Dynamic lot sizing models with bounded inventory and backlogging

This paper addresses a real life single item dynamic lot sizing problem arising in a refinery for crude oil procurement. It can be considered as a lot-sizing problem with bounded inventory and backlogging. The production capacity can be considered to be unlimited and the production cost functions are assumed to be linear but time-varying. The results can be easily extended to concave piecewise linear production cost functions. The goal is to minimize the total costs of production, inventory holding and backlogging. We show that the problem can be solved in O(T2) time with general concave inventory holding and backlogging cost functions where T is the number of periods in the planning horizon. We show that the complexity is reduced to O(T) when the inventory holding cost functions are linear and have some required properties.