Abstract
This research deal the probabilistic multi-product multi-vendor inventory model include varying order cost and zero lead-time under linear and non-linear constraints for the number of periods Nrs, the first linear constraint on the expected holding cost, the second nonlinear constraint on the buffer stock and the third linear constraint on the storage space. The goal is to limit the expected holding cost by an upper limit k(1), the limit for the buffer stock by an upper limit k(2) and the limit for the storage space by an upper limit k3. The searchers' aim is to determine the minimum expected total cost, the optimal number of period N-rs* an(d) the optimal maximum inventory level Q(mrs)* by using a geometric programming approach. Then, applying the results of the models by a numerical example and graphs. Also, two special cases are deduced. (C) 2018 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University.