Fault-Tolerant Families of Production Plans: Mathematical Model, Computational Complexity, and Branch-and-Bound Algorithms

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...

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Veröffentlicht in:Computational mathematics and mathematical physics Jg. 64; H. 6; S. 1193 - 1210
Hauptverfasser: Ogorodnikov, Yu. Yu, Rudakov, R. A., Khachai, D. M., Khachai, M. Yu
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Moscow Pleiades Publishing 01.06.2024
Springer Nature B.V
Schlagworte:
Adaptive search techniques
Algorithms
Branch and bound methods
Computational Mathematics and Numerical Analysis
Costs
Fault tolerance
Integer programming
Libraries
Linear programming
Mathematics
Mathematics and Statistics
Mixed integer
Optimal Control
Stochastic models
Supply chains
Transportation networks
Traveling salesman problem
MILP-model
reliable production process design problem
branch-and-bound method
adaptive large neighborhood search heuristic
ISSN:0965-5425, 1555-6662
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Zusammenfassung: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.
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ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542524700441