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The design of fault-tolerant production and delivery systems is one of the priority areas in modern operations research. The traditional approach to modeling such systems is based on the use of stochastic models that describe the choice of a possible scenario of actions in the event of problems in a production or transportation network. Along with a number of advantages, this approach has a known drawback. The occurrence of problems of an unknown nature that can jeopardize the performance of the entire simulated system significantly complicates its use. This paper introduces the minimax problem of constructing fault-tolerant production plans (reliable production process design problem, RPPDP), the purpose of which is to ensure the uninterrupted operation of a distributed production system with minimal guaranteed cost. It is shown that the RPPDP is NP-hard in the strong sense and remains intractable under quite specific conditions. To find exact and approximate solutions with accuracy guarantees for this problem, branch-and-bound methods are developed based on the proposed compact model of the mixed integer linear program (MILP) and novel heuristic of adaptive search in large neighborhoods (adaptive large neighborhood search, ALNS) as part of extensions of the well-known Gurobi MIP solver. The high performance and complementarity of the proposed algorithms is confirmed by the results of numerical experiments carried out on a public library of benchmarking instances developed by the authors based on instances from the PCGTSPLIB library. [ABSTRACT FROM AUTHOR]

In this paper, the first fixed-ratio approximation algorithms are proposed for a series of asymmetric settings of well-known combinatorial routing problems. Among them are the Steiner cycle problem, the prize-collecting traveling salesman problem, the minimum cost cycle cover problem by a bounded number of cycles, etc. Almost all of the proposed algorithms rely on original reductions of the considered problems to auxiliary instances of the asymmetric traveling salesman problem and employ the breakthrough approximation results for this problem obtained recently by O. Svensson, J. Tarnawski, L. Végh, V. Traub, and J. Vygen. On the other hand, approximation of the cycle cover problem was proved by applying a deeper extension of their approach. [ABSTRACT FROM AUTHOR]

The capacitated vehicle routing problem (CVRP) is a classical combinatorial optimization problem having a wide range of practically important applications in operations research. As most combinatorial problems, CVRP is strongly NP-hard (even on the Euclidean plane). A metric instance of CVRP is APX-complete, so it cannot be approximated to arbitrary prescribed accuracy in the class of polynomial time algorithms (assuming that ). Nevertheless, in the case of finite-dimensional Euclidean spaces, a quasi-polynomial or even polynomial time approximation scheme can be found for the problem by applying an approach based on works by S. Arora, A. Das, and C. Mathieu. Below, this approach has been extended for the first time to a significantly larger class of metric spaces of fixed doubling dimension. It is shown that CVRP formulated in such a space has a quasi-polynomial time approximation scheme whenever the number of routes in its optimal solution is bounded above by a polynomial in the logarithm of the input size. [ABSTRACT FROM AUTHOR]

In this paper, for the first time, we provide a quasi-polynomial time approximation scheme for the well-known capacitated vehicle routing problem formulated in metric spaces of an arbitrary fixed doubling dimension. [ABSTRACT FROM AUTHOR]

The capacitated vehicle routing problem with time windows (CVRPTW) is a well-known NP-hard combinatorial optimization problem. We present a further development of the approach first proposed by M. Haimovich and A. H. G. Rinnooy Kan and propose an algorithm that, for an arbitrary ε > 0, finds a (1 + ε)-approximate solution for the Euclidean CVRPTW in , where q is an upper bound for the capacities of the vehicles, p is the number of time windows, and TIME(TSP, ρ, n) is the complexity of finding a ρ-approximation solution of an auxiliary instance of the Euclidean TSP. Thus, the algorithm is a polynomial-time approximation scheme for the CVRPTW with p3q4 = O(log n) and an efficient polynomial-time approximation scheme for arbitrary fixed values of p and q. [ABSTRACT FROM AUTHOR]