Dual Lp Model Solution Of An Inventory Problem Using Dynamic Programming Technique

摘要

In this paper an inventory problem that seeks to determine the quantity of an item to be ordered into a warehouse and quantity to be sold (in each period) that will maximize total profit in A' periods has been identified. The warehouse has a fixed capacity with an initial stock considered to be less than the capacity of the warehouse. The primal linear programming (LP) model of the inventory problem is formulated with linear constraints that are based on the periodic warehouse excess supply and demand. The unit procuring cost and unit selling price with the corresponding quantities supplied and sold respectively are used to evaluate the objective function subject to the excess supply and demand constraints. The dual LP model of the inventory problem is also presented and subsequently modified to an alternative method of solution to the inventory problem by dynamic programming approach. The results of a numerical example obtained by dynamic programming technique are exactly the optimal solution of the inventory problem when the primal LP is solved. This alternative method is a short cut procedure, which has the advantage of being computationally less cumbersome when compared to the primal LP approach.