DC programming and DCA for supply chain and production management: state-of-the-art models and methods

It is undoubtedly that mathematical modelling and optimisation play a key role in the supply chain and the production management (SCPM). In this paper, we provide a survey on DC (Difference of Convex function) programming and DCA (DC Algorithm), a state-of-the-art optimisation approach for challenging problems in SCPM. DC programming and DCA constitute the backbone of non-convex programming and global optimisation. Whilst DC programming and DCA were widely and successfully investigated in many areas, it seems that they were not so much popular in the community of SCPM. There is therefore a need to further develop this efficient and scalable approach for SCPM applications, especially for large-scale problems in the context of Big data. For such purpose, this paper aims to present benchmark models and state-of-the-art DCA-based methods for solving challenging problems in SCPM systems. We prove that all the benchmark classes of optimisation models appeared in SCPM systems can be formulated/reformulated as a DC program and show how to solve these classes of problems by DCA-based algorithms. We offer the community of researchers in SCPM efficient algorithms in a unified DC programming framework to tackle various applications such as supply chain design, scheduling, multi-stage production/inventory system, vehicle routing, …