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There are the following characteristics in decision on lot size in material requirements planning (MRP) systems: multiple time periods, a finite time horizon, discrete demand, and time-varying costs etc. In MRP system there are several different types of lot size techniques, such as the economic order quantity (EOQ), lot-for-lot, periodic order quantity, Wagner-Whitin algorithm, Silver-Meal algorithm and part-period algorithm. Although these lot size approaches focus on controlling the cost of holding cost and order cost, none of them, with the exception of the Wagner-Whitin algorithm, assures an optimal or minimum cost solution for time-varying demand patterns and copes with quantity discount. And Zangwill(1966), Blackburn and Kunreuther (1974) et al extended the Wagner-Whitin algorithm by following demand to go unsatisfied during some period, provided it is satisfied eventually by production in some subsequent period. R. M. Hill (1997), Stanislaw Bylka, Ryszarda Rempala (2001) give dynamic programming formulation to decide lot sizing for a finite rate input process. But the Wagner-Whitin algorithm and its extensions commonly are criticized as being difficult to explain and compute because the algorithms are complicated dynamic programming algorithms. In this paper, we propose a series of inventory models in which backorder and a finite replenishment rate are considered according to the characteristics in MRP ordering and the optimal solutions can be obtained by using general-purpose linear program solver, like EXCEL, LINDO, etc.