bi-objective programming

Scheduling and timetabling for university system have been a source of attention and an important challenge for the people in charge of administrations. The regulations and infrastructures are very diverse between universities, making it impossible to come up with a universal model for all. We, in this research, focused on coming up with an algorithm to help with timetabling of class courses for Islamic Azad university of Robat Karim. Our goal was to define an algorithm that could improve teacher satisfaction, and overall efficiency of the university timetabling. Instead, we managed to come up with an efficient algorithm.This research considers different factors such as teacher satisfaction, knowledge and skillset, categorizes students based on undergraduate versus post graduate degree, their research background, their scores and finally student satisfaction as well. This multi-objective mathematic model accounts for all the rules, regulations, and limitations of the university setting while following challenging confinements that guarantee the feasibility of the solution. Using metaheuristic algorithm of Whale and Genetic, while avoiding any breach of the soft limitations, we managed to come up with a system that provides the most satisfaction between the teachers and students. In our research, we compared Whale and Genetic algorithm with 4 other metaheuristic algorithms. We concluded that the results of Whale and Genetic algorithm are superior to other algorithms in regards to: Improved function goals, less run time, more Pareto front averages, more efficient solutions and results.

Todays, the variety of new products will raise the competition between manufacturers. Product portfolio management (PPM) as a suitable tool can influence the customer’s taste and increase the profit of firms. In this paper, the factors of PPM, production planning and a two-player continuous game theory are considered simultaneously. Some constraints are also assumed such as the availability of raw materials and the demand of each product based on some criteria. Two firms have same offered products and compete with each other. The relationships between two producers will be modeled by a non-zero two- player game. A numerical example is presented too. The proposed model is single period that the inventory is equal to zero in the start and finish of period. The objective functions show the profit of products and the constraints are included the utility of products for each customer, the marketchr('39')s share as a function of the probability of customer selection for each section, the type of distribution function for sale quantity, the accessible quantity of the sum of used materials by two producers and etc.The results shows that demand changing effects on the profit of two players, but effects more on the second player. Also the sale price changing effects on the profit of two players, but effects more on the first player. The obtained data shows that if extra sale price increase the profit of first player will increase while the profit of second player is constant approximately.