Carbon emissions effect on vendor-managed inventory system considering displaced re-start-up production time

Background: The classical mathematical formulation of the vendor-managed inventory (VMI) model assumes an infinite planning horizon, and consequently, the solution derived ignored the impact of the first cycle. The classical formulation is associated with another implicit assumption that input parameters remain static indefinitely. Methods: This paper develops two mathematical models for VMI for a joint economic lot-sizing (JELS) policy. Each model considers investment in green production, energy used for keeping items in storage, and carbon emissions from production, storage, and transportation activities under the carbon cap-and-trade policy. The first model underlies the first cycle, while the second underlies subsequent cycles. Results: The re-start-up production time for subsequent cycles commences only at the time required to produce and replenish the first lot, which implies further cost reduction. Mathematical formulations are perceived as important both for academics and practitioners. For example, the base model of the first cycle (subsequent cycles) generates an optimal produced quantity with 18.42% (4.35%) less total system cost when compared with the pest scenario in favor of the existing literature. Moreover, such a percentage of total system cost reduction increases as the production rate increases. Further, the proposed models not only produce better results but also offer the opportunity to adjust the input parameters for subsequent cycles, where each cycle is independent from the previous one. Conclusions: The emissions generated by the system are very much related to the demand rate and the amount of investment in green production. Illustrative examples, special cases, model overview, and managerial insights are given. The discussion related to the contribution of the proposed model, the concluding remarks, and further research are also provided. The proposed model rectifies the base model adopted by the existing literature, which can be further extended to be implemented in several interesting further inquiries related to JELS inventory mathematical modeling.