INVENTORY MANAGEMENT THROUGH EXTENDED STAR-RING SUPPLY CHAIN NETWORK

Objectives: The production-distribution inventory problem has two main sectors namely production and distribution. In this paper, the nonlinearmathematical model of extended star-ring supply chain network is developed.Methods: Planning a distribution network plays a vital role in minimizing the total expenditure of the project; to prove this, a ring network topology is taken to supply goods to the SWs and extended star network topology to supply goods to the selling stores. However, setting up separate SWs for each and every selling store will be highly expensive. Hence, keeping the minimum number of SWs is very important. Selection of SWs from the available SWs is done by replacing diverse values based on the distance limitation.Results: The suggested model is validated with the mathematical problem, and the optimum set of SWs is identified from the result. The result has been substantiated using analytic hierarchy process. Conclusion: The system of optimum number of SWs is obtained from the result.Â

Roman and inverse roman domination in network of triangles

In graph G (V, E), a function f : V → {0, 1 2} is said to be a Roman Dominating Function (RDF). If ∀u ∈ V, f(u) = 0 is adjacent to at least one vertex v ∈ V such that f(v) = 2. The weight of f is given by w(f) = P v∈V f(v). The Roman Domination Number (RDN) denoted by γR(G) is the minimum weight among all RDF in G. If V −D contains a RDF f 1 : V → {0, 1, 2}, where D is the set of vertices v, f(v) > 0, then f 1 is called Inverse Roman Dominating Function (IRDF) on a graph G with respect to the RDF f. The Inverse Roman Domination Number (IRDN) denoted by γ 1 R(G) is the minimum weight among all IRDF in G. In this paper we find RDN and IRDN of few triangulations graphs.Publisher's Versio