arXiv subjects

Martin Grunow

Publications and source records attributed to Martin Grunow.

3 recordsLinked to original sources

arXiv2026

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

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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arXiv2026

Network Flexibility Design Under Endogenous Uncertainty

Manufacturing firms face uncertainty in both supply and demand. They implement process flexibility, enabling plants to produce multiple products, to hedge against supply--demand mismatches. Assigning more products to a plant results in efficiency losses at the plant, whereas limited flexibility may improve efficiency because of the specialization effect. Furthermore, the flexibility design determines the sourcing locations of products, thereby affecting demand due to the country-of-origin effect and exposure to tariffs. We incorporate these mechanisms into the supply network flexibility design problem by modeling supply and demand uncertainties as endogenous, that is, as functions of the first-stage design decisions. We propose a two-stage stochastic program and solve it via a decomposition scheme that relies on distribution-specific optimality cuts. To avoid exhaustive enumeration of all distributions, we derive distribution-free formulations that are valid for all distributions and for subsets of supply and demand distributions. Through extensive computational experiments, we demonstrate the superior performance of our solution approach and distribution-free formulations relative to exhaustive distribution enumeration and state-of-the-art inequalities, respectively. Moreover, we explain how the problem structure affects the effectiveness of the proposed formulations. From a managerial perspective, we show the trade-offs between endogenous effects and how they affect the optimal flexibility design.

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arXiv2025

On Branch-and-Price for Project Scheduling

Integer programs for resource-constrained project scheduling problems are notoriously hard to solve due to their weak linear relaxations. Several papers have proposed reformulating project scheduling problems via Dantzig-Wolfe decomposition to strengthen their linear relaxation and decompose large problem instances. The reformulation gives rise to a master problem that has a large number of variables. Therefore, the master problem is solved by a column generation procedure embedded in a branching framework, also known as branch-and-price. While branch-and-price has been successfully applied to many problem classes, it turns out to be ineffective for most project scheduling problems. This paper identifies drivers of the ineffectiveness by analyzing the structure of the reformulated problem and the strength of different branching schemes. Our analysis shows that the reformulated problem has an unfavorable structure for column generation: It is highly degenerate, slowing down the convergence of column generation, and for many project scheduling problems, it yields the same or only slightly stronger linear relaxations as classical formulations at the expense of large increases in runtime. Our computational experiments complement our theoretical findings.

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