Literature Review of Single Machine Scheduling Problem with Uniform Parallel Machines <s> Miscellaneous Problems with Non-Preemptive <s> In this note we consider a problem of scheduling n single-operation jobs on m non-identical machines where the sequencing of the jobs and their processing times are decision variables. It is assumed that the cost of performing a job is a linear function of its processing time. The scheduling cost to be minimized is: (A) the total processing cost plus total flow time, (B) the total processing cost plus total weighted earliness and weighted tardiness. We reduce each problem to a transportation problem that can be solved by a polynomial time algorithm. <s> BIB001 </s> Literature Review of Single Machine Scheduling Problem with Uniform Parallel Machines <s> Miscellaneous Problems with Non-Preemptive <s> In this paper a single machine scheduling problem with varying processing times is considered. The scheduling objectives are makespan, total flow time, and sum of deviations of jobs completion times from a common due date. Polynomial time algorithms for optimal solutions of the problems are given. <s> BIB002 </s> Literature Review of Single Machine Scheduling Problem with Uniform Parallel Machines <s> Miscellaneous Problems with Non-Preemptive <s> Abstract In this paper, we consider the problem of on-line uniform machine scheduling with rejection. For the two machine case and a special three machine case, we present the best possible on-line algorithms for certain values of speed ratio s. <s> BIB003 </s> Literature Review of Single Machine Scheduling Problem with Uniform Parallel Machines <s> Miscellaneous Problems with Non-Preemptive <s> In this study, we address an operational fixed interval scheduling problem on uniform parallel machines. Our objective is to maximize the total weight of the jobs processed. We show that the problem is NP-hard in the strong sense and develop polynomial time algorithms for some special cases. We propose a branch and bound algorithm that employs dominance conditions and tight bounds. The results of our computational tests have revealed that the algorithm returns optimal solutions for problem instances with up to 70 jobs very quickly. <s> BIB004
Jobs Bahram Alidaee and Ahmad Ahmadian BIB001 have considered the problem of scheduling n single-operation jobs on 2 non-identical parallel machines where the sequencing of the jobs and their processing times are decision variables. In this research, the authors have assumed that the cost of processing a job is directly proportional to its processing time. The objectives of their research are as listed below. 1) Minimizing the total processing cost plus total flow time. 2) Minimizing the total processing cost plus weighted earliness and weighted tardiness. They have reduced each of these problems to a transportation problem, which can be solved by a polynomial time algorithm. Bahram Alidaee and Ahmad Ahmadian BIB002 have considered the single machine scheduling problem with variable speed. They have established polynomial time algorithms to minimize the makespan, total flow time and sum of the deviations of jobs from a common due date. Vahid, Mahmoud and Mohsen  have presented a new deadline-based algorithm for the online uniform parallel machines scheduling problem with overloading situations. Then, they compared its performance with that of earliest due date first (EDF) algorithm. It is shown that their algorithm not only demonstrated a performance close to that of EDF in non-overloaded conditions but also has supremacy over EDF in overloaded situations in many aspects. Furthermore, it imposes much less overhead on the system. Bekki and Meral Azizoglu BIB004 studied an operational fixed interval scheduling problem on uniform parallel machines. Here, the objective is to maximize the total weight of the jobs processed. They showed that the problem is NP-hard in the strong sense and develop polynomial time algorithms for some special cases. They proposed a branch and bound algorithm that employs dominance conditions and tight bounds. He and Min BIB003 have considered the problem of online uniform machine scheduling with rejection. For the two machine case and a special three machine case, they presented the best possible online algorithms for certain values of speed ratio s.