A two-stage and bi-level stochastic programming for customer involvement in engineer-to-order product design decision

AbstractThe paper studies what kind of support could be applied to the management of partly configurable modular systems. The main tasks of product management, product portfolio management and product variety management are defined. In addition, a partly configurable product structure and modular system are defined. Because the limited support in the literature for managing partly configurable modular systems, the article reviews previous product development cases in which authors have been involved on lessons learnt basis, i.e., if the methods and tools used in the cases could provide support for the research objective. As a result, the existing definition of the modular system should be extended by the concepts of non-module and design decision sequence description when dealing with partly configurable modular systems. This is because engineer-to-order should be made possible in cases where it brings clear added value to the customer compared to completely pre-defined solutions that may limit the customer's interest in the offering. Tools to assess the impact of changes to the product offering are required. These should be taken into account in frameworks that are used in method and tool development.

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A column-and-constraint generation algorithm for two-stage stochastic programming problems

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10.1007/s11750-021-00593-2 ◽

2021 ◽

Author(s):

Denise D. Tönissen ◽

Joachim J. Arts ◽

Zuo-Jun Max Shen

Keyword(s):

Stochastic Programming ◽

Benders Decomposition ◽

Equivalent Model ◽

Computational Time ◽

Two Stage ◽

Generation Algorithm ◽

Constraint Generation ◽

Deterministic Equivalent ◽

Location Routing ◽

Relative Tolerance

AbstractThis paper presents a column-and-constraint generation algorithm for two-stage stochastic programming problems. A distinctive feature of the algorithm is that it does not assume fixed recourse and as a consequence the values and dimensions of the recourse matrix can be uncertain. The proposed algorithm contains multi-cut (partial) Benders decomposition and the deterministic equivalent model as special cases and can be used to trade-off computational speed and memory requirements. The algorithm outperforms multi-cut (partial) Benders decomposition in computational time and the deterministic equivalent model in memory requirements for a maintenance location routing problem. In addition, for instances with a large number of scenarios, the algorithm outperforms the deterministic equivalent model in both computational time and memory requirements. Furthermore, we present an adaptive relative tolerance for instances for which the solution time of the master problem is the bottleneck and the slave problems can be solved relatively efficiently. The adaptive relative tolerance is large in early iterations and converges to zero for the final iteration(s) of the algorithm. The combination of this relative adaptive tolerance with the proposed algorithm decreases the computational time of our instances even further.

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