augmented epsilon constraint method

The physician assignment and course timetabling problem at medical universities is a generalized version of the academic timetabling problem. This problem entails assigning courses, educational and clinical tasks to physician faculty members over a semester or academic year. The problem of timetabling academic courses and scheduling physicians in a hospital has been investigated independently in previous studies in this field. These two fields of research are brought together in this article through the presentation of a multi-objective Mixed-Integer Linear Programming (MILP) model. The proposed model is based on two optimization criteria: minimizing workload imbalance and maximizing physician preferences. The model is applied to a case study involving the assignment of physicians to courses, educational and clinical tasks at Kurdistan University of Medical Sciences' Department of Infectious Diseases. Pareto solutions are obtained using an enhanced version of the augmented epsilon constraint implemented in the General Algebraic Modeling System (GAMS) optimization software; one is selected as the most desirable solution using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method. The proposed model is generic and could be adapted for use in other departments or medical schools.

According to the conducted research, oil and gas industry projects have many complexities and uncertainties, and investment in these projects is associated with high risks. In this research, while identifying the most critical risks that have an impact on investing in oil and gas projects, they have been identified in the first place. Then, the importance of each of the specified criteria is determined. To achieve the aforementioned goals, modern computing methods have been used. In the phase of identifying factors from fuzzy Delphi; In the importance and prioritization stage, multi-criteria decision-making methods are used, and in the allocation stage, multi-objective mathematical modeling is used. Therefore, first, a list of 21 investment risks in industry and gas was collected by reviewing the literature and research backgrounds. The collected risks were refined and finalized using the fuzzy Delphi approach. Finally, the risks of sanctions by an institution or country, liquidity, health risks (such as the corona epidemic), financial potential, exchange rate fluctuations, and sudden changes in inflation as risks. considered in this research. Then, considering factors such as quality, cost, technology, time, and information preparation as indicators influencing the occurrence of considered risks, their importance has been determined using the best-worst method. According to the weight calculated for each of these factors, respectively equal to 0.23; 0.09; 0.52; 0.07, and 0.09 are estimated. Then, according to the importance obtained by using the GRA-VIKOR approach, the risk ranking was determined by considering the factors affecting them. Finally, by using the three-objective linear programming model with the objectives of maximizing the level of quality, minimizing cost and time, and solving it using the epsilon-constraint method, an appropriate response strategy is determined for each of the considered investment risks.