Rescheduling after vehicle failures in the multi-depot rural postman problem with rechargeable and reusable vehicles

We present a centralized auction algorithm to solve the Multi-Depot Rural Postman Problem with Rechargeable and Reusable Vehicles (MD-RPP-RRV), focusing on rescheduling arc routing after vehicle failures. The problem involves finding heuristically obtained best feasible routes for multiple rechargeable and reusable vehicles with capacity constraints capable of performing multiple trips from multiple depots, with the possibility of vehicle failures. Our algorithm auctions the failed trips to active (non-failed) vehicles through local auctioning, modifying initial routes to handle dynamic vehicle failures efficiently. When a failure occurs, the algorithm searches for the best active vehicle to perform the failed trip and inserts the trip into that vehicle's route, which avoids a complete rescheduling and reduces the computational effort. We compare the algorithm's solutions against offline optimal solutions obtained from solving a Mixed Integer Linear Programming (MILP) formulation using the Gurobi solver; this formulation assumes that perfect information about the vehicle failures and failure times is given. The results demonstrate that the centralized auction algorithm produces solutions that are, in some cases, near optimal; moreover, the execution time for the proposed approach is much more consistent and is, for some instances, orders of magnitude less than the execution time of the Gurobi solver. The theoretical analysis provides an upper bound for the competitive ratio and computational complexity of our algorithm, offering a formal performance guarantee in dynamic failure scenarios.

Lookahead and Hybrid Sample Allocation Procedures for Multiple Attribute Selection Decisions

Attributes provide critical information about the alternatives that a decision-maker is considering. When their magnitudes are uncertain, the decision-maker may be unsure about which alternative is truly the best, so measuring the attributes may help the decision-maker make a better decision. This paper considers settings in which each measurement yields one sample of one attribute for one alternative. When given a fixed number of samples to collect, the decision-maker must determine which samples to obtain, make the measurements, update prior beliefs about the attribute magnitudes, and then select an alternative. This paper presents the sample allocation problem for multiple attribute selection decisions and proposes two sequential, lookahead procedures for the case in which discrete distributions are used to model the uncertain attribute magnitudes. The two procedures are similar but reflect different quality measures (and loss functions), which motivate different decision rules: (1) select the alternative with the greatest expected utility and (2) select the alternative that is most likely to be the truly best alternative. We conducted a simulation study to evaluate the performance of the sequential procedures and hybrid procedures that first allocate some samples using a uniform allocation procedure and then use the sequential, lookahead procedure. The results indicate that the hybrid procedures are effective; allocating many (but not all) of the initial samples with the uniform allocation procedure not only reduces overall computational effort but also selects alternatives that have lower average opportunity cost and are more often truly best.