近年來，技術和科技發展導致工業設備的複雜性增加。由於技術創新迅速，維護成本高，企業擁有設備已非一經濟措施。因此，最常見和最廣泛的解決方案之一是從原始設備製造商(OEM)租賃設備。
在本研究中，我們提出了一個多目標二階規劃模型來解決閉環供應鏈(CLSC)系統下的回收再製造的租賃計劃問題，本系統包括多個產品，在多個時期內具有共用性的零件。根據賽局理論，所提出的租賃模式是以領導者-追隨者之結構建立。領導者模型是整數非線性計劃(INLP)形式的定價模型，目標是確定不同租賃期間租賃產品的最佳租賃價格和最佳數量，以達到最大化租賃收入。追隨者模型是整數線性計劃(ILP)形式的生產計劃模型。目標是在考慮週期性需求和碳稅成本的情況下，在生產能力約束範圍內確定最佳生產計劃以達到最小化生產及碳稅成本。其中跟隨者模型的生產步驟中的成本和數量將影響領導者模型的租賃價格和最佳數量。此模式將以一示例進行說明和驗證。

Due to rapid technological innovation and high maintenance costs, it is no longer economic for a customer to own some products. In particular, a customer may be forced to update the products to raise its quality or requirement. Therefore, one of the most common and widespread solutions is to lease the product from an Original Equipment Manufacturer (OEM). However, the current literature on the cyclical leasing model has not considered the cost of carbon emissions.
In this study, in order to resolve the issues of resource exultation and carbon emission, as well as the uncertainty of reuse quantity and quality, we propose a mathematical model to determine an optimal a leasing strategy under a Closed-Loop Supply Chain (CLSC) system that includes multiple products with component commonality over multiple periods. Based on Game Theory, the leasing model is in the form of a Leader-Follower structure. The leader model is a pricing model in the form of an Integer Nonlinear Program (INLP) and the goal is to determine the best leasing price and the best quantity for the leased product for different leasing periods such that the leasing revenue is maximized. The follower model is a production planning model in the form of an Integer Linear Program (ILP). The goal is to determine the production quantity within production capacity constraints such that the total production cost and the carbon tax costs are minimized. Since the costs and quantities of assembly, disassembly, upgrading and inventory in production steps of the follower model will affect the leasing price and the quantity of the leader model, the Leader-Follower 2-Level Optimization structure is thus funded. Numerical example will be provided for illustration and validation.
The contribution of our research is 1. Developed a Leader-Follower module (bi-level program) to determine the optimal price for leasing. 2.Within production capacity constraints, taking into account cyclical demand and carbon emissions cost for optimal production planning.

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