Companies and governments are actively looking for methods of curbing global warming. Management of inventory systems while considering environmental issues is an important problem. Therefore, this paper explores an Economic Order Quantity model by incorporating environmental issues under partial trade credit and partial backordering. The selling price and carbon emission-dependent demand function is adopted in this paper. The paper first formulates an inventory model with an exogenous price under cap-and-trade and carbon tax mechanisms. The study then extends the proposed problem when the selling price is an endogenous variable. These models are formulated as a nonlinear programming problem of profit maximization, and they are optimized applying global optimization of signomial geometric programming. Further, numerical examples and sensitivity analysis are presented to examine the effects of different shortage rates, credit periods, carbon tax, and price on the retailer’s replenishment strategies.