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This paper investigates a variant of the dial-a-ride problem (DARP), namelyRisk-aware DARP (RDARP). Our RDARP extends the DARP by (1) minimizing aweighted sum of travel cost and disease-transmission risk exposure for onboardpassengers and (2) introducing a maximum cumulative exposure risk constraintfor each vehicle to ensure a trip with lower external exposure. Both extensionsrequire that the risk exposure of each onboard passenger is propagated in aminimized fashion while satisfying other existing constraints of the DARP. Tofully describe the RDARP, we first provide a three-index arc-based formulationand reformulate the RDARP into an equivalent min-max trip-based formulation,which is solved by an exact Branch-Cut-and-Price (BCP) algorithm. For each nodein the branching tree, we adopt the column generation method by decomposing theproblem into a master problem and a subproblem. The latter takes the form of anelementary shortest path problem with resource constraints and minimizedmaximum risk (ESPPRCMMR). To solve the ESPPRCMMR efficiently, we develop a newlabeling algorithm and establish families of resource extension functions incompliance with the risk-related resources. We adopt a real-world paratransittrip dataset to generate the RDARP instances ranging from 17 to 55heterogeneous passengers with 3 to 13 vehicles during the morning and afternoonperiods. Computational results show that our BCP algorithm can optimally solveall small- and medium-sized instances (32 or fewer passengers) within 5minutes. For the large instances (39 to 55 passengers), our BCP algorithm cansolve 23 of 30 instances optimally within a time limit of one hour.

A branch-cut-and-price algorithm for a dial-a-ride problem with minimum disease-transmission risk