Purpose
Main constraints for an assembly line balancing problem (ALBP) are cycle time/number of stations and task precedence relations. However, due to the technological and organizational limitations, several other restrictions can be encountered in real production systems. These restrictions are called as assignment restrictions and can be task assignment, station, resource and distance limitations. The purpose of the study is to evaluate the effects of these restrictions on ALBP using constraint programming (CP) model.
Design/methodology/approach
A novel CP model is proposed and compared to mixed-integer programming (MIP) as a benchmark. The objective is to minimize the cycle time for a given number of stations. The authors also provide explicit anthology of the assignment restriction effects on line efficiency, the solution quality and the computation time.
Findings
The proposed approach is verified with the literature test instances and a real-life problem from a furniture manufacturing company. Computational experiments show that, despite the fact that additional assignment restrictions are problematic in mathematical solutions, CP is a versatile exact solution alternative in modelling and the solution quality.
Practical implications
Assembly line is a popular manufacturing system in the making of standardized high volume products. The problem of assembly line balancing is a crucial challenge in these settings and consists of assigning tasks to the stations by optimizing one or more objectives. Type-2 AR-ALBP is a specific case with the objective function of minimizing the cycle time for a given number of stations. It further assumes assignment restrictions that can be confronted due to the technological limitations or the strategic decisions of the company management. This is especially encountered in rebalancing lines.
Originality/value
Several solution approaches such as mathematical modelling, heuristic and meta-heuristic are proposed to solve the ALBP in the literature. In this study, a new approach has been presented using CP. Efficient models are developed for Type-2 ALBP with several assignment restrictions. Previous studies have not considered the problem to the presented extent. Furthermore, to the best of the authors’ knowledge, the paper is the first study that solves ALBP with assignment restrictions using CP.
In this study, multivariate statistical techniques are experimented for a spur gear system and a methodology is proposed. The approach is based on the analysis of multidimensional gear vibration data without any feature extradiction and data transformation. The scheme is performed using the vibration signals acquired from a lab-scale single stage gearbox in three dimensions of x, y and z directions. As a groundwork, multi-normality assumptions are established using homogeneity, autocorrelation, and univariate normality tests. The bi-dimensional frequency histograms are also plotted to show bi-normality for experimental gear data. Then, mean vectors and covariance matrices of conditions of good, worn, 1-tooth broken from wheel gear and 1-tooth broken from each pinion and wheel gear are estimated. To compare gear conditions statistically, multivariate analysis of variance is proposed and applied. Moreover, the single metric of Mahalanobis distances are calculated to classify unknown test samples, utilizing the maximum likelihood estimates. The numerical results indicate that multivariate statistical analysis techniques can be applied in early detection of spur gear faults, in which univariate tests fail.
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