Constrained Periodic-Review Probabilistic Inventory Model with Increasing Holding Cost for Two Different Cases of the Relational Function

The periodic-review inventory process is a review of the level of stock for each item over a number of periods. The main problem with an inventory model is determining the optimal number of periods, the optimal maximum inventory level, and the minimum expected total inventory cost. This research deals with two different cases of relational function in periodic-review probabilistic inventory models, where the holding cost is an increasing function of the number of periods under nonlinear and linear constraints. The nonlinear constraint is the expected ordering cost and the linear constraint is storage space. The goal of this research is to find the minimum expected total cost for the two different probabilistic inventory models based on two different relational functions using a geometric programming approach. The classical inventory model without any constraints is derived as a special case. A numerical example is analyzed for each model