Forest ecosystems play an important role in mitigating global climate change, and this role has recently been further reinforced by the Paris Agreement. However, our knowledge with respect to the trade-offs between timber production and carbon sequestration in forest ecosystems is still seriously deficient. Therefore, the overall goal of this study is to quantitatively analyze the effects of a set of economic and ecological constraints on the joint production capacity for forest timber and carbon by alternative forest management strategies for a large forest in northeastern China. The proposed forest planning models integrate four alternative forest management strategies, namely, the timber-oriented management strategy (TMS), the carbon-oriented management strategy (CMS), the multiobjective management strategy (MMS), and the resource-restricted management strategy (RMS). Four different planning scenarios for each strategy were further generated by successively adding one additional constraint, which mainly included the even-flow of timber production, the adjacent constraints of harvest activities, and the minimum targets of carbon sequestration, over a 50-year planning horizon. The results showed that increasing the prices of carbon resulted in positive quadratic polynomial total and carbon net present values (NPVs), positive logistic carbon sequestration and stocks, and negative logistic harvest of timber and its NPV for optimal forest management plans, in which the carbon price of $100 per ton was a significant threshold for balancing the harvest of timber and carbon sequestration. In addition to the CMS, our tested spatial and nonspatial constraints all showed significant effects on optimal forest management plans when a realistic carbon price (i.e., $20 ton −1 ) from the carbon trading market in China during 2014–2017 was employed, in which decreases of approximately 29.34% and 25.08% were observed for total NPV when twenty-percent deviations in harvest volume between any two consecutive periods were employed. Additionally, two periods of green-up constraints could further reduce the total NPV by approximately 17.87% and 15.73% for TMS and MMS, respectively, when compared with their base scenarios. However, increasing the minimum carbon target by one percent reduced the total NPV by approximately $29.44 per hectare per year when evaluated for RMS. Our optimization framework not only can be replicated in other regions with similar characteristics but also contributes to the ongoing debate about the trade-offs between carbon sequestration and wood production benefits.