Can Reject The Sorting Problem With Learning Effect

With the progress of the society and the development of science and technology, the scheduling problems had been widely used in our life and work. In the classical scheduling literatures, people often studies the manufacturer to complete one or some of the customer's orders, and will not to reject the part of order for outsourcing. In practice , manufacturers often reject orders with longer processing time but lower profits, and they can also outsource these orders to process. To some extent, this will enable manufacturers to gain greater profits over a certain period of time. The design of algorithms for the scheduling problems with rejection are studied in this paper. First, we research the scheduling problems with machine availability constraints and rejection, and then studies the supply chain scheduling on two machines minimizing the holding costs with outsourcing. In the end, a single machine scheduling problem with learning effect is considered. The objective functions referred in this paper are to minimized the sum of the weighted total completion time of the accepted jobs and the total rejection penalty of the rejected jobs, to minimize the sum of holding and delivery costs. This paper mainly considers the following problems.In chapter 1 , the basic concepts, basic knowledge and terminology of the scheduling problems are presented. the development of the scheduling problems and the main results of this paper are briefly introduced.In chapter 2 , this paper mainly studied the scheduling problems with a learning effect and an availability constraint and rejection. It is assumed that the machine is not available for processing during some given time interval. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on the machine. The objective is to minimize the sum of the total completion time of all accepted orders plus the total penalty of all rejected orders. In addition, this paper also studied the scheduling problems with a learning and deteriorating effect and rejection. The objective is to minimized the sum of the weighted total completion time of the accepted jobs and the total rejection penalty of the rejected jobs. The dynamic programming algorithm are provided for the machine maintenance at any time, respectively. The complexity of algorithms are analyzed.In chapter 3 , this paper considers a "two machines scheduling" problem, in which the jobs have identical processing times and the jobs can be either processed in house, or outsourced to a third-party supplier. The objective is to minimize the sum of holding and delivery costs. For the problem with limited outsourcing budgets, a pseudo-polynomial algorithm and a fully polynomial time approximation scheme are presented.In chapter 4 , a single machine scheduling problem with learning effect is considered , in which jobs can be either processed in house, or outsourced to a third-party supplier, but an order-dependent penalty will be incurred. For the problem with limited outsourcing budgets,the objective is to minimize the sum of holding and delivery costs, a pseudo-polynomial algorithm are presented.