MODELING INVENTORY INFORMATION VISIBILITY IN SUPPLY CHAIN NETWORKS By SANDEEP SRIVATHSAN Bachelor of Engineering University of Madras Chennai, Tamil Nadu, India May 2002 Master of Science Oklahoma State University Stillwater, Oklahoma, USA December 2004 Submitted to the Faculty of the Graduate College of Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY May, 2012 COPYRIGHT c By SANDEEP SRIVATHSAN May, 2012 MODELING INVENTORY INFORMATION VISIBILITY IN SUPPLY CHAIN NETWORKS Dissertation Approved: Dr. Manjunath Kamath Dissertation advisor Dr. Ramesh Sharda Dr. Ricki Ingalls Dr. Tieming Liu Dr. Balabhaskar Balasundaram Dr. Sheryl A. Tucker Dean of the Graduate College iii TABLE OF CONTENTS Chapter Page 1 INTRODUCTION 1 1.1 Information Sharing in Supply Chains . 4 1.2 Performance Evaluation and Performance Optimization Models . 5 1.3MotivationfortheProposedResearch.................. 6 1.3.1 ProblemStatement........................ 7 1.4OutlineoftheDissertation........................ 7 2 LITERATURE REVIEW 9 2.1LiteratureonValueofInformationSharing............... 9 2.2 Modeling Production-Inventory and Supply Chain Networks . 14 2.2.1 ModelingProduction-InventoryNetworks............ 14 2.2.2 Modeling Supply Chain Networks and its Constituents . 20 2.3SummaryoftheLiteratureReview................... 23 3 RESEARCH STATEMENT 25 3.1ResearchObjectives............................ 25 3.2ResearchScope.............................. 29 3.3ResearchContributions.......................... 29 4 RESEARCH APPROACH 30 4.1ResearchMethodology.......................... 30 4.1.1 MarkovChainApproach..................... 31 4.1.2 Parametric Decomposition Approach . 32 iv 4.2PerformanceMeasures.......................... 34 4.3NumericalValidationProcedure..................... 36 5 CTMC MODELS OF THE 1R/2P SCN CONFIGURATION 37 5.11R/2PSCNStructure.......................... 37 5.2 CTMC Model for Poisson Arrivals and Exponential Processing Times 38 5.3CTMCModelof1R/2PSCNwithHiVis................ 44 5.4CTMCModelofthe1R/2PSCNwithMedVis............. 48 5.5CTMCModelofthe1R/2PSCNwithLoVis.............. 53 5.6 CTMC Model of the 1R/2P SCN with NoVis . 58 5.7ValueofInformationSharing....................... 63 5.8Conclusions................................ 70 6 QUEUEING MODELS OF THE 1R/2P SCN CONFIGURATION WITH POISSON ARRIVALS AND EXPONENTIAL PROCESS- ING TIMES 71 6.1 Queueing Model of the 1R/2P SCN Configuration with HiVis . 71 6.1.1 Validation of the M/M/2 Approximation of the 1R/2P SCN ConfigurationwithHiVis..................... 76 6.1.2 Queueing Model of SCN with Lower Levels of Information Sharing 79 6.2AnAsymmetric1R/2PSCNConfiguration............... 92 6.2.1 ModelValidation......................... 98 6.3Conclusions................................ 103 7 QUEUEING MODELS OF THE 1R/2P SCN CONFIGURATION WITH GENERAL INTER-ARRIVAL AND PROCESSING TIME DISTRIBUTIONS 105 7.1 Queueing Model of the General 1R/2P SCN Configuration with HiVis 105 7.1.1 Validation of the GI/G/2 Approximation . 107 v 7.2 Queueing Model of a General 1R/2P SCN Configuration with NoVis . 108 7.2.1 QueueingModel.......................... 109 7.3 Effect of Inter-arrival Time and Processing Time SCVs on the Value ofInformationSharing.......................... 111 7.4Conclusions................................ 116 8 ANALYTICAL MODELS OF THE 2R/2P SCN CONFIGURATION122 8.12R/2PSCNStructure.......................... 122 8.2 Analytical Model for Poisson Arrivals and Exponential Processing Times123 8.2.1 Queueing Model of the 2R/2P SCN Configuration with HiVis 124 8.2.2 Validation of the M/M/2 Approximation . 129 8.3 Queueing Model of the 2R/2P SCN Configuration with Lower Levels ofInformationSharing(MedVisandLoVis).............. 135 8.4 Analytical Model for General Inter-Arrival and Processing Time Dis- tributions................................. 140 8.4.1 Validation of the GI/G/2 Approximation . 143 8.4.2 InsightsfromtheAnalyticalModel............... 144 8.5Conclusions................................ 148 9 MODELING TRANSIT TIMES IN SCNs WITH INVENTORY IN- FORMATION SHARING 151 9.1 Analytical Model of 1R/2P SCN Configuration with Transit Delay . 151 9.1.1 Effect of Transit Delay on the Performance of the Retail Stores inthe1R/2PConfiguration................... 154 9.2 Analytical Model of the 2R/2P SCN Configuration with Transit Delays 156 9.2.1 Effect of Transit Delays on the Performance of the Retail Stores inthe2R/2PConfiguration................... 159 9.3Conclusions................................ 162 vi 10 CONCLUSIONS 165 10.1SummaryofResearch........................... 165 10.2ResearchContributions.......................... 167 10.3FutureResearch.............................. 168 BIBLIOGRAPHY 171 A DETERMINATION OF THE PARAMETERS FOR SIMULATION EXPERIMENTS 179 A.1 Determination of the Warm-up Period using Welch’s Method . 