In this study, a mathematical inventory model for a supply chain system made up of a vendor and a buyer under stochastic demand is formulated. The vendor serves as a manufacturer who produces items, while the buyer serves as a retailer who buys the items from the vendor and sells them to end customers. In addition to utilizing regular production as a production base, the vendor also uses green production. Green production adopts green technology, which comprises environmentally friendly inventions that are used to reduce emissions. Green production is more costly than regular production, but it generates lower emissions. The production rate is adjustable, which enables decision makers to control the emissions and production cost. The objective of this study is to find the optimal production allocation, ordering quantity, shipment frequency, safety factor, and production rate such that the joint total cost is minimized. An algorithm is suggested to solve the mathematical problems and its application is validated with a numerical example. The results show that the changes in the emissions, carbon tax, and production cost parameters exhibit significant effects in determining the optimal production allocation. Furthermore, by controlling the production rate flexibly, the supply chain can lessen the emissions released during production and maintain the total cost. Finally, a sensitivity analysis is carried out to explain the usage of the proposed model.

Original languageEnglish
Pages (from-to)840-868
Number of pages29
JournalApplied Mathematical Modelling
Publication statusPublished - Aug 2022


  • Carbon emissions
  • Green production
  • Hybrid production
  • Stochastic demand
  • Supply chain


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