Seite - 165 - in Algorithms for Scheduling Problems

algorithms Article Entropy-BasedAlgorithmforSupply-Chain ComplexityAssessment BorisKriheli 1 andEugeneLevner2,* 1 SchoolofEconomics,AshkelonAcademicCollege,Ashkelon84101, Israel;borisk@hit.ac.il 2 DepartmentofComputerScience,HolonInstituteofTechnology,Holon58102, Israel * Correspondence: levner@hit.ac.il;Tel.:+972-2-583-2290 Received: 28February2018;Accepted: 21March2018;Published: 24March2018 Abstract:Thispaperconsidersagraphmodelofhierarchical supplychains. Thegoal is tomeasure thecomplexityof linksbetweendifferentcomponentsof thechain, for instance,betweentheprincipal equipmentmanufacturer (arootnode)andits suppliers (precedingsupplynodes). The information entropy isusedtoserveasameasureofknowledgeabout thecomplexityof shortagesandpitfalls in relationshipbetweenthesupplychaincomponentsunderuncertainty. Theconceptofconditional (relative)entropyis introducedwhich isageneralizationof theconventional (non-relative)entropy. An entropy-based algorithmproviding efficient assessment of the supply chain complexity as a functionof theSCsize isdeveloped. Keywords: industrial supplychain; supplychaincomplexity; informationentropy 1. Introduction Thispaperpresents theentropy-basedoptimizationmodel forestimatingstructural complexity ofsupplychain (SC),and, inparticular, complexityof relationshipbetweentheprincipalequipment manufacturer (arootnode)anditssuppliers (precedingsupplynodes). The informationentropyis usedasameasureofdecisionmaker’sknowledgeabout therisksof shortagesandpitfalls inrelations betweenthesupplychaincomponentsunderuncertainty, themainattentionbeingpaidtorelationships betweentheprincipalequipmentmanufacturer (arootnodeof thecorrespondinggraphmodel)and its suppliers.Aconceptof theconditional (relative)entropyis introducedwhich isageneralizationof theconventional (non-relative)entropythatprovidesmorepreciseestimationofcomplexity insupply chainsas it takes intoaccount informationflowsbetweenthecomponentsofdifferent layers.Amain advantageof thesuggestedentropy-basedapproach is that it canessentiallysimplify thehierarchical tree-likemodelof thesupplychain,at thesametimeretainingthebasicknowledgeaboutmainsources of risks in inter-layerrelationships. Processesofproduction, storage, transportation,andutilizationofproducts inSCsmayleadto many negative effects on the environment, such as emissions of pollutants into the air and soil; discharges of pollutants into surface and groundwater basins; pollution of soil andwater with wasteproductsofproduction, all thesephenomena in their entiretydeteriorating therelationships betweenmanufacturingcomponentsandtheirsuppliers. Theseandmanyotherriskysituations for manufacturing lead to theuncertainty in SC’s phases, i.e., engineering, procurement, production, anddistribution[1]. Theentropicapproachdevelopedin thispaperaimsatdefiningthebest (minimal but sufficient) level of information going through the several supply chain phases. This paper analyzes the structural complexity of the supply chain affected by technological, organizational andenvironmentaladverseevents in theSCs,consequencesofwhich lead,asaresult, toviolations ofcorrect functioningof theSC.Thedetaileddefinitionandanalysisof thesupply-chainstructural complexitycanbefoundin[2–10]. Algorithms 2018,11, 35;doi:10.3390/a11040035 www.mdpi.com/journal/algorithms165