Latin rectangle

Latin rectangle

Experiments with Blocks

Published in Julian J. Faraway, Linear Models with Python, 2021

The Latin square can be even more efficient than the RCBD provided that the blocking effects are sizable. There are some variations on the Latin square. The Latin square can be replicated if more runs are available. We need to have both block sizes to be equal to the number of treatments. This may be difficult to achieve. Latin rectangle designs are possible by adjoining Latin squares. When there are three blocking variables, a Graeco–Latin square may be used but these rarely arise in practice.

Minimizing maximum job dependent ergonomic risk

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Journal Information

Published in International Journal of Production Research, 2021

Sergey Kovalev, Isabelle Chalamon, Stephane E. Collignon

Consider a special case in which the number of time intervals T is an integer multiple of n. For this case, construct a solution, in which each worker executes each job exactly T/n times. The corresponding feasible assignment can be represented by a Latin rectangle, two examples of which are shown in Table 2. We call such a solution an LR-matrix or LR-solution, where LR is an abbreviation for Latin rectangle. Columns of an LR-matrix correspond to the time intervals. Its rows correspond either to jobs, in which case the entries are workers, or they correspond to workers, in which case the entries are jobs. The value of an LR-solution is equal to LB. Hence, it is optimal. Since LR-solution in Table 2 can be described in time, the following statement holds.

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Experiments with Blocks

Minimizing maximum job dependent ergonomic risk