Abstract

In this research thesis, we address the intricate challenges presented by multi-item lot-sizing problems in production environments, considering stochastic demand, capacity constraints, and inventory limitations. Our objective is to formulate an optimized production schedule, drawing inspiration from existing literature models. We introduce two mathematical models for the lotsizing problem, incorporating aggregate service levels β and γ, and employ novel piece-wise linear approximations to address and extend existing formulations. Our research presents an iterative optimization-based solution approach for the piecewise linear approximation of the stochastic lotsizing problem. This process involves breaking down the overall planning horizon into smaller intervals, creating a more manageable planning horizon, and iteratively addressing a series of subproblems. Extensive computational experiments explore the implications of aggregate service levels, comparing the solution quality of the actual piecewise linear approximation model and the Fix-and-Optimize heuristic using four different interval lengths. Results highlight the nuanced relationship between interval lengths and computational efficiency, emphasizing the strategic importance of selecting intervals aligned with operational objectives. For instance, solving the piecewise linear approximation model for the β service level with a higher interval length (9) reduces computational time by 60% on average, with a corresponding average increase of 4.5% in the relative gap (cost). Similarly, for the γ service level, computational time decreases by 38% on average, with an average relative gap increase of 3.7%.