A series-parallel inventory-redundancy green allocation system using a max-min approach via the interior point method

The purpose of this study is to develop a novel and practical series-parallel inventory-redundancy allocation system in a green supply chain including a single manufacturer and multiple retailers operating in several positions without any conflict of interests. The manufacturer first produces multi-product and then dispatches them to the retailers at different wholesale prices based on a common replenishment cycle policy. In contrast, the retailers sell the purchased products to customers at different retail prices. In this way, the manufacturer encounters a redundancy allocation problem (RAP), in which the solution subsequently enhances system production reliability. Furthermore, to emphasize on global warming and human health concerns, this paper pays attention both the tax cost of industrial greenhouse gas (GHG) emissions of all produced products and the limitation for total GHG emissions.

The manufacturer intends not only to maximize the total net profit but also to minimize the mean time to failure of his production system using a RAP. To achieve these objectives, the max-min approach associated with the solution method known as the interior point method is utilized to maximize the minimum (the worst) value of the objective functions. Finally, numerical experiments are presented to further demonstrate the applicability of the proposed methodology. Sensitivity analysis on the green supply chain approach is also performed to obtain more insight.

The computational results showed that increasing the number of products and retailers might lead into a substantial increase in the total net profit. This indicated that the manufacturer would feel adding a new retailer to the green supply chain strongly. Moreover, an increase in the number of machines provides significant improvement in the reliability of the production system. Furthermore, the results of the performed sensitivity analysis on the green approach indicated that increasing the number of machines has a substantial impact on both the total net profit and the total tax cost. In addition, not only the proposed green supply chain was more efficient than the supply chain without green but also the proposed green supply chain was very sensitive to the tax cost of GHG emission rather than the number of machines.

In summary, the motivations are as follows: the development of a bi-objective series-parallel inventory-RAP in a green supply chain; proposing a hybrid inventory-RAP; and considering the interior point solution method. The novel method comes from both theoretical and experimental techniques. The paper also has industrial applications. The advantage of using the proposed approach is to generate additional opportunities and cost effectiveness for businesses and companies that operate utilizing the green supply chain under an inventory model.