Abstract: With the establishment and development of China's emissions trading market, the reduction of carbon emissions intensity has become a medium and long term mandatory target in companies' production operations management. A dynamic lot sizing model is proposed to investigate the optimal production, emissions trading and abatement investment decisions of a manufacturer under cap-and-trade. At the beginning of the planning horizon, the manufacturer determines the optimal abatement investment decisions, including the timing of investment in an abatement technology and the optimal abatement capacity. In each period, the manufacturer decides the optimal emission abatement size according to the production planning. It is assumed that the abatement technology can reduce both carbon emissions and energy consumption in the production process. Based on the generalized Benders decomposition approach, the dynamic model is analyzed and some properties of the optimal solution are derived. Numerical experiments are conducted to examine the effects of emission cap and emission allowance price on the manufacturer's total cost, total emissions level, and the optimal abatement investment decisions. It is found that: (1) when the supply of emission allowances in the market is abundant, reducing the carbon cap or changing the initial allocation rule of free emission allowances will not reduce the manufacturer's carbon emissions level; (2) carbon emission allowance price is the key factor to control the manufacturer's carbon emissions level and abatement capacity; (3) with the increase of carbon price, the manufacturer will expand the abatement capacity even if it has already held enough allowances to cover all its emissions. Our research provides useful managerial insights for manufacturing firms to make investment in carbon emissions abatement under the cap-and-trade system.

Key words: dynamic lot sizing, abatement investment, cap-and-trade, generalized benders decomposition