Note on inventory model with a mixture of back orders and lost sales

Competitiveness is an important means of determining whether a company will prosper. Business organizations compete with one another in a variety of ways. Among these competitive methods are time and cost factors. The purpose of this paper is to examine the inventory models presented by Padmanabhan and Vrat with a mixture of back orders and lost sales. We develop the criterion for the optimal solution for the total cost function. If the criterion is not satisfied, this model will degenerate into one cycle inventory model with a finite inventory period. This implies an extension of shortage period as long as possible to produce lower cost. However, we know that time is another important factor in company competitiveness. Customers will not indefinitely wait for back orders. A tradeoff will be made between the two most important factors; time and cost. The minimum total cost is evaluated under the diversity cycle time and illustrations are applied to explain the calculation process. This work provides a reference for decision-makers.