This paper discusses a special situation in project management in which an analyst wants to prioritize several independent activities to handle all them one after another, in such a way that there are no precedence relationships over the activities. As a novel idea, in this research, the notion is that the structure of prioritized activities is a linear arrangement, and therefore it could be taken into account as a Combinatorial Optimization problem. The paper formulates a mathematical model, develops a row-generation solving procedure, and reports the computational results for the problem instances of size up to 300 activities. The results demonstrate the applicability and efficiency of the proposed methodology.

Combinatorial Optimization is the procedure of optimizing an objective function over the discrete configuration space. A genetic algorithm (GA) has been applied successfully to solve various NP-complete Combinatorial Optimization problems. One of the most challenging problems in applying GA is selecting mutation operators and associated probabilities for each situation. GA uses just one type of mutation operator with a specified probability in the basic form. The mutation operator is often selected randomly in improved GAs that leverage several mutation operators. While an effective GA search occurs when the mutation type for each chromosome is selected according to mutant genes and the problem landscape. This paper proposes an adaptive genetic algorithm that uses Q-learning to learn the best mutation strategy for each chromosome. In the proposed method, the success history of the mutant in solving the problem is utilized for specifying the best mutation type. For evaluating adaptive genetic algorithm, we adopted the traveling salesman problem (TSP) as a well-known problem in the field of Optimization. The results of the adaptive genetic algorithm on five datasets show that this algorithm performs better than single mutation GAs up to 14% for average cases. It is also indicated that the proposed algorithm converges faster than single mutation GAs.

Optimization of inventory costs is the most important goal in industries. But in many models, the constraints are considered simple and relaxed. Some actual con-straints are to consider the Combinatorial production and purchase models in multi-products environment. The purpose of this article is to improve the e ciency of inventory management and  nd the economic order quantity and economic production quantity that can minimize the cost of inventory and customer satisfac-tion. In this study, the models with these targets in Combinatorial production and purchase systems with the assumption the warehouse and budget constraints are proposed. Since a long time for solving the problem with an exact method is required, we develop a genetic algorithm.