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Inventory Positioning/Partitioning for Backorders Optimization for a Class of Multi‐Echelon Inventory Problems *
Author(s) -
Rogers David F.,
Tsubakitani Shigeru
Publication year - 1991
Publication title -
decision sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.238
H-Index - 108
eISSN - 1540-5915
pISSN - 0011-7315
DOI - 10.1111/j.1540-5915.1991.tb01280.x
Subject(s) - inventory theory , newsvendor model , computer science , inventory control , operations research , mathematical optimization , perpetual inventory , inventory investment , inventory management , service level , safety stock , stock (firearms) , economics , operations management , supply chain , mathematics , econometrics , business , mechanical engineering , statistics , marketing , engineering
Inventory management has undergone significant philosophical changes in recent decades such as the advent of the zero inventory concept. However, as attractive as the concept of minimal inventories may be, it is often unrealistic in application. Attention to basic features of inventory control systems such as order quantities, base stock levels, and reorder points remain crucial to ensure customer service at minimal cost. A nonlinear optimization model for determining base stock levels in a multi‐echelon inventory network is presented. Lagrangian relaxation results in (1) newsboy‐style relations that provide the optimal solutions, and (2) instantaneous shadow prices for the budget constraint. Sensitivity analysis of this model will facilitate making decisions concerning the desired investment in inventory for the entire system. This model may be solved on standard nonlinear programming software and is generalizable to problems in both production and distribution settings.