A hybridization of Mathematical Programming and search techniques for integrated operation and workforce planning

Decision-support tools are essential to assist planners when scheduling operations in complex systems. It is critical that real-world operational and workforce details be taken into account when constructing models of the system, so as to ensure the feasibility and implementability of the final solution. However, the level of detail can greatly impact the tractability of the model - for example, increased modeling complexity can decrease the performance of mathematical programming (MP) techniques. Furthermore, high levels of detail are often important for ensuring feasibility but may not dramatically impact system cost. This research is motivated by our efforts to develop decision-support tools that simultaneously create workforce and detailed operational plans. The focus of this paper is to solve the first phase of an integrated workforce and operation plan, that is, to determine the minimum amount of time workers are required to meet demand. In our initial experience, we were able to model the real-world problem with sufficient accuracy, but found that MP approaches to finding optimal solutions to this model were inefficient. In this paper, we describe how using MP to find feasible solutions, then embedding these feasibility problems in a search-based algorithm, allowed us to find high-quality solutions. We present the general model and algorithm and then an automotive supply chain example to illustrate this technique.