<p>One of the most important defences for environmental concern and human health is the management process of biomedical wastes. Considering the management techniques are hygienic, safe, and budget-friendly, we need to find optimized values for parameters such as total cost and the error involved in the procedure, with a focus on environmental protection, social acceptance, and health risk. In the selection process for the best management of biomedical wastes, any decision-maker has targets with a range of acceptance, non-acceptance, and neutrality situations. Therefore, we have used the goal programming approach, incorporating a picture fuzzy set with membership, non-membership, and neutrality, to solve such a problem. This technique enhanced its value by providing an excellent feature that allows setting specific goals for each objective function with a particular ambition level. The most recent versions of fuzzy goal programming problems are in neutrosophic and intuitionistic forms, where the effect of dependency between membership functions is absent. In this article, for the first time, we have constructed the goal programming problem by incorporating three realistic dependent choices of decision-makers. Finding the solution to the goal programming problem in a picture-fuzzy environment is more efficient. Also, this work introduces four variations of the membership functions: exponential, parabolic, linear, and hyperbolic, along with all generalized forms corresponding to the respective weights. Eventually, the proposed work is applied to finding the optimized parameters for the management of biomedical wastes in the Indian context. In addition, the comparative analysis with executive implications has demonstrated the reliability and sustainability of the proposed methodology for decision-making.</p>