Abstract
This paper presents a sufficient condition of optimality in the production scheduling of a single item with deterministic time-varying demand, setup and variable costs, in the backlog and no backlog cases. A simple linear programming model is developed for the dynamic lot size problem, along with an algorithm which checks the problem's optimality conditions. The sparseness of the table in this lot sizing problem allows a given production policy to be improved and eventually an optimal solution to be obtained. This algorithm results in significant computational efficiency as tested extensively against well-known methods.
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