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Mass customization design of engineer-to-order products using Benders’ decomposition and bi-level stochastic programming

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Leveraging product differentiation and mass production efficiency in mass customization basically entails a configure-to-order paradigm. In the engineer-to-order (ETO) business, however, companies build unique products in response to ‘foreseeable’ customer specifications. The key challenge of ETO mass customization lies in the complexity of accommodating future design changes when customers are involved in customizing design specifications. This paper proposes a two-stage, bi-level stochastic programming framework to tackle ETO mass customization. At the first stage, product platform configuration is integrated with production reconfiguration, which is formulated as a shortest path problem with resource constraints (SPPRC) to optimize production delays within the capabilities of the process platform. Benders’ decomposition algorithm is applied to solve this optimal configuration problem owing to its high computational efficiency. The second stage scrutinizes the optimal configuration resulting from the first stage for scaling optimization of design parameters (DPs) for each module. All DPs are differentiated by standard or customizable DPs. A bi-level stochastic program is implemented to leverage conflicting goals between the producer (leader) and consumer (follower) surpluses. As a result, ETO customization design is anchored with optimal values of standard DPs and optimal value ranges of customizable DPs. A case study of ship engine and power generator ETO design is presented, demonstrating the feasibility and potential of the ETO mass customization framework.
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... Most of the earlier studies focused on configuration modeling and solving [10] such as product configuration knowledge [16] and conceptual modeling [17], and product configuration process [18]. For complex ETO products, a two-step strategy including product architecture configuration and module configuration is proposed in [19]. ...
... However, the two articles only describe configuration solution concepts. Kristianto et al. [18] explored the mass-customization problem of ETO products in two stages: integration configuration of the product and process platform, and module parameter value configuration. They solved the problem using Benders decomposition and double-layer stochastic programming. ...
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... They also applied the BLP to find advertising expenditures, optimal equilibrium prices, and production policies. Kristianto et al. [39] presented a two-stage bi-level stochastic model for the mass production problem and considered the manufacturer as the leader and the consumer as the follower in order to model the contradictory objectives between them. They applied the BDA to solve the proposed complex model and obtain an optimum solution. ...
... Third step: Eqs.(38) and(39) are added to the constraints of the original model. ...
... More complex approaches combine the use of the KKT conditions with other techniques. For example, in Kristianto et al. (2013) the stochastic bilevel problem is reduced to a single level using KKT conditions and is then solved using Benders' decomposition. Related approaches include (Saharidis and Ierapetritou 2009), where an algorithm for solving mixed-integer bilevel linear problems based on Benders' decomposition is presented. ...
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... The response to this question could depend on the environment the ETO company operates in. The solution would help understand whether the current order-fulfilment strategy supports the achievement of the desired performance outcome (Haug et al., 2009;Kristianto et al., 2013;Schoenwitz et al., 2017). Hence, in this study, the authors aim to understand the sources of differentiation between the environments that ETO companies can face and how ETO companies react to strategically fit the order-fulfilment strategy in the environment. ...
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... Secondly, the upper objective and the lower objective can form their own optimal values through game theory. e mathematical description of the bi-level programming model is as follows [17]: ...
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