Title :
Optimal control of a multi-product inventory system with substitution
Author :
Chen, Jinfa ; Yao, David D. ; Zheng, Shaohui
Author_Institution :
Columbia Univ., New York, NY, USA
Abstract :
We study a single-period, multi-product inventory model that allows substitution among the products. The main decision is the replenishment (order) quantity for each product at the beginning of the period, before demands are realized. This decision, however, has to take into account the substitution rule, which will be carried out, also in an optimal fashion, at the end of the period when demands are realized. We first derive an optimal substitution rule, and show that under this rule, the objective function is both concave and submodular in the order quantities-decision variables. Hence, the optimal replenishment decision can be effectively generated by solving a concave program
Keywords :
decision theory; optimal control; production control; stock control; concave program; decision variables; multi-product inventory system; objective function; optimal control; optimal replenishment decision; optimal substitution rule; order quantities; replenishment quantity; substitution; substitution rule; Costs; Councils; Customer service; Integrated circuit modeling; Inventory management; Optimal control; Quality management; Random variables;
Conference_Titel :
Decision and Control, 1999. Proceedings of the 38th IEEE Conference on
Conference_Location :
Phoenix, AZ
Print_ISBN :
0-7803-5250-5
DOI :
10.1109/CDC.1999.832822