–2475) and Hill and Omar (2006. Int. J. Prod. Res. 44, 791–800). In particular, the comparison considers the equal-sized shipments case without delayed deliveries taking into account different reciprocal values for the stockholding costs.
