Research on single-level lot-sizing problem under the time-varying environment

Lot-sizing problem is one of the most important issues in the production planning area and a large number of related research works can be found in literature. However, most of the works only consider the problem in a steady environment, without taking into account the time-varying production conditions that may change timely in some industrial applications. In this paper, we present the time-varying single-level lot-sizing (TV-SLLS) problem and describe it with a mathematical programming model. New properties of this problem has been analyzed, and several theorems have been developed. We propose a dynamic programming algorithm as an exact solution approach for the TV-SLLS. Problem examples and numerical calculation have been provided to evaluate the solution approach and the optimality.