text: This chapter presents a novel idea for the general case of the Common Due-Date (CDD) scheduling problem. The problem is about scheduling a certain number of jobs on a single or parallel machines where all the jobs possess different processing times but a common due-date. The objective of the problem is to minimize the total penalty incurred due to earliness or tardiness of the job completions. This work presents exact polynomial algorithms for optimizing a given job sequence for single and identical parallel machines with the run-time complexities of O(nlogn) for both cases, where n is the number of jobs. Besides, we show that our approach for the parallel machine case is also suitable for non-identical parallel machines. We prove the optimality for the single machine case and the run-time complexities of both. Henceforth, we extend our approach to one particular dynamic case of the CDD and conclude the chapter with our results for the benchmark instances provided in the OR library.
  @cite_3: This paper investigates the single-machine multiple common due dates assignment and scheduling problems in which the processing time of a job depends on its position in a job sequence and its resource allocation. We examine the general position-dependent deterioration effect and two models of resource allocation. The objective function is to minimize a total penalty function containing earliness, tardiness, due date, and resource consumption costs. We introduce two polynomial time algorithms to solve the considered problems. Since the two algorithms solve the problems in polynomial time, they can solve large-scale instances of the problem under study in little time.
  @cite_8: In this paper, we study single-machine scheduling problem when each job is considered with linear earliness and quadratic tardiness penalties with no machine idle time. Here the objective is to find the best sequence of jobs in the reasonable time. This model was studied in several researches, and some algorithms were proposed to solve it such as genetic algorithm. As the size of problem increased, such algorithms were not effective and efficient. Hence, we proposed the hybrid imperialist competitive algorithm. The proposed algorithm is based upon the imperialist competitive algorithm and genetic algorithm concepts. This algorithm was tested in problems with different sizes. The results denoted that the hybrid algorithm can solve different size of problem in reasonable time. This procedure showed its efficiency in medium- and large-sized problems as compared with other available methods.
summary: In @math , Banisadr studied the single-machine scheduling problem for the case that each job is considered to have linear earliness and quadratic tardiness penalties with no machine idle time. They proposed a hybrid approach for the problem based upon evolutionary algorithm concepts @cite_8 . Yang investigated the single-machine multiple common due dates assignment and scheduling problems in which the processing time of any job depends on its position in a job sequence and its resource allocation. They proposed a polynomial algorithm to minimize the total penalty function containing earliness, tardiness, due date, and resource consumption costs @cite_3 .