Multi-product, multi-venders inventory models with different cases of the rational function under linear and non-linear constraints via geometric programming approach

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 k1, the limit for the buffer stock by an upper limit k2 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 Nrs∗ and the optimal maximum inventory level Qmrs∗ 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.