Multi-item sustainable green production system under trade-credit and partial backordering

This study develops a green production quantity model with random imperfect quality items, trade-credit policy, service level constraints, and failure in reworking. In practice, not only the green production system but also the rework process is often imperfect. The presence of a single machine in the production system outcomes in limits for green production and partial backordering. It is assumed that the green production system may generate defective items, which are reworked. As a reworked process is also not perfect, it produces a random number of scrapped items. On the other hand, the supplier also offers a trade-credit policy to the buyer, which minimizes the on-hand stock and boosts sales. In fact, this model will help organizations to minimize their costs through cooperation in industry. The objective of this research is to find the optimal green production and backordered quantity of each item such that the projected total cost is minimized. The optimal solution for each scenario is derived and the application of the designed model is validated with two numerical examples. The results for both examples show that the minimum total cost for the green production system is achieved when the permissible delay-period given by the supplier to the buyer is greater than or equal to the aggregated sum of production uptime, reworking time, production downtime, and allowed shortage time. Sensitivity analysis of the proposed study is also done to illustrate the realistic usage.