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This paper develops a mathematical model for supply chain inventory system of a manufacturer and a retailer under stochastic demand and carbon reduction policy. The objective of the model is to obtain the decisions regarding inventory management in supply chain system by minimizing the joint total cost. The model contributes to the current stochastic joint lot-sizing literature by allowing the investigation of the impact of carbon cap policy to inventory decisions. The carbon mainly emitted from several activities in the supply chain system, including the production, transportation and storage activities. The regulator, for example the government, uses a carbon cap policy to restrict the amount of emissions generated from the system. As we use strict carbon cap, the carbon emissions generated from the system must not exceed the carbon emission level set by regulator. A list of procedure is proposed to obtain the optimal solutions, which are ordering lot, safety factor, number of shipments and production rate. A numerical instance is provided to show the applicability of the model and to explore the impact of different levels of carbon cap on inventory decisions.

Lot-Sizing Decisions in Manufacturer-Retailer Inventory System under Carbon Emissions Reduction