Production planning with limited inventory capacity and allowed stockout

In production planning, there is a situation where the production quantity is limited by inventory capacity rather than production capacity. This situation often happens in petrochemical manufacturing, food processing, glass manufacturing, etc. Only a few studies can be found in literature for this situation, among which the stockout strategy is not well studied. In this paper, we consider the production-planning problem with inventory capacity as a limiting factor. We further consider the problem with the following features: (1) the stockout is allowed, (2) production and lost sale cost functions are time varying and non-increasing, and (3) inventory capacity is constant. These features have their roots in practice. In this paper, first we present a stockout model, and then we prove some properties at an optimal solution to our model. Based on these properties, we further develop an algorithm with polynomial time complexity using the network flow approach. The paper also provides a case study to further justify practicability of the stockout strategy with limited inventory and to show the effectiveness of our model and algorithm.