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Optimizing Flexibility and Commitments: Partially-Adaptive Multi-Stage Matrix Assembly Layout Design Problem

Baturhan Bayraktar, Merve Bodur, Martin Grunow, Rainer Kolisch · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.27401 · cited by 0 works (OpenAlex) · open-access PDF

Spanish

El diseño periódico aprovecha esta flexibilidad, pero los modelos existentes solo permiten revisiones anuales. Los calendarios más finos exponen un intercambio de compromiso de flexibilidad: el diseño avanzado apoya la coordinación de compromisos de diseño, los acuerdos de proveedores y los descuentos a través de estaciones de producción reconfigurables localmente. Introducimos el problema de tiempo de revisión de diseño, eligiendo conjuntamente los puntos de revisión y las secuencias de diseño comprometidas bajo la incertidumbre de la demanda, mientras que la producción se adapta dentro de esos diseños. Lo formulamos como un programa estocástico multistage parcialmente adaptativo con dos compromisos de diseño complementarios. Nuestra extensión basada en costes coloca el valor económico del compromiso de revisión en el objetivo en lugar de prescribir presupuestos de revisión; nuestra extensión

Machine translation (Meta M2M100); the English original follows.

Abstract

Matrix assembly layouts provide manufacturing flexibility under product variety and demand volatility through locally reconfigurable production stations. Periodic redesign exploits this flexibility, yet existing models allow only annual revisions. Finer calendars expose a flexibility-commitment trade-off: advance layout commitments support coordination, supplier agreements, and discounts. We introduce the layout revision timing problem, jointly choosing revision points and committed layout sequences under demand uncertainty while production adapts within those layouts. We formulate it as a partially adaptive multistage stochastic program with two complementary extensions. Our cost-based extension places the economic value of advance commitment in the objective rather than prescribing revision budgets; our scenario-adaptive extension adapts revision timing to revealed information. For station-use minimization, we establish a cost decomposition across commitment intervals, yielding an exact dynamic program that reuses station subproblem solutions across model variants and parameter settings. As a more general alternative, we develop an integer L-shaped method strengthened by monotonicity-based cuts for budgeted formulations and enhanced cuts exploiting this decomposition. On automotive instances, including scenario trees with nearly 10,000 nodes, our combined model's average savings in expected station-use cost at the base-case discount reach 4.99% versus full adaptivity and 28.65% versus full commitment. Scenario adaptivity is most valuable when demand paths diverge and discounts justify commitment on some paths but not others, as in electrification-driven scenarios.

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Topics: Flexibility (engineering), Mathematical optimization, Computer science, Benders' decomposition, Production (economics), Exploit

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