let $ m , n in mathbb{n}$, $d$ be a division ring, and $m_{m times n}(d)$ denote the bimodule of all $m times n$ matrices with entries from $d$. first, we characterize one-sided submodules of $m_{m times n}(d)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $d$. next, we introduce the notion of a nest module of matrices with entries from $d$. we ...

Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We ...

The paper studies the two-echelon capacitated vehicle routing problem with time windows, in which delivery of freight from depots to customers is performed using intermediate facilities called satellites. We consider variant precedence constraints for unloading and loading at In this allows storage consolidation Thus, total transportation cost may decrease comparison alternative exact synchroni...

Clark and Scarf [1960] characterize optimal policies in a two-echelon, twolocation inventory model. We extend their result to the infinite-horizon case (for both discounted and average costs). The computations required are far easier than for the finite horizon problem. Further simplification is achieved for normal demands. We also consider the more interesting case of multiple locations at the...

In this paper, the previously introduced fuzzy modeling method is used to model the input impedance of two coupled dipole antennas in the echelon form. The initial data of two coupled dipole antennas in the parallel and collinear form, which are required for the model, are obtained using the MoM (Method of Moments). Then, the knowledge of two coupled dipole antennas in the echelon form is easil...

Cetacean mother-calf dyads demonstrate formation locomotion that may provide hydrodynamic and/or social benefits. For example, echelon position (calf in close proximity of its mother’s mid-lateral flank) enables calves to increase swim performance at reduced locomotor effort compared to periods of solitary swimming. Yet cetacean mother-calf dyads are also observed in infant position (calf in cl...

The paper addresses the issue of stability for re-entrant flow lines, producing multiple products, with capacitated machines, random demand and random yield. The policies of interest are multi-echelon base stock policies, combined with a set of static and dynamic management rules of the available capacity. We introduce three classes of capacitated echelon base stock policies: Π0, the pure multi...

In today’s globalization, the success of an industry is dependent on cost effective supply chain management under various markets, logistics and production uncertainties. Uncertainties in the supply chain usually decrease profit, i.e. increase total supply chain cost. Demand uncertainty and constraints posed by the every echelon are important factors to be considered in the supply chain design ...