A Multi-Item Replenishment Problem with Carbon Cap-and-Trade under Uncertainty

Recently, as global warming has become a major issue, many companies have increased their efforts to control carbon emissions in green supply chain management (GSCM) activities. This paper deals with the multi-item replenishment problem in GSCM, from both economic and environmental perspectives. A single buyer orders multiple items from a single supplier, and simultaneously considers carbon cap-and-trade under limited storage capacity and limited budget. In this case we can apply a can-order policy, which is a well-known multi-item replenishment policy. Depending on the market characteristics, we develop two mixed-integer programming (MIP) models based on the can-order policy. The deterministic model considers a monopoly market in which a company fully knows the market information, such that both storage capacity and budget are already determined. In contrast, the fuzzy model considers a competitive or a new market, in which case both of those resources are considered as fuzzy numbers. We performed numerical experiments to validate and assess the efficiency of the developed models. The results of the experiments showed that the proposed can-order policy performed far better than the traditional can-order policy in GSCM. In addition, we verified that the fuzzy model can cope with uncertainties better than the deterministic model in terms of total expected costs.