Single-machine Scheduling Problem With Effects Of Learning,Deterioration And Resource Allocation

With the coming of the information age, rapid economic development, every minute can create value, how to achieve the highest efficiency in this fierce competition environment with the limited resources is an important problem for all companies, especially in the production department, how to make the jobs completed in the shortest time and use the least resources is the most common problem that they are facing, so as a business management and decision-makers must understand the theory and application of the scheduling problems.The actual processing time of a job will increase or decrease affected by external factors,which called deterioration effects and learning effects, while it is also affected by the amounts of resource allocation. Currently, most scholars have only carried out one or two kinds of factors in the scheduling problems, but there is few papers including the three all. While in real life, this situation is very common. In order to making the study closer to production,based on the results of previous studies, this paper takes all three factors into account,proposes the scheduling model with deterioration, learning effects and resource allocation. It is more general and significant in practical application. This paper solves the minimization problems of cost functions for liner and convex resource allocation models; finds the optimal sequence and the optimal resource amount of jobs. Under convex resource allocation model,we discuss the problem of minimizing controlling cost under the limitation of completion time cost; and the problem of minimizing completion time cost under the limitation of controlling cost. We prove that these problems have polynomial time algorithms...