Optimal inventory policies under decreasing cost functions via geometric programming

In this paper, we establish and analyze two economic order quantity based inventory models under total cost minimization and profit maximization via geometric programming (GP) techniques. Through GP, optimal solutions for both models are found and managerial implications on the optimal policy are determined through bounding and sensitivity analysis. We investigate the effects on the changes in the optimal order quantity and the demand per unit time according to varied parameters by studying optimality conditions. In addition, a comparative analysis between the total cost minimization model and the profit maximization model is conducted. By investigating the error in the optimal order quantity of these two models, several interesting economic implications and managerial insights can be observed.