Mixed-integer programming models and heuristic algorithms for the maximum value dynamic network flow scheduling problem

• Published in: Computers & operations research Vol. 175; p. 106897
• Main Authors: Nixon, Tanner, Curry, Robert M., Allaissem B., Phanuel
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.2025
• Subjects: Heuristic methods; Mixed-integer programming; Network flow optimization; Network flow optimization; Mixed-integer programming; Heuristic methods
• ISSN: 0305-0548
• DOI: 10.1016/j.cor.2024.106897

Various applications in contested logistics and infrastructure restoration require dynamic flow solutions characterized by a schedule of network flows consecutively transmitted over a sequence of successive periods. For these schedules, we assume flows transmit via arcs during periods while flows reside at nodes from one period to the next. Within this context, we introduce the Maximum Value Dynamic Network Flow Problem (MVDFP) in which we seek to maximize the cumulative value of a non-simultaneous network flow schedule that accumulates node value whenever some minimum amount of flow resides at a node between periods. For solving the MVDFP, we first introduce a large mixed-integer program (MIP). As this MIP can become computationally-expensive for large networks, we present a trio of computationally-effective, easy to implement heuristic approaches that solve a series of smaller, more manageable MIPs. These heuristic approaches typically determine high-quality solutions significantly faster than the MIP obtains an optimal solution by dividing the full network flow schedule into a sequence of consecutive shorter network flow subschedules. In many cases, at least one of our heuristic approaches produces an optimal solution in a fraction of the MIP’s computational time. We present extensive computational results to highlight our heuristics’ efficacy, discuss for what instances each approach may be most applicable, and detail future research avenues. •Introduced a novel dynamic network flow optimization problem to the literature having applications in contested logistics and infrastructure restoration.•Developed a mixed-integer programming (MIP) model solution method.•Developed three novel heuristic approaches as computationally effective and easy to implement alternatives to the mixed-integer programming model.•Heuristic approaches typically determine high-quality solutions significantly faster than the MIP obtains an optimal solution.•In many cases, at least one heuristic approach produces an optimal solution in a fraction of the MIP’s computational time.