Optimal Sequencing of Projects with Uncertain Regulatory Costs

Businesses often face uncertain costs when pursuing compliance with external requirements, such as regulatory mandates or industry standards. These uncertainties complicate long-term planning and require decision-makers to evaluate a wide range of operational and economic-political factors. This research, sponsored by CapTech-a Richmond, Virginiabased consultancy-contributes toward a decision-support tool for problems of this nature. In particular, it provides methods for specifying solvable optimization models in contexts where uncertainty must be quantified using expert judgment, available data, or a combination of both. This contribution consists of three components: (i) a stochastic optimization model, (ii) a judgmental forecasting procedure, and (iii) a statistical cost analysis. A stochastic optimization model forms the core of the decision system, selecting and sequencing multi-year mitigation projects and mitigation instruments to reduce a compliance metric to a target threshold with sufficiently high probability and to minimize expected total cost. To operationalize the model for a specific application, the uncertainty about its random inputs-future mitigation costs and the compliance metric’s value at the end of the planning horizon-must first be quantified. In the case study presented here, the compliance metric is emissions, mitigation projects correspond to engineering or business initiatives that reduce emissions, and mitigation instruments correspond to emission offsets that can be purchased to meet a compliance threshold. Due to the absence of data, expert judgment is solely used to quantify uncertainty about future project costs and future emissions. For each, a judgmental forecasting procedure elicits expertassessed quantiles guided by relevant operational and economicpolitical factors. For emission offset costs, limited historical data exists and was used to identify distinct volatility regimes and to model distributions of cost change. They provide central credible intervals to guide the spread of expert-assessed quantiles, while expert’s beliefs forecast the future volatility regime and the cost change direction. Together, the three components form a decision system for compliance planning under uncertainty, the core engine of CapTech’s decision-support tool.