Jonathan Diaz

For companies involved in the supply chain, proper warehousing management is crucial. Warehouse layout arrangement and operation play a critical role in a company’s ability to maintain and improve its competitiveness. Reducing costs and increasing efficiency are two of the most crucial warehousing goals. Deciding on the best warehouse layout is a remarkable optimization problem. This paper uses an optimization method to set bin allocations within an automated warehouse with particular characteristics. The warehouse’s initial layout and the automated platforms limit the search and define the time required to move goods within the warehouse. With the help of historical data and the definition of the time needed to move goods, a mathematical model of warehouse operation was created. An optimization procedure based on the well-known Variable Neighbourhood Search algorithm is defined and applied to the problem. Experimental results demonstrate increments in the efficiency of warehousing operations.

There is a constructive method to define a structure of simple k -cyclic Post algebra of order p , L p , k , on a given finite field F ( p k ), and conversely. There exists an interpretation Φ 1 of the variety $${\mathcal{V}(L_{p,k})}$$ generated by L p , k into the variety $${\mathcal{V}(F(p^k))}$$ generated by F ( p k ) and an interpretation Φ 2 of $${\mathcal{V}(F(p^k))}$$ into $${\mathcal{V}(L_{p,k})}$$ such that Φ 2 Φ 1 ( B ) = B for every $${B \in \mathcal{V}(L_{p,k})}$$ and Φ 1 Φ 2 ( R ) = R for every $${R \in \mathcal{V}(F(p^k))}$$. In this paper we show how we can solve an algebraic system of equations over an arbitrary cyclic Post algebra of order p, p prime, using the above interpretation, Gröbner bases and algorithms programmed in Maple