Introduction
The classical dynamic lot sizing problem specifies a
discrete-time finite horizon single product inventory
management problem subject to deterministic timevarying demand that must be satisfied.This problem has been the subject of extensive research since it sintroduction in the late 1950 s until today.When the production cost and the inventory cost of each period are linear,
several authors have presented theorems that can reduce
the computational effort required in solving the problem.
Wagner and Whitin(1958) and Zabel (1964) give results
for the no-backlogging case,while Zangwill (1969)
analyzes the backlog case.Many generalizations of the
basic model have been considered including introducing
bounds on inventory and/or production capacity,as well