Constrained multi-item inventory systeṁs an implicit approach

This paper examines the N-item deterministic inventory model subject to a single linear constraint. Functional relationships between the Lagrangian multipliers and shifts occurring simultaneously in multiple system parameters are identified and used to establish effective initial bounds on the optimal multiplier, Φ^*, in closed form. A recursive process which rapidly converges to Φ^* is also presented. Finally, a comparative analysis highlighting the efficiency of the proposed process in relation to existing algorithms is exhibited.