Inventory Management Problem Without Future Information and Its Competitive Analysis
Zhu Zhi-jun · Yunchou yu guanli · 2005
The theory of on-line inventory management is concerned with decision problems of when and how much to buy of certain commodities whose future demand for production or trade,is uncertain.The player's objective is to issue orders so that the competitive ratio,which is defined as sup(π~(OPT)_D/π~A_D),where D is a random demand sequence,π~(OPT)_D is the profit obtained by off-line optimal algorithm,and π~A_D is the profit obtained by the on-line algorithm A,is minimized.This paper formulates a simplified on-line inventory model when M,m and n are known and devises two on-line adaptive algorithms FNA and PDBA.Furthermore,we prove that FNA has the optimal competitive ratio compared to decisions of fixed purchases.Several different cases of the demand sequence are discussed and different competitive ratios are presented according to PDBA algorithm.