Computer implemented system for determining the most profitable distribution policy for a single period inventory system subject to a stochastic metric constraint, optimization application therefor, and method therefor, and decision support tool for facilitating user determination of a distribution policy for a single period inventory system

Computer implemented method for determining the most profitable distribution policy for a single period inventory system subject to a stochastic metric constraint, the method comprising the steps of:

• (a) storing historical sales data of the sales information of each ith consumer item where i=1, 2, . . . , m at each ith location where j=1, 2, . . . , n of the single period inventory system;
• (b) forecasting the mean demand λij of each ith consumer item at each jth location of the single period inventory system on the basis of the historical sales data;
• (c) receiving the unit retail price pij, the unit production cost cij, the unit return cost gij, and the unit stockout cost bij of each ith consumer item at each ith location of the single period inventory system
• (d) receiving a threshold for the stochastic metric constraint;
• (e) determining the optimal constrained draw matrix D{circumflex over ( )} for the most profitable distribution policy for the single period inventory system satisfying the threshold;
• and
• (f) communicating the optimal constrained draw matrix D{circumflex over ( )} for the most profitable distribution policy for the single period inventory system.

Computer implemented Decision Support Tool (DST) for facilitating user determination of a distribution policy for a single period inventory system, wherein:

• the DST is operable to receive the unit retail price pij, the unit production cost cij, the unit return cost gij, and the unit stockout cost bij of each ith consumer item where i=1, 2, . . . , m at each jth location where j=1, 2, . . . , n of the single period inventory system
• the DST is operable to calculate the expected values of at least one stochastic metric realizable by a draw matrix D for the single period inventory system for at least two total draws;
• and
• the DST is operable to output the expected values of the at least one stochastic metric for the at least two draws together with their associated expected total profit (ETP) and/or the expected total bookkeeping profit (ETBP) respectively given by:
• 22 ETP = ⁢ ∑ ij ⁢ EP ij = ⁢ ∑ ij ⁢ [ ( p ij - c ij ) ⁢ D ij - ( p ij - g ij ) ⁢ ER ⁡ ( λ ij , D ij ) - b ij ⁢ EST ⁡ ( λ ij , D ij ) ] and ETBP = ∑ ij ⁢ EBP ij = ∑ ij ⁢ [ ( p ij - c ij ) ⁢ D ij - ( p ij - g ij ) ⁢ ER ⁡ ( λ ij , D ij ) ]
• where Dij is the delivered quantity of the ith consumer item at the jth location of the single period inventory system, ER(λij,Dij) is its expected returns therefrom, and EST(λij,Dij) is its expected stockout thereat.

Computer implemented method for facilitating user determination of a distribution policy for a single period inventory system, the method comprising the steps of:

• (a) receiving the unit retail price pij, the unit production cost cij, the unit return cost gij, and the unit stockout cost bij of each ith consumer item at each jth location where j=1, 2, . . . , n of the single period inventory system;
• (b) calculating the expected values of at least one stochastic metric realizable by a draw matrix D for the single period inventory system for at least two total draws;
• and
• (c) outputting the expected values of the at least one stochastic metric for the at least two draws together with their associated expected total profit (ETP) and/or the expected total bookkeeping profit (ETBP) respectively given by:
• 23 ETP = ⁢ ∑ ij ⁢ EP ij = ⁢ ∑ ij ⁢ [ ( p ij - c ij ) ⁢ D ij - ( p ij - g ij ) ⁢ ER ⁡ ( λ ij , D ij ) - b ij ⁢ EST ⁡ ( λ ij , D ij ) ] and ETBP = ∑ ij ⁢ EBP ij = ∑ ij ⁢ [ ( p ij - c ij ) ⁢ D ij - ( p ij - g ij ) ⁢ ER ⁡ ( λ ij , D ij ) ]
• where Dij is the delivered quantity of the ith consumer item at the jth location, ER(λij,Dij) is its expected returns therefrom, and EST(λij,Dij) is its expected stockout thereat.