Conference Agenda

Planning in logistics and transportation is oftentimes complicated by a high degree of uncertainty about the actual travel distances, times, or costs. While stochastic optimization is concerned with making optimal decisions under such uncertainty, it disregards that in many practical applications, uncertainty can be reduced upfront through research and tests, also known as "explorable uncertainty". However, while uncertainty reduction through exploration can improve decision-making, it oftentimes comes at a cost, and one needs to balance exploration costs and solution quality. We study the vehicle routing problem with time windows (VRPTW) and stochastic travel times where uncertainty about travel times can be reduced by making queries to a traffic data provider while respecting an overall querying budget. This converts the stochastic VRPTW into a partially deterministic problem that we solve via point-based approximation and sample average approximation to deal with the remaining uncertainty. We present different methods to make good and fast querying decisions based on statistical features and learning and show their effectiveness in an extensive numerical study. By assuming different degrees of uncertainty, correlations, and time-window restrictions, we give detailed insights into the value of uncertainty exploration in routing.

Stochastic programming is widely used for energy system design optimization under uncertainty, but its computational demand can increase exponentially with the number of scenarios. Common scenario reduction techniques, like moments-matching or distribution-driven clustering, pre-select representative scenarios based on input parameters. In contrast, decision-based clustering groups scenarios by similarity in resulting model decisions. Although decision-based clustering has shown promise in network design and fleet planning, its utility in industrial energy system design remains unexplored.

To address this, we examine the effectiveness of decision-based clustering in energy system design using a four-step method: 1) Determining the optimal design for each scenario; 2) Selecting features reflecting optimal decisions, such as installed capacities or total cost; 3) Using these features for k-medoids clustering to identify representative scenarios; 4) Utilizing these scenarios in stochastic programming.

We apply our method to a real-world case study describing a sector-coupled industrial energy system with a superstructure comprising 20 components, modeled as mixed-integer linear program. We generate 1000 single-year scenarios via Monte Carlo sampling, which we reduce using decision-based clustering. For benchmarking, we conduct distribution-driven k-medoids clustering based on the input parameters. Our results indicate that decision-based clustering provides better designs compared to distribution-driven clustering when dealing with numerous uncertain parameters with low influence on model decisions. However, distribution-driven clustering performs better when only key influential uncertain parameters are present. To our knowledge, this is the first application of decision-based clustering on energy system design optimization, suggesting it can potentially yield better designs with the same number of clusters.