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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

Indonesian

Reka bentuk ulang berjangka memanfaatkan fleksibilitas ini, namun model yang ada hanya memungkinkan revisi tahunan. Kalender yang lebih halus mengungkapkan kompromi fleksibilitas-komitmen: promosi promosi komitmen koordinasi multistage stochastic dengan dua ekstensi tambahan, perjanjian pemasok berbasis biaya, dan diskon. Kami memperkenalkan masalah waktu revisi tata letak, bersama-sama memilih poin revisi dan berkomitmen urutan tata letak di bawah ketidakpastian permintaan sementara produksi beradaptasi dalam tata letak tersebut. Kami merumuskan itu sebagai program adaptif multistage stochastic yang beradaptasi dengan dua ekstensi tambahan. Pada perpanjangan berbasis biaya kami menempatkan nilai ekonomi dari komitmen promosi di objektif daripada meresepkan anggaran revisi; skenario-adaptasi penuh kami memperpanjang revisi waktu untuk

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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