Investigating carbon emissions in a production-inventory model under imperfect production, inspection errors and service-level constraint

This paper discusses an integrated inventory model for vendor-buyer system with stochastic demand and service-level constraint. The buyer's demand follows a normal distribution and the lead time depends upon lot size. The buyer uses a periodic review policy to manage the inventory level. An imperfect production processes and inspection errors are considered in the model. Carbon emissions and energy impacts which are generated from transportation activity and production activity are also included in the model. An incentive and penalty policy are adopted to reduce the carbon emissions generated from supply chain system. The model contributes to the current literature by allowing the inclusion of imperfect production, inspection errors, carbon emissions and setup cost reduction. The objective of the model is to determine the review period, setup cost and the number of deliveries so that the total cost incurred has the minimum value. An iterative procedure is suggested to solve the model. A numerical example and sensitivity analysis are performed to illustrate the application of the model and to show the impact of the changes of key parameters on model behaviour.