A multi-linear constraint inventory system

A problem common to many retail businesses and manufacturing systems is the determination of an appropriate inventory policy. The first inventory model developed to support this effort was the Harris–Wilson economic order quantity (model). This model, although still in wide use today, does not consider budget and/or space constraints common to such inventory systems. Based on three distinct functional regions found to exist between optimal Lagrangian multiplier(s) and the relative strengths of linear (space and budget) constraints, this paper expands the current research by including multiple linear constraints and by establishing an algorithm which (1) identifies, directly from system parameters, that portion of the constraint set which is binding at the optimal solution and (2) presents a simple linear approximation which ensures near-optimal feasible solutions, in closed form, when both constraints are found binding. Computational effectiveness of the algorithm is also highlighted.