This paper presents a model for minimizing the MAKESPAN in the flow shop scheduling problem. Due to the impact of increased workloads, flow shops are becoming more popular and widely used in industries. To solve the challenge of minimizing MAKESPAN, a Hybrid-Heuristic-Metaheuristic-Genetic-Algorithm (HHMGA) is proposed. The proposed HHMGA algorithm is tested using the simulation software and demonstrated with steel industry data. The results are compared with those of the best available flow shop problem algorithms such as Palmer’s slope index, Campbell-Dudek-Smith (CDS), Nawaz-Enscore-Ham (NEH), genetic algorithm (GA) and particle swarm optimization (PSO). According to empirical results and relative differences from the lower bound, the proposed technique outperforms the three heuristics and two metaheuristics algorithms in three of six cases, while the remaining three produce the same results as the NEH heuristic. In comparison to the steel industry's regular job scheduling technique, the simulation model based on HHMGA can save 4642 hours. It was discovered that the suggested model enhanced the job sequence based on the MAKESPAN requirements.

The research on project scheduling has widely expanded over the last few decades. The vast majority of these research efforts focus on exact and suboptimal procedures for constructing a workable schedule, assuming complete information and a static deterministic problem environment. Project activities are scheduled subject to both technological precedence constraints and resource constraints, mostly under the objective of minimizing the project duration. The resulting schedule serves as the baseline for the execution of the project. During execution, however, the project is subject to considerable uncertainty, which may lead to numerous schedule disruptions. It is surprising to see that, given the large amount of projects that have finished late during the last decades, management still fails to quote accurate project due dates. This is problematic because virtually all organizations use their project plans not only as tools with which to manage the projects, but also as a foundation to make delivery commitments to clients. Therefore, a vitally important purpose of project plans and effective scheduling methods is to enable organizations to estimate completion dates of the corresponding projects. A project schedule also serves as a baseline for material procurement, contacts with subcontractors, coordination of internal resources and corrective actions the ultimate goal which is more akin to deterministic scheduling, is to make scheduling and resource allocation decisions that will allow quoting a due date that should be as low as possible. Such optimizations decisions need not only be taken before the project is actually started, but also scheduling and resource allocation should also be able during project execution in order protect promised dates from any sources of uncertainty that may occur. Additionally, if advance knowledge about the nature of the uncertainty in the project is available, it is desirable that the project schedule be robust to disruptions that may arise. One of the important approaches in this issue is constructing robust project schedule. Generally, this approach tries to construct robust project baseline schedule by considering uncertainty in such a way that any variations cannot make disruption in it as far as possible. In this article, we introduce the concept of schedule robustness and then we develop a bi-objective resource constrained project scheduling model. We consider the objectives of robustness maximization along with MAKESPAN minimization. Then, we present a tabu search algorithm that operates on surrogate functions. This algorithm is developed in order to generate an approximate set of efficient solutions. Many random project scheduling problems are generated, and then solved by the algorithm. Finally, the efficiency of the algorithm and the robustness surrogate functions are evaluated by simulation. Finally, the results show efficiency of the algorithm and developed surrogate function.

In this paper the problem of job shop scheduling with parallel machines in each stages is discussed. The objective is to minimize the maximum completion time (MAKESPAN). This problem is a combination of two classic problems of job shop and parallel machines which in this case parallel machines has been used as kind of flexibility in the job shop problem. The review of literature has shown that this problem has not been discussed yet. After presenting the mathematical mode, heuristic algorithms are used for solving this NP-hard problem. Regarding this, five algorithms are presented and a lower bound is developed. Finally all these algorithms have been analyzed. According to results the proposed algorithm of H2 works better than the others when there are few jobs. As the number of jobs increases H1 is more efficient than H2 asymptotically. Also the efficiency of H3 algorithm is the worst among the rest.