180 A.2DeterminationoftheRunLength.................... 181 B CTMC MODEL RESULTS FOR THE 1R/2P SCN CONFIGURA- TION 182 B.1 Validation of the CTMC Model of 1R/2P SCN Configuration with HiVis182 B.2 Validation of the CTMC Model of 1R/2P SCN Configuration with MedVis.................................. 184 B.3 Validation of the CTMC Model of 1R/2P SCN Configuration with LoVis185 B.4 CTMC Model Results for 1R/2P SCN Configuration with NoVis . 187 C QUEUEING RESULTS FOR THE 1R/2P SCN CONFIGURATION WITH POISSON ARRIVALS AND EXPONENTIAL PROCESS- ING TIMES 188 C.1 Validation of the M/M/2 Approximation . 188 C.2 Validation of the Modified M/M/2 Model . 191 C.3 Validation of the M/G/2 based model for the 1R/2P SCN with Het- erogeneous Production Facilities . 194 D QUEUEING RESULTS FOR THE SCN CONFIGURATION 1R/2P: GENERAL INTER-ARRIVAL AND PROCESSING TIME DIS- vii TRIBUTIONS 199 E QUEUEING RESULTS FOR THE 2R/2P SCN CONFIGURATION218 E.1 Results for the Validation of the M/M/2 based Queueing Model for the2R/2PSCNConfiguration...................... 218 E.2 Results for the Validation of the Modified M/M/2 Model for the 2R/2P SCNConfiguration............................ 222 E.3 Results for the Validation of the GI/G/2 based Model for the 2R/2P SCNConfiguration............................ 225 F QUEUEING RESULTS FOR SCN CONFIGURATIONS WITH TRAN- SIT TIME 274 F.1 Validation of the Analytical Model for the 1R/2P SCN Configuration withTransitTime............................ 274 F.2 Validation of the Analytical Model for the 2R/2P SCN Configuration withTransitTime............................ 279 viii LIST OF TABLES Table Page 3.1 Order Routing Policy for SCN with Low Level of Inventory Information Sharing.................................. 27 3.2 Order Routing Policy for SCN with Medium Level of Inventory Infor- mationSharing.............................. 27 3.3 Order Routing Policy for SCN with High Level of Inventory Informa- tionSharing................................ 28 5.1 Rate Balance Equations for the Reduced CTMC Model of the 1R/2P SCNwithHiVis.............................. 47 5.2 Rate Balance Equations of the Reduced CTMC Model of the 1R/2P SCNwithMedVis............................. 51 5.3 Rate Balance Equations of the Reduced CTMC Model of the 1R/2P SCNwithLoVis.............................. 56 5.4 Rate Balance Equations of the CTMC Model of the 1R/2P SCN with NoVis................................... 59 6.1 Experiments for the 1R/2P SCN Configuration under Poisson Arrivals andExponentialProcessingTimes................... 77 6.2 Dependence of π0, 0 on the Base-stock Level and Production Facility Utilization . 83 6.3 Experiments for the Asymmetric 1R/2P SCN Configuration . 98 6.4SummaryofResults........................... 104 ix 7.1 1R/2P SCN Experiments for General Inter-arrival and Processing Time Distributions............................... 108 7.2SummaryofResults........................... 108 8.1 Experiments for the 2R/2P SCN Configuration under Poisson Arrivals andExponentialProcessingTimes................... 129 8.2 Experiments for 2R/2P SCN configuration under General Inter-arrival andProcessingTimeDistributions................... 143 8.3SummaryofResults........................... 144 9.1 Experiments for 1R/2P SCN Configuration with Transit Delay . 153 9.2SummaryofResults........................... 153 9.3 Experiments for the 2R/2P SCN Configuration with Transit Delay . 159 9.4SummaryofResults........................... 159 B.1 Validation of CTMC Model of SCN with HiVis (Production Facility) 183 B.2 Validation of CTMC Model of SCN with HiVis (Retail Store) . 183 B.3 Validation of CTMC Model of SCN with MedVis (Production Facility) 184 B.4 Validation of CTMC Model of SCN with MedVis (Retail Store) . 185 B.5 Validation of CTMC Model of SCN with LoVis (Production Facility) 186 B.6 Validation of CTMC Model of SCN with LoVis (Retail Store) . 186 B.7 Exact Results for the SCN with NoVis (Production Facility) . 187 B.8 Exact Results for the SCN with NoVis (Retail Store) . 187 C.1 Fill Rate and Expected Number of Backorders at the Retail Store . 189 C.2 Expected Inventory Level and Expected Time to Fulfill a Backorder at theRetailStore.............................. 189 C.3 Fill Rate and Expected Number of Backorders at a Production Facility 190 x C.4 Expected Inventory Level and Expected Time to Fulfill a Backorder at a Production Facility . 190 C.5 Expected Time Spent by an Order at the Retail Store and a Production Facility . 191 C.6 Fill Rate and Expected Number of Backorders at the Retail Store . 192 C.7 Expected Inventory Level and Expected Time to Fulfill a Backorder at theRetailStore.............................. 192 C.8 Fill Rate and Expected Number of Backorders