Alias structures for two-level fractional designs are commonly used to describe the correlations between different terms. The concept of alias structures can be extended to other types of designs such as fractional mixed-level designs. This paper proposes an algorithm that uses the Pearson’s correlation coefficient and the correlation matrix to construct alias structures for these designs, which can help experimenters to more easily visualize which terms are correlated (or confounded) in the mixed-level fraction and constitute the basis for efficient sequential experimentation.

Mixed-level designs have a wide application in the fields of medicine, science, and agriculture, being very useful for experiments where there are both, quantitative, and qualitative factors. Traditional construction methods often make use of complex programing specialized software and powerful computer equipment. This article is focused on a subgroup of these designs in which none of the factor levels are multiples of each other, which we have called pure asymmetrical arrays. For this subgroup we present two algorithms of zero computational cost: the first with capacity to build fractions of a desired size; and the second, a strategy to increase these fractions with M additional new runs determined by the experimenter; this is an advantage over the folding methods presented in the literature in which at least half of the initial runs are required. In both algorithms, the constructed fractions are comparable to those showed in the literature as the best in terms of balance and orthogonality.

This article aims to serve as a guide for the construction of supply chain simulation models designed with a lean approach, using Promodel software. To achieve this, a supply chain was designed for a fictitious company located in the City of Celaya, Guanajuato and a set of suppliers located in different cities within the same State. It was used as a google tool to define the distances between each of the companies. As a final result, a representative model of a supply chain was obtained, as well as a methodology that allows the construction of lean supply chains regardless of the number of companies that comprise it. The effect of the variability in the delivery times between suppliers was incorporated into the simulation model, as well as an equation that calculates the pollution emissions of the vehicles that integrate the network that moves the products between the companies. With this work it is possible to represent networks of supply chains of real world companies, where the variability and contamination factor is included, to facilitate the decision making regarding the number of vehicles, inventory levels, quantities to be shipped, frequency in the shipments, etc. with the purpose of contaminating as little as possible and at the same time preventing interruptions in the supply chain using the least amount of resources possible.