A Multi-product model considering holding and purchasing Costs as an increasing function of order cycle time

In this paper classical inventory models, EOQ and EPQ, are developed considering holding and purchasing costs as an increasing continuous function of the ordering cycle time. Two models are presented: first one is economic order quantity and the second one is economic production quantity. Both models are formulated such that backorder is not permitted. Since the obtained model is a type of nonlinear continuous program, solving it with exact methods is impossible at the reasonable time, hence genetic algorithm and particle swarm optimization algorithm are presented to solve the problems. In addition, to increase effectiveness of algorithms, Taguchi method is used for parameters tuning. Finally a numerical example is presented to comprise two methods and results are illustrated.