Optimization of capacity loading and *production under congestion

Production planning is an important function in managing supply chains. It is a collaborative process of gathering, creating, and updating information and decisions, which are critical to achieve consistency within the planning hierarchy and the supply chain. As one of the most important items of information, capacity in production planning has been mostly regarded as a fixed, deterministic limit. Thus existing production planning models fail to capture effect of capacity loading on lead times, which creates a major problem, known as the planning circularity. While lead time in production systems depends on resource utilization, the utilization is determined by production planning decisions, which require lead time in order to match supply to demand. First, I developed nonlinear capacity models called clearing function that can capture the relationship between throughput, lot size, and work-in-process in single stage production system with single and multiple products. Second, I extended nonlinear capacity models for multi-stage production systems with single and multiple products. The multi-stage models can capture both interactions between stages and variability of job arrivals between stages. Finally, dynamic lot sizing problems using clearing functions are formulated for all production systems. A contribution of the research is that the developed lot sizing models are proved to be a convex programming problem. An important characteristic of the developed lot sizing models is a joint optimization of lead time and lot sizes. Computational study clearly indicates that the proposed models perform better than the benchmark