Linear relationships for constrained multiple-item inventory systems

Inventory control is a problem common to many businesses and manufacturing systems. Management spends a fair amount of time trying to determine appropriate inventory policies. The first inventory model, which is still used widely today, is the economic order quantity (EOQ) model of Harris. This model, however, does not consider constraints on the problem such as storage capacity or budget limitations. It is the purpose of this paper to examine the multiple-item deterministic inventory system with one linear constraint, and establish linear relationships between the Lagrange Multiplier of the constraint and certain system characteristics. It is then discussed how the insights from these relationships can be used to provide tight bounds to the optimal multiplier. Computational results for these bounds are also included.