Forecast horizons for dynamic lot-sizing model with short life cycle and capacity constraints

In this paper, we consider the forecast and decision horizons of products with limitation on short life cycle and production capacity. The upper bound on production is the same for each period and the stockouts are permitted. To obtain the forecast horizon in infinite periods, we transform the integer programming problem to dynamic programming recursive formulation, then solve the recursive formulation by the forward algorithm and compare the time complexity. A few of necessary conditions are stated and proved since the necessary conditions can reduce complexity of computations in searching for an optimal solution by the forward algorithm. At the end of the paper, we conclude and give suggestions for future research.