## 1 Introduction  
In the new global economy, the concept of a circular economy has become a central issue of international concern. Many studies by researchers and policymakers in recent years have focused on circular economies as possible solutions to pursue the global issue of sustainable development goals. There are multiple definitions of a circular economy. In general terms, a circular economy can be viewed as a closed-loop industrial system that has activities for the reduction, reuse, and recycling of resources for the purpose of developing sustainability. The feedback loops indicate that recycling and recovery are the main concerns in a circular economy [1]. The strategy of a circular economy is to retain services in use for as long as possible in order to gain maximum value from them during use, and then to recover and restore them at the end of any lifetime of service [2]. Remanufacturing is the backbone of the circular economy, which helps in salvaging used products via recovery strategies to extend product life cycles. Such processes start with the acquisition of cores to be remanufactured into new products. The remanufactured products should fulfill a performance that is at least equal to the original products as a representation of customer requirements. The three main activities in any remanufacturing system include core acquisition, remanufacturing operations, and re-marketing. Core acquisition is challenging for remanufacturers as remanufacturing in closed-loop supply chains is characterized by uncertainty for the quality, time, and volume of returns. The term uncertainty is generally understood to mean lack or incompleteness of information, i.e., known only as incompletely or imprecisely. Incompleteness is characterized as a measure of an inexistence of basic source data that should be provided to complete a given business process of remanufacturing. As a result, uncertainty leads to economic (cost and feasibility) and technical (remanufacturability, scheduling, and process planning) risks for remanufacturing companies. Therefore, these uncertainties need to be mitigated to achieve the desired performance. The quality of a product is concerned with the degree to which the requirements are fulfilled by a set of key characteristics. Quality variation of a new material is one of the most significant factors causing non-conformance to the requirements for final product quality in manufacturing systems. The important factor of the incoming core quality in remanufacturing system is comparable to the new material quality in manufacturing system. Quality is an essential criterion for the performance evaluation of used products and is a key driver in remanufacturing decisions. The quality of incoming cores has a significant effect on the remanufacturing cost and cost of quality. Whenever the sorting of incoming cores is possible, it may lead to easy remanufacturing planning for minimizing these costs. If the quality level of incoming cores is better, remanufacturing costs will be low, and any used products can be saved at a value that increases with their level of quality. In order to return the used products into a good functional state, the highest quality cores may need a limited reconditioning process (thus entailing lower process costs), whereas the worst quality cores will need comprehensive processes or part replacements [3]. An example of this can be seen from study carried out by [PERSON] and [PERSON] [4], in which they formulated a model to deal with the issue of upgrading a used part and bringing it to a desired quality level at the end of its life by considering the current quality levels of the parts. The evidence of the important role of quality inspection and sorting also can be seen in the case of the decision-making process for upgrade planning, in which the incoming products are classified into several different quality classes upon arrival, and shortly after they are transferred to the remanufacturing unit [5]. A quantitative study by [PERSON] et al.