An integrated production planning model with load-dependent lead-times and safety stocks

The divergence over the years of research paradigms addressing the production planning problem has led to the development of an extensive set of techniques, each of which can address a particular aspect of the practical problem and none of which provides a complete solution. In particular, most approaches fail to address the circular, non-linear dependency between resource utilization, lead-times and safety stocks. We present a non-linear programming formulation of the integrated problem using clearing functions that determines a work release schedule guaranteeing a specified service level in the face of stochastic demand. We introduce an iterative heuristic solution procedure that solves a relaxed LP approximation of the original NLP at each iteration to determine the lead-time profile to set safety-stock levels. Computational experiments suggest that our proposed iterative procedure performs well relative to conventional LP models that assume fixed, workload-independent lead-times.