A polynomial time algorithm for production planning with bounded inventory

Abstract

In petrochemical manufacturing, food processing, glass manufacturing, etc., there is a situation where the production planning is subject to the limit of inventory capacity (or bounded inventory) rather than production capacity. Only a few studies can be found in the literature for this situation. In this paper, the production planning problem with bounded inventory is discussed. Specifically, the problem considered had the following features: (i) backlogging is not allowed, (ii) lost sale is allowed, (iii) the lost sale cost function is time varying and non-increasing, and (iv) inventory capacity is non-decreasing. An algorithm for this problem with the polynomial O(T3) time complexity is proposed. Though the complexity of the algorithm is the same as that of the other work, see Sandbothe and Thompson (Oper Res 38(3):474–486, 1990), the problem in the other’s work problem is less complex than ours; for instance only a fixed cost function is considered. A case study taken from a real-life production line is provided to further justify the application of the lost sale strategy, demonstrating the effectiveness of our model and algorithm.