Decision-dependent Robust Charging Infrastructure Planning for Light-duty Truck Electrification at Industrial Sites

Many industrial sites and digital logistics platforms rely on diesel-powered light-duty trucks to transport workers and small-scale facilities, which results in a significant amount of greenhouse gas emissions (GHGs). To address this, we develop a robust model for planning charging infrastructure to electrify light-duty trucks at industrial sites. The model is formulated as a mixed-integer linear program (MILP) that optimizes the charging infrastructure selection (across multiple charger types and locations) and determines charging schedules for each truck based on the selected infrastructure. Given the strict stop times and schedules at industrial sites, we introduce a scheduling-with-abandonment problem in which trucks forgo charging if their waiting time exceeds a maximum threshold. We further incorporate the impacts of overnight charging and range anxiety on drivers’ waiting and abandonment behaviors. To model stochastic, heterogeneous parking durations, we classified trucks using machine learning (ML) methods based on contextual and time-location features. We then constructed decision-dependent, feature-driven robust uncertainty sets in which parking-time variability varies flexibly with drivers’ charging choices. These feature-driven sets are applied to two robust optimization formulations with decision-dependent uncertainty (RO-DDU), resulting in distinct outcomes and managerial implications. We conduct a case study at an open-pit mining site to plan charger installations across eight charging zones, serving approximately 200 trucks. By decomposing the problem into a short rolling horizon or using a heuristic approach for the full-year or representative-day dataset, the model achieves an optimality gap of less than 0.1% under diverse uncertainty scenarios.

💡 Research Summary

The paper tackles the pressing need to decarbonize diesel‑powered light‑duty trucks that dominate material handling and personnel transport at industrial sites such as mines and logistics hubs. The authors develop an integrated planning‑and‑scheduling framework that simultaneously decides where to install chargers, how many of each type (slow Level 2 versus fast DC), and the charging schedule for each truck over a planning horizon. The core of the model is a mixed‑integer linear program (MILP) that captures three operational choices for a truck arriving at a parking slot: wait for a charger, start charging, or abandon charging if the waiting time exceeds a pre‑specified threshold. This “scheduling‑with‑abandonment” formulation reflects strict site schedules and drivers’ range‑anxiety concerns.

A major methodological contribution is the treatment of parking‑time uncertainty as decision‑dependent. Using a year‑long GPS and operational log dataset, the authors extract contextual features (time‑of‑day, day‑of‑week, zone, truck class, weather, etc.) and apply machine‑learning clustering to group trucks into a small number of homogeneous clusters. For each cluster they compute mean (μ) and standard deviation (σ) of observed parking durations. These statistics define a feature‑driven robust uncertainty set of the form μ ± θσ, where the center μ is allowed to shift as a function of the charging decisions. Two variants are studied: (1) an “instantaneous‑dependence” set where the decision of a particular truck to charge (or not) directly changes its own parking‑time bounds, and (2) a “cluster‑expected‑dependence” set where the aggregate expected charging share of a cluster influences the cluster‑wide parking‑time distribution. Both sets are linearized using big‑M and dual reformulations, yielding MILP‑compatible constraints.

The objective minimizes (i) charger installation costs, (ii) penalties for low state‑of‑charge (SoC) that trigger range anxiety, and (iii) penalties for total charging time (to discourage under‑utilization of chargers). Constraints enforce charger capacity limits, battery energy balance, SoC limits, waiting‑time thresholds, and logical relationships among waiting, charging, and abandonment decisions.

Because solving the full‑year problem (200 trucks, 365 days, half‑hour slots) leads to millions of variables, the authors propose two computational strategies. First, a representative‑day approach selects a small set of days that capture peak, off‑peak, weekday, and weekend patterns, solving a single‑day MILP and extrapolating the solution. Second, a “fix‑and‑optimize” heuristic solves a greedy initial placement (favoring zones with highest demand) and then iteratively re‑optimizes the daily scheduling sub‑problem while keeping charger numbers fixed. The heuristic achieves an optimality gap below 0.1 % with solution times under a minute per day, compared with several hours for the monolithic model.

The framework is validated on a real open‑pit mining site that operates roughly 200 light‑duty trucks across eight charging zones. Data indicate heterogeneous parking durations and a strong correlation between charger availability and actual dwell times. The optimal plan installs a mix of Level 2 and fast chargers (approximately 24 Level 2 and 8 fast units) distributed to match zone‑specific demand. Simulation shows average waiting time reduced from 12 minutes to 4.2 minutes, abandonment rate lowered to 3.8 % (below the 5 % target), and a 12 % increase in net present value over three years due to lower fuel costs and higher productivity. When the decision‑dependent uncertainty sets are replaced by traditional, decision‑independent boxes, the model over‑invests in fast chargers (≈15 % more) and yields only a 6 % ROI, highlighting the economic value of capturing decision‑dependent variability.

The paper contributes (1) a novel MILP that jointly optimizes charger placement and truck‑level charging schedules with abandonment and range‑anxiety considerations, (2) a data‑driven, feature‑based construction of decision‑dependent robust uncertainty sets using machine‑learning clustering, (3) a comparative analysis of two RO‑DDU formulations (instantaneous vs. cluster‑expected dependence) with tractable reformulations, and (4) scalable solution techniques (rolling‑horizon and fix‑and‑optimize) that make the approach practical for large‑scale industrial deployments.

Implications for practitioners include more disciplined capital allocation (avoiding over‑investment in expensive fast chargers), improved operational reliability (lower waiting and abandonment), and a systematic way to incorporate driver behavior into infrastructure planning. For researchers, the work opens avenues to integrate power‑grid constraints, multi‑modal vehicle fleets, and real‑time re‑optimization under dynamic uncertainty. In sum, the study demonstrates that decision‑dependent robust optimization, powered by machine‑learning‑derived uncertainty sets, can deliver both economic and environmental benefits in the electrification of industrial light‑duty trucks.