This paper presents an alternative method using artificial neural network (ANN) to develop a scheduling scheme which is used to determine the MAKESPAN or cycle time of a group of jobs going through a series of stages or workstations. The common conventional method uses mathematical programming techniques and presented in Gantt charts forms. The contribution of this paper is in three fold. Firstly, the learning curve which is characterized by a coefficient is considered in the computation work. Secondly, this work is limited to small number of jobs and is useful for project based pilot runs which involve learning. Lastly, the scheduling scheme is developed in ANN as an alternate method. Extensive and successful training using the input and output vector pairs were done to establish the proposed method. Comparison was done for the tested outputs and results produced seem reliable.

This paper deals with a Flexible Flow Shop (FFS) scheduling problem with unrelated parallel machines and a renewable resource shared among the stages. The FFS scheduling problem is one of the most common manufacturing environments, in which there is more than a machine in at least one production stage. In such a system, to decrease the processing times, additional renewable resources are assigned to the jobs or machines, which can lead to a decrease in the total completion time. For this purpose, a Mixed Integer Linear Programming (MILP) model is proposed to minimize the maximum completion time (MAKESPAN) in an FFS environment. The proposed model is computationally intractable. Therefore, a Particle Swarm Optimization (PSO) algorithm, as well as a hybrid PSO and Simulated Annealing (SA) algorithm named SA-PSO, are developed to solve the model. Through numerical experiments on randomly generated test problems, the authors demonstrate that the hybrid SA-PSO algorithm outperforms the PSO, especially for large size test problems.

The purpose of this paper is to consider the problem of scheduling a set of start time-dependent jobs in a two-machine flow shop, in which the actual processing times of jobs increase linearly according to their starting time. The objective of this problem is to minimize the MAKESPAN. The problem is known to be NP-hardness; therefore, there is no polynomial-time algorithm to solve it optimally in a reasonable time. So, a branch-and-bound algorithm is proposed to find the optimal solution by means of dominance rules, upper and lower bounds. Several easy heuristic procedures are also proposed to derive near-optimal solutions. To evaluate the performance of the proposed algorithms, the computational experiments are extracted based on the recent literature. Deteriorating jobs lead to an increase in the MAKESPAN of the problems; therefore, it is important to obtain the optimal or near-optimal solution. Considering the complexity of the problem, the branch-and-bound algorithm is capable of solving problems of up to 26 jobs. Additionally, the average error percentage of heuristic algorithms is less than 1. 37%; therefore, the best one is recommended to obtain a near-optimal solution for large-scale problems.

This paper considers minimizing MAKESPAN (Cmax) on a single batch-processing machine. A batch processing machine can process a group of jobs simultaneously, as long as the total size of jobs in the batch does not exceed the machine capacity (B). For each job, we assume a specific job size and job processing time. The processing time of a batch is just the longest processing time of all jobs in the batch. We introduce two new procedures for obtaining lower bounds of the optimal MAKESPAN, entitled LB2 and LB3, respectively. We prove that both of the new bounds are tighter than the only existing bound called LB1. We also prove that LB3 is at least as tight as LB2.

In previous investigations in the eld of exible ow shop scheduling problems, the rework probability for operations was ignored. As these kinds of problems are NPhard, we present an Enhanced Invasive Weed Optimization (EIWO) algorithm in order to solve the addressed problem with probable rework times, transportation times with a conveyor between two subsequent stages, dierent ready times and anticipatory sequence dependent setup times. The optimization criterion is to minimize MAKESPAN. Although Invasive Weed Optimization (IWO) is an ecient meta-heuristic algorithm and has been used by many researchers recently, to increase the capability of IWO, we added a mutation operation to enhance the exploration in order to prevent sticking in local optimum. In addition, an anity function is embedded to obstruct premature convergence. With these changes, we balance the exploration and exploitation of IWO. Since the performance of our proposed algorithm depends on parameters values, we apply the popular design of an experimental methodology, called the Response Surface Method (RSM). To evaluate the proposed algorithm, rst, some random test problems are generated and compared with three benchmark algorithms. The related results are analyzed by statistical tools. The experimental results and statistical analyses demonstrate that the proposed EIWO is eective for the problem.