Linear Relationships for Constrained Multiple-item Inventory Systems

Inventory control is a problem common to many businesses andmanufacturing systems. Management spends a fair amount of timetrying to determine appropriate inventory policies. The firstinventory model, which is still used widely today, is the economicorder quantity (EOQ) model of Harris. This model, however, doesnot consider constraints on the problem such as storage capacityor budget Limitations. It is the purpose of this paper to examinethe multiple-item deterministic inventory system with one linearconstraint, and establish linear relationships between the Lagrangemultiplier of the constrgint and artain system characteristics.It is then discussed how the insights from these relationshipscan be used to provide tight hunds to the optimal multiplier.Computational results for these bounds are also included.