The linear dynamic lot size problem with minimum order quantities

This paper continues the analysis of a special uncapacitated single item lot sizing problem where a minimum order quantity restriction, instead of the setup cost, guarantees a certain level of production lots. A detailed analysis of the model and an investigation of the particularities of the cumulative demand structure allowed us to develop a solution algorithm based on the concept of minimal sub-problems. We present an optimal solution to a minimal sub-problem in an explicit form and prove that it serves as a construction block for the optimal solution of the initial problem. The computational tests and the comparison with the published algorithm confirm the efficiency of the solution algorithm developed here.