This paper aims to develop an optimal real-life energy-efficient design for a production plant within the concept of the circular economy. The problem is to install a Heat Recovery System (HRS) that utilizes the hot oil used by the compressors to heat the water for the central heating system. To achieve the desired level of energy efficiency this design problem must be formulated from both the optimization and sustainability points of view. Additionally, this design problem must also consider the investment cost. In line with this purpose, this paper formulates this design problem as an optimization problem employing a mathematical programming approach as a single objective, and as a multi-objective optimization problem through a goal programming approach. Besides, this paper uses the return on investment as a key performance indicator, since it deals with a real-life design problem with an investment cost. The related design problem is solved with the single objective and multiobjective versions of the developed mathematical programming model via a commercial solver to identify different design alternatives and hence giving the decision-maker to make a selection option. Finally, the capability of the developed mathematical programming model is tested on a set of randomly generated problems. The obtained results indicate that the developed mathematical programming model is a successful decision support system since its single and multi-objective versions are capable of identifying energy-efficient production designs within the context of the real-life problem on hand and the circular economy.