Production-inventory system with finite production rate, stock-dependent demand, and variable holding cost

In general, traditional production-inventory systems are based on a number of simplifying – but somewhat unrealistic – assumptions, including constant demand rate, constant holding cost, and instantaneous order replenishment. These assumptions have been individually challenged in numerous variations of production-inventory models. Finite production rate models, such as economic production quantity (EPQ) systems consider gradual order replenishment. Stock-dependent demand models assume the demand rate to be an elastic function of the inventory level. Variable holding cost models assume the holding cost per unit per time period to be a function of the time spent in storage. In this paper, the three simplifying assumptions are simultaneously relaxed in a new production-inventory system with a finite production rate, stock-level dependent demand rate, and variable holding cost. Mathematical models and optimum solution procedures, including nonlinear programming, are presented for two functional forms of holding cost variability. The main contribution of this paper is the formulation and solution of a new production-inventory model that more closely represents real-world situations. The realistic assumptions and efficient solution algorithms should make the model practical and useful for industrial applications.