Distributionally Robust Optimization for Chemotherapy Scheduling under Asymmetric and Multi-Modal Uncertainty

TL;DR

This paper addresses chemotherapy template design under uncertainty by proposing a Distributionally Robust Optimization framework that captures multimodal and asymmetric treatment-time distributions through a two-layer ambiguity set. It jointly decides patient-type grouping and group-specific time-slot durations, using a closed-form expression for the inner worst-case cost and exact/heuristic algorithms, including clustering-based approaches, to solve the nonconvex problem. The authors derive dual reformulations, provide meaningful lower/upper bounds linking cost to the span of group means, and validate the approach on synthetic data and Mayo Clinic real data, showing improved robustness and substantial reductions in overrides. The proposed MMA-DRO framework offers a data-driven, robust template design that can reduce idle time, overtime, and overrides in real-world clinical operations, with practical implications for resource utilization and patient care quality.

Abstract

We consider a real-world chemotherapy scheduling template design problem, where we cluster patient types into groups and find a representative time-slot duration for each group to accommodate all patient types assigned to that group, aiming to minimize the total expected idle time and overtime. From Mayo Clinic's real data, most patients' treatment durations are asymmetric (e.g., shorter/longer durations tend to have a longer right/left tail). Motivated by this observation, we consider a distributionally robust optimization (DRO) model under an asymmetric and multi-modal ambiguity set, where the distribution of the random treatment duration is modeled as a mixture of distributions from different patient types. The ambiguity set captures uncertainty in both the mode probabilities, modeled via a variation-distance-based set, and the distributions within each mode, characterized by moment information such as the empirical mean, variance, and semivariance. We reformulate the DRO model as a semi-infinite program, which cannot be solved by off-the-shelf solvers. To overcome this, we derive a closed-form expression for the worst-case expected cost and establish lower and upper bounds that are positively related to the variability of patient types assigned to each group, based on which we develop exact algorithms and highly efficient clustering-based heuristics. The lower and upper bounds on the worst-case cost imply that the optimal cost tends to decrease if we group patient types with similar treatment times. Through numerical experiments based on both synthetic datasets and Mayo Clinic's real data, we illustrate the effectiveness and efficiency of the proposed exact algorithms and heuristics and showcase the benefits of incorporating asymmetric information into the DRO formulation.

Figures (7)

• Figure 1: Mayo Clinic example template
• Figure 2: Histograms of treatment durations across seven patient types (Mayo Clinic's real data).
• Figure 3: A flowchart of the MMA-DRO model, where $\Theta_1,\ \Theta_2,\ \Theta_3$ denote the multimodal asymmetric ambiguity sets of the uncertain chemotherapy durations and $t_1^*,\ t_2^*,\ t_3^*$ denote the optimal time-slot durations for groups 1, 2, 3, respectively.
• Figure 4: A toy example illustration for $L=2$.
• Figure 5: OOS comparisons of MMA-DRO$^{\text{mis}}$ and SAA.

Theorems & Definitions (16)

• Theorem 1: Dual representation of $\Pi_l(t_g)$
• Theorem 2: Dual representation of $\Omega_g(t_g)$
• Theorem 3
• Theorem 4
• Proposition 1
• Corollary 1
• Proposition 2: Lower bound of Problem \ref{['eq:heuristic problem']}
• Proposition 3: Upper bound of Problem \ref{['eq:heuristic problem']}
• proof
• proof