A Single-Product Inventory Model for Multiple Demand Classes

We consider a single-product inventory system that serves multiple demand classes, which differ in their shortage costs or service level requirements. We assume a critical-level control policy, and show the equivalence between this inventory system and a serial inventory system. Based on this equivalence, we develop a model for cost evaluation and optimization, under the assumptions of Poisson demand, deterministic replenishment lead-time, and a continuous–review (Q, R) policy with rationing. We propose a computationally-efficient heuristic and develop a bound on its performance. We provide a numerical experiment to show the effectiveness of the heuristic and the value from a rationing policy. Finally, we describe how to extend the model to permit service times, and to embed within a multi-echelon setting. 1 This research has been supported in part by the MIT Leaders for Manufacturing Program, a partnership between MIT and global manufacturing firms; and by the Singapore-MIT Alliance, an engineering education and research collaboration among the National University of Singapore, Nanyang Technological University, and MIT. 2 Sawyer School of Management, Suffolk University, Boston MA, 02108-2770, [email protected] 3 Leaders for Manufacturing Program and A. P. Sloan School of Management, MIT, Cambridge MA 02139-4307, [email protected] 4 Leaders for Manufacturing Program and A. P. Sloan School of Management, MIT, Cambridge MA 02139-4307, [email protected]