Optimal Inventory Control Decision Rules for a Large Supply System

Mathematical decision rules for the control of inventories in a large supply system are derived. These rules allow the minimization of total system shortages where this minimization is subject to specified system expenditures. Alternatively, the rules permit the minimization of system expenditures for a given level of system shortages. The mathematical model used to derive these rules includes the features random demands, random lead times, set-up and order costs, interest costs, obsolescence costs, physical holding costs, item unit costs, relative essentialities of items, and a measure of shortage costs which takes into account the durations that shortages persist. Derivation of the optimal rules employs an iterative solution of a nonlinear programming problem. Comparisons with presently-used decision rules for a large supply system indicate that significant improvements in system effectiveness can be obtained by the use of the optimal rules.