## 1 Introduction  
Throughout the past few decades, massive carbon emissions have caused serious global environmental damage, such as thick haze and worsening greenhouse gas effects. The Intergovernmental Panel on Climate Change (IPCC), which is the international body for the assessment of climate change, has pointed out in its fifth assessment report that it is necessary to curb the global greenhouse gas (GHG) emissions by 40%-70% from the 2010 level before 2050, and to curb the global GHG emissions to the level of near zero by the end of the 21 st century [1]. The IPCC has defined a complete method to standardize the computation of GHG emissions at the national level. Today, most countries are monitoring GHG emissions by using IPCC guidelines to perform annual inventories assessing the quantity of six main gases (CO\({}_{2}\): carbon dioxide, CH\({}_{4}\): methane, N\({}_{2}\)O: nitrous oxide, HFCs: hydrofluorocarbons, PFCs: perfluorocarbon, SF\({}_{6}\): sulfur hexafluoride) [2]. It was found that CO\({}_{2}\) makes up the broad majority of GHG emissions--it represents about three-quarters of total GHG emissions. For instance, in the USA, the emissions from the industry occupies 24% of total emissions. Indeed, GHG emissions from industry primarily come from burning fossil fuels for energy, as well as GHG emissions from certain chemical reactions necessary to produce goods from raw materials [3, 4]. To achieve the IPCC targets,the development of climate change mitigation technologies have played a pivotal role [5]. Therefore, the industrial companies have adopted new technologies and strategies to alleviate climate change impact associated with their activities. For example, to reduce the carbon emissions, several companies are devoted to recuperating and remanufacturing worn products instead of producing new ones. Indeed, carbon emissions from producing new parts is higher than that for remanufactured ones. Nowadays, carbon emission control as well as maintaining sustainable economic development has become an increasing challenge, and many countries have attempted to curb carbon emission compulsively through enacting legislation [6]. Several governments promulgated some carbon emission laws, such as carbon taxes, mandatory carbon emissions capacity, and carbon emission cap and trade [7]. The most known regulations are carbon pricing and emissions trading [8]. Those policies can be classified into two categories: mandatory and non-mandatory. The mandatory policy are strict regulations where governments set a strict emissions cap on a firm for a given period. Non-mandatory policies allow companies to choose between reducing and paying for emissions [9], including carbon tax and emission trade (also known as cap and trade). According to the European Commission, European Union Emission Trading System (EU-ETS) is the first and largest emission trading scheme: 75% of international carbon trading covers more than 11,000 companies in 31 countries. Under this policy, companies are allocated a cap or quota on carbon emissions [10]. Indeed, when a company exceeds the allocated cap, it can purchase extra carbon allowance trough the carbon market trading. Conversely, when its carbon emission is under the cap, it can sell its surplus via trading [11]. Besides, carbon tax is a tax on carbon emissions. Companies under this policy are charged a tax proportional to the amount of carbon emitted [12]. Since the implementation of the Kyoto Protocol in 1997, several countries have enacted a variety of carbon tax schemes that have attracted wide attention in the manufacturing management [13]. According to the International Monetary Fund (IMF), carbon tax is the most effective policy to mitigate carbon emissions. With these environmental regulations, companies are constrained to adopt new production policies in order to curb their carbon emissions. From the beginning of the nineties until today, several published papers in the literature have dealt with production decision, taking into account carbon emissions regulations.