The presented study investigated the scheduling regarding  jobs on a single machine. Each  job will be processed with no interruptions and becomes available for the processing at time 0. The aim is finding a processing order with regard to jobs, minimizing total completion time , total late work , and maximal tardiness  which is an NP-hard problem. In the theoretical part of the present work, the mathematical formula for the examined problem will be presented, and a sub-problem of the original problem of minimizing the multi-objective functions  is introduced. Also, then the importance regarding the dominance rule (DR) that could be applied to the problem to improve good solutions will be shown. While in the practical part, two

Machine scheduling problems (MSP) are     considered as one of the most important classes of combinatorial optimization problems. In this paper, the problem of job scheduling on a single machine is studied to minimize the multiobjective and multiobjective objective function. This objective function is: total completion time, total lead time and maximum tardiness time, respectively, which are formulated as  are formulated. In this study, a mathematical model is created to solve the research problem. This problem can be divided into several sub-problems and simple algorithms have been found to find the solutions to these sub-problems and compare them with efficient solutions. For this problem, some rules that provide efficient solutio

Within this research, The problem of scheduling jobs on a single machine is the subject of study to minimize the multi-criteria and multi-objective functions. The first problem, minimizing the multi-criteria, which include Total Completion Time, Total Late Work, and Maximum Earliness Time (∑𝐶𝑗, ∑𝑉𝑗, 𝐸𝑚𝑎𝑥), and the second problem, minimizing the multi-objective functions ∑𝐶𝑗 + ∑𝑉𝑗 +𝐸𝑚𝑎𝑥 are the problems at hand in this paper. In this study, a mathematical model is created to address the research problems, and some rules provide efficient (optimal) solutions to these problems. It has also been proven that each optimal solution for ∑𝐶𝑗 + ∑𝑉𝑗 + 𝐸𝑚𝑎𝑥 is an effic

Scheduling problems have been treated as single criterion problems until recently. Many of these problems are computationally hard to solve three as single criterion problems. However, there is a need to consider multiple criteria in a real life scheduling problem in general. In this paper, we study the problem of scheduling jobs on a single machine to minimize total tardiness subject to maximum earliness or tardiness for each job. And we give algorithm (ETST) to solve the first problem (p1) and algorithm (TEST) to solve the second problem (p2) to find an efficient solution.  

In this paper, the main work is to minimize a function of three cost criteria for scheduling n jobs on a single machine. We proposed algorithms to solve the single machine scheduling multiobjective problem. In this problem, we consider minimizing the total completion times, total tardiness and maximum tardiness criteria. First a branch and bound (BAB) algorithm is applied for the 1//∑Ci+∑Ti+Tmax problem. Second we compare two multiobjective algorithms one of them based on (BAB) algorithm to find the set of efficient (non dominated) solutions for the 1//(∑Ci ,∑Ti ,Tmax) problem. The computational results show that the algorithm based on (BAB) algorithm is better than the other one for generated the total number of

In this paper, the problem of scheduling jobs on one machine for a variety multicriteria
are considered to minimize total completion time and maximum late work. A set of n
independent jobs has to be scheduled on a single machine that is continuously available from
time zero onwards and that can handle no more than one job at a time. Job i,(i=1,…,n)
requires processing during a given positive uninterrupted time pi, and its due date d
i.
For the bicriteria problems, some algorithms are proposed to find efficient (Pareto)
solutions for simultaneous case. Also for the multicriteria problem we proposed general
algorithms which gives efficient solutions within the efficient range

This paper proposes a new algorithm (F2SE) and algorithm (Alg(n – 1)) for solving the
two-machine flow shop problem with the objective of minimizing total earliness. This
complexity result leads us to use an enumeration solution approach for the algorithm (F2SE)
and (DM) is more effective than algorithm Alg( n – 1) to obtain approximate solution.

    In this paper, we studied the scheduling of  jobs on a single machine.  Each of n jobs is to be processed without interruption and becomes available for processing at time zero. The objective is to find a processing order of the jobs, minimizing the sum of maximum earliness and maximum tardiness. This problem is to minimize the earliness and tardiness values, so this model is equivalent to the just-in-time production system. Our lower bound depended on the decomposition of the problem into two subprograms. We presented a novel heuristic approach to find a near-optimal solution for the problem. This approach depends on finding efficient solutions for two problems. The first problem is minimizing total completi

     In this paper, we present a Branch and Bound (B&B) algorithm of scheduling (n) jobs on a single machine to minimize the sum total completion time, total tardiness, total earliness, number of tardy jobs and total late work with unequal release dates. We proposed six heuristic methods for account upper bound. Also to obtain lower bound (LB) to this problem we modified a (LB) select from literature, with (Moore algorithm and Lawler's algorithm).  And some dominance rules were suggested. Also, two special cases were derived. Computational experience showed the proposed (B&B) algorithm was effective in solving problems with up to (16) jobs, also the upper bounds and the lower bound were effective in restr

   Real life scheduling problems require the decision maker to consider a number of criteria before arriving at any decision. In this paper, we consider the multi-criteria scheduling problem of n jobs on single machine to minimize a function of five criteria denoted by total completion times (∑), total tardiness (∑), total earliness (∑), maximum tardiness () and maximum earliness (). The single machine total tardiness problem and total earliness problem are already NP-hard, so the considered problem is strongly NP-hard.

We apply two local search algorithms (LSAs) descent method (DM) and simulated annealing method (SM) for the 1// (∑∑∑