Multi-Product Inventory System Under Constraint

摘要

This Dissertation is comprised of the following research efforts: (1) ImplicitFoundation: Functional relationships between the Lagrangian multipliers and multiple system parameters are identified and used to establish improved bounds on the optimal multiplier in closed form. A recursive process which rapidly converges to the optimal Lagrangian multiplier value is also presented. (2) Horizon Extension: Given an existing inventory system and its related optimal Lagrangian multiplier, an ability to project the multiplier needed to optimize an inventory defined as various shifts occur in the given systems is developed. A recursive process which identifies the series of Lagrangian multipliers needed to optimize an inventory horizon in which constrained conditions extend over several periods is also developed. (3) Dual Constraint System: The ability to determine that portion of the constraint set which will be binding at the optimal solution is developed. A routine is also developed which effectively estimates both Lagrangian multipliers needed to optimize the system when both a budget and a storage space constraint remains binding. (4) Real World Application: Potential benefit gained from implementing the algorithms developed within this study is demonstrated within a small hardware company's large volume inventory.