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This paper analyzes the performance of a robotic system with two machines in which machines are configured in a circular layout and produce non-identical parts repetitively. The non-destructive testing (NDT) is performed by a stationary robotic arm located in the center of the circle, or a cluster tool. The robotic arm integrates multiple tasks, mainly the NDT of the part and its transition between a pair of machines. The robotic arm cannot complete the transition if it identifies a fault in the part. The main feature of the NDT technology is that its required time is changed by altering the testing cost. This generates a trade-off between cost and cycle time. Initially, the problem of robotic arm scheduling and part sequencing is jointly solved to supports the decision making for reliability improvement of small-scale robotic systems with NDT technologies. We show how the case of non-identical parts can be converted into a travelling salesman problem (TSP). Then, we provide a generalization of the framework based on three characteristics: pickup criterion, layout and travel time metric. The results are extended for the interval and no-wait pickup criteria, and then some notes are provided for travel time saving of different layout and travel time metric. It is shown whether circular systems are equivalent to linear systems, or they dominate linear cases in general terms.

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Here, scalarization techniques for multi-objective optimization problems are addressed. A new scalarization approach, called unified Pascoletti-Serafini approach, is utilized and a new algorithm to construct the Pareto front of a given bi-objective optimization problem is formulated. It is shown that we can restrict the parameters of the scalarized problem. The computed efficient points provide a nearly equidistant approximation of the whole Pareto front. The performance of the proposed algorithm is illustrated by various test problems and its effectiveness with respect to some existing methods is shown.