Patent ID: 7313532

Claim:
Computer implemented system for determining the most profitable distribution policy for a single period inventory system subject to a stochastic metric constraint, the system comprising: (a) a database for storing historical sales data of sales information of each i th consumer item where I=1, 2, . . . , m at each j th location where j=1, 2, . . . , n of the single period inventory system; (b) a forecast engine for forecasting the mean demand λ ij of each i th consumer item at each j th location of the single period inventory system on the basis of the historical sales data; (c) a unit cost file for storing the unit retail price p ij , the unit production cost c ij , the unit return cost g ij , and the unit stockout cost b ij of each i th consumer item at each j th location of the single period inventory system; and (d) an optimization application for receiving a threshold for the stochastic metric constraint imposed on the single period inventory system, and determining the optimal constrained draw matrix D^ for the most profitable distribution policy for the single period inventory system satisfying the threshold, wherein the stochastic metric constraint is a sales target ES(λ, D*)≧G for some pre-determined threshold G; and wherein, in the case that ES(λ, D)<G, said optimization application numerically solves the Lagrange system of equations: F ⁡ ( λ i ⁢ ⁢ j , D i ⁢ ⁢ j ) = p i ⁢ ⁢ j - c i ⁢ ⁢ j + b i ⁢ ⁢ j + Mw i ⁢ ⁢ j p i ⁢ ⁢ j - g i ⁢ ⁢ j + b i ⁢ ⁢ j + Mw i ⁢ ⁢ j ⁢ ⁢ for ⁢ ⁢ all ⁢ ⁢ i , j and ∑ i ⁢ ⁢ j ⁢ w i ⁢ ⁢ j ⁡ ( D i ⁢ ⁢ j - ER ⁡ ( λ i ⁢ ⁢ j , D i ⁢ ⁢ j ) ) = G ⁢ for determining the optimal constrained draw matrix D^.