Improved augmented Lagrangian coordination for optimizing supply chain configuration with multiple sharing elements in industrial cluster

Purpose The purpose of this paper is to study various combination forms of the three basic sharing elements (i.e. orders sharing, manufacturers capacity sharing and suppliers capacity sharing) in the cluster supply chain (CSC), formulate a distributed model to protect enterprises’ decision privacy and seek to develop an effective method for solving the distributed complex model. Design/methodology/approach A distributed assembly cluster supply chain configuration (ACSCC) model is formulated. An improved augmented Lagrangian coordination (ALC) is proposed and used to solve the ACSCC model. A series of experiments are conducted to validate the improved ALC and the model. Findings Two major findings are obtained. First, the market order’s quantity change and the sales price of the product have a great impact on both the optimal results of the ACSCC and the cooperative strategy, especially, when the market order increases sharply, enterprises have to adopt multiple cooperative strategies to complete the order; meanwhile, the lower sales price of the product helps independent suppliers to get more orders. Second, the efficiency and computational accuracy of the improved ALC method are validated as compared to the centralized ALC and Lingo11. Research limitations/implications This paper formulated the single-period ACSCC model under certain assumptions, yet a multi-period ACSCC model is to be developed, a more comprehensive investigation of the relationships among combination forms is to be extended further and a rigid proof of the improved ALC is necessary. Practical implications Enterprises in the industrial cluster should adopt different cooperative strategies in terms of the market order’s quantity change and the sales price of the product. Social implications The proposed various combination forms of sharing elements and the formulated ACSCC model provide guidance to managers in the industrial cluster to choose the proper policy. Originality/value This research studies various combination forms of the three basic sharing elements in the CSC. A distributed ACSCC model has been established considering simultaneously multiple sharing elements. An improved ALC is presented and applied to the ACSCC problem.

Improving the Performance of the Augmented Lagrangian Coordination: Decomposition Variants and Dual Residuals

The augmented Lagrangian coordination (ALC), as an effective coordination method for decomposition-based optimization, offers significant flexibility by providing different variants when solving nonhierarchically decomposed problems. In this paper, these ALC variants are analyzed with respect to the number of levels and multipliers, and the resulting advantages and disadvantages are explored through numerical tests. The efficiency, accuracy, and parallelism of three ALC variants (distributed ALC, centralized ALC, and analytical target cascading (ATC) extended by ALC) are discussed and compared. Furthermore, the dual residual theory for the centralized ALC is extended to the distributed ALC, and a new flexible nonmonotone weight update is proposed and tested. Numerical tests show that the proposed update effectively improves the accuracy and robustness of the distributed ALC on a benchmark engineering test problem.

Dual Residual for Distributed Augmented Lagrangian Coordination Based on Optimality Conditions

Augmented Lagrangian Coordination (ALC) is one of the more popular coordination strategies for decomposition based optimization. It employs the augmented Lagrangian relaxation approach and has shown great improvements in terms of efficiency and solution accuracy when compared to other methods addressing the same type of problem. Additionally, by offering two variants: the centralized ALC in which an artificial master problem in the upper level is created to coordinate all the sub-problems in the lower level, and the distributed ALC in which coordination can be performed directly between sub-problems without a master problem, ALC provides more flexibility than other methods. However, the initial setting and the update strategy of the penalty weights in ALC still significantly affect its performance and thus are worth further research. For centralized ALC, the non-monotone weight update strategy based on the theory of dual residual has shown very good improvements over the traditional monotone update, in which the penalty weights can either increase or decrease. In this paper, we extend the research on the dual residual in centralized ALC to the distributed ALC. Through applying the Karush-Kuhn-Tucker (KKT) optimality conditions to the All-In-One (AIO) and decomposed problems, the necessary conditions for the decomposed solution to be optimal are derived, which leads to the definition of primal and dual residuals in distributed ALC. A new non-monotone weight based on both residuals is then proposed, by which all AIO KKT conditions are guaranteed after decomposition. Numerical tests are conducted on two mathematical problems and one engineering problem and the performances of the new update are compared to those of the traditional update. The results show that our proposed methods improve the process efficiency, accuracy, and robustness for distributed ALC.