International Journal of Industrial Engineering & Production Research

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Flexible flow shop scheduling problem (FFS) with unrelated parallel machines contains sequencing in flow shop where, at any stage, there exists one or more processors. The objective consists of minimizing the maximum completion time. Because of NP-completeness of FFS problem, it is necessary to use heuristics method to address problems of moderate to large scale problem. Therefore, for assessment the quality of this heuristic, this paper develop a global lower bound on FFS makespan problems with unrelated parallel machines.

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In hybrid flow shop scheduling problem (HFS) with unrelated parallel machines, a set of n jobs are processed on k machines. A mixed integer linear programming (MILP) model for the HFS scheduling problems with unrelated parallel machines has been proposed to minimize the maximum completion time (makespan). Since the problem is shown to be NP-complete, it is necessary to use heuristic methods to tackle the moderate to large scale problems. This article presents a new bottleneck-based heuristic to solve the problem. To improve the performance of the heuristic method, a local search approach is embedded in the structure of the heuristic method. To evaluate the performance of the proposed heuristic method, a new lower bound is developed based on Kurz and Askin [1] lower bound. For evaluation purposes, two series of test problems, small and large size problems, are generated under different production scenarios.  The empirical results show that average difference between lower bound and optimal solution as well as lower bound and heuristic method are equal to 2.56% and 5.23%, respectively. For more investigation, the proposed heuristic method is compared by other well-known heuristics in the literature. The results verify the efficiency of the proposed heuristic method in term of number of best solution.

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Natural disasters, such as earthquakes, tsunamis, and hurricanes cause enormous harm during each year. To reduce casualties and economic losses in the response phase, rescue units must be allocated and scheduled efficiently, such that it is a key issues in emergency response. In this paper, a multi-objective mix integer nonlinear programming model (MOMINLP) is proposed to minimize sum of weighted completion times of relief operations as first objective function and makespan as second objective with considering time-window for incidents. The rescue units also have different capability and each incident just can be allocated to a rescue unit that has the ability to do it. By assuming the incidents and rescue units as jobs and machine, respectively, the research problem can be formulated as a parallel-machine scheduling problem with unrelated machines. Multi-Choice Goal programming (MCGP) is applied to solve research problem as single objective problem. The experimental results shows the superiority of the proposed approach to allocate and schedule the rescue units in the natural disasters.

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In the study of the reliability of systems in reliability engineering, it has been defined several measures in the reliability and survival analysis literature. The reliability function, the mean residual lifetime and the hazard rate are helpful tools to analyze the maintenance policies and burn-in. In this paper, we consider a network consisting of n components having the property that the network has two states up and down (connected and disconnected). Suppose that the network is subject to shocks that each may cause the component failures. We further suppose that the number of failures at each shock follows a truncated binomial distribution and the process of shocks is nonhomogeneous Poisson process. This paper investigates the reliability function, the mean residual lifetime and the hazard rate of the network under shock model. An example and illustrative graph is also provided.

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In many real scheduling situations, it is necessary to deal with the worker assignment and job scheduling together. However, in traditional scheduling problems, only the machine is assumed to be a constraint and there isn’t any constraint about workers. This assumption could be due to the lower cost of workers compared to machines or the complexity of workers' assignment problems. This research proposes a flexible flow shop scheduling problem with two simultaneous issues: finding the best worker assignment, and solving the corresponding scheduling problem. We present a mathematical model that extends flexible flow shop scheduling problem to admit the worker assignment. Due to the NP-hardness of the research problem, two approximation approaches based on particle swarm optimization, named PSO and SPSO, are applied to minimize the makespan. The experimental results show that the proposed algorithms can efficiently minimize the makespan but the SPSO generates better solutions especially for large-size problems.

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