An integrated reliable five-level closed-loop supply chain with multi-stage products under quality control and green policies: generalised outer approximation with exact penalty

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Abstract
In this paper, we design and optimise an integrated five-level Supply Chain (SC), which contains a supplier, a producer, a wholesaler, multiple retailers, and a collector. Accordingly, a Closed-loop Supply Chain (CLSC) with multi-stage products is designed with respect to the green production principles and Quality Control (QC) policy under back-logged and lost sale types of the shortage. Levels cooperate with each other to make an Integrated Supply Chain (ISC) so that the total cost function is minimised and the total reliability function is maximised, simultaneously. The model is constrained by real stochastic constraints. The total inventory cost includes the ordering costs, holding costs, shortage costs, setup costs, production costs, screening costs, reworking costs, disposal costs, tax cost of GHG emissions, collection costs, and disassembling costs. The final objective is to optimise the number and volume of the stockpiles of the products. The integrated CLSC model is a hyper-scale Mixed Integer Nonlinear Programming (MINLP) model. In this regards, a Generalised Outer Approximation with Exact Penalty (GOA/EP) is presented to optimise the MINLP model of research based on decomposition principles, Outer Approximation (OA), and relaxation techniques. Numerical analyses revealed the excellent performance of the presented method for solving the hyper-scale MINLPs.

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