A new lot sizing model for controllable processing times and inventory deterioration

Production planning for real cases situations is a very complicated work that is contributed with some of simplification for obtaining efficient results. In this paper a new problem is studied in lot sizing, which is the extension of a well-known NP-Hard problem in the case of inventory deterioration and controllable processing times and a set of technological constraints. Two models are constructed for the case of dealing with linear time / cost relation and quadratic time / cost trade-off when compressing process times. Afterwards, some of the theorems and lemmas are proved about mathematical characteristics of the both model. Then a new algorithm is proposed to explore the feasible solution space in order to extract a near optimal solution. Finally some of the test problems are analyzed beside a real world case to approve the validity of the algorithm and the model.