The implementation of scrap recovery activities has been shown to improve the financial performance of many firms, and this kind of circular economy (CE) is particularly evident in industries with green manufacturing (GM). In this paper, we consider an imperfect multiple-stage production system that manufactures paired products made from mixed materials containing scrap returns, in which the scrap returns are converted from defective products. The feed rates of scrap returns for two products are different, and the product with the higher feed rate is placed in the second order of the process to avoid unlimited accumulation of scrap returns. The proposed problem is formulated as a joint economic order quantity (EOQ) and economic production quantity (EPQ) model aimed at cost minimization. The decision variables of the proposed model include the production run time of two products, order quantity of new material, and the extent of investment in converted equipment. We also prove that the optimal solution exists uniquely and provide an algorithm for the computation of the optimal solution. Finally, a numerical example involving the pulp and paper manufacturing industry is provided to illustrate the solution process, and the results of its sensitivity analysis are also presented to show some managerial implications.

To protect our environment, current firms are committed to the circular economy and process maintenance strategies to reduce the waste of resources. In this way, they can also save costs and create an enterprise image and value. Therefore, this study explores an imperfect production system with a circular economy and process maintenance activities, wherein the defective products can be converted into scrap returns (i.e., secondary raw materials) and products can be manufactured using mixed materials containing scrap returns. The proposed system considers multiple products with varying feed rates of scrap returns. According to the scenario of the aforementioned production system, this paper develops a production–inventory model aimed at cost minimization, in which the production run time, purchased quantity of material, number of maintenance times, and recovery rate are decision variables. Furthermore, we also develop a computational algorithm to obtain these optimal solutions efficiently. Finally, the numerical and sensitivity analyses based on a practical case are presented to illustrate the applicability of our method and some managerial implications. For example, both strategies efficiently reduce the total cost per unit time in the proposed numerical example. The sensitivity results can be used to determine the optimal combination of two strategies and the execution moment under various changes in cost parameters.

The achievable capacity index (ACI) is a simple and efficient approach for estimating the profitability of newsboy-type products, wherein profitability is defined as the probability of achieving the target profit by optimizing the order quantity. At present, the ACI is applicable to single retail stores (i.e., single demand) but not to multiple sales channels (i.e., multiple demand). This paper presents an integrated achievable capacity index (IACI) by which to measure the aggregate profitability of multiple mutually independent channels under normally distributed demand. An unbiased IACI estimator is also developed, to which is applied the Taylor expansion to approximate its sampling distribution, wherein the sizes, means, and variances of demand differ in each channel. Furthermore, overestimates due to sampling error are avoided by deriving the lower confidence bound for the IACI. This paper also provides generic tables to aid managers seeking conservative estimates of profitability. The applicability of the proposed scheme is demonstrated numerically using a real-world example involving an own-branding-and-manufacturing (OBM) enterprise with multiple owned channels.