A Network-Based Impact Measure for Propagated Losses in a Supply Chain Network Consisting of Resilient Components

Jesus Felix Bayta Valenzuela, Xiuju Fu, Gaoxi Xiao, Rick Siow Mong Goh

Abstract: The topology of a supply chain network affects the impacts of disruptions in it. We formulate a network-based measure of the impact of a disruption loss in a supply chain propagating downstream from an originating node. The measure takes into account the loss profile of the originating node, the structure of the supply network, and the resilience of the network components. We obtain an analytical expression for the impact measure under a beta-distributed initial loss (generalizable to any continuous distribution supported on the interval <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-2.15067pt" id="M1" height="11.439pt" version="1.1" viewBox="-0.0498162 -9.28833 26.7843 11.439" width="26.7843pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-92" d="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 675V703H120V-163H290Z"/></g><g transform="matrix(.013,0,0,-0.013,4.485,0)"><path id="g113-49" d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"/></g><g transform="matrix(.013,0,0,-0.013,10.725,0)"><path id="g113-45" d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"/></g><g transform="matrix(.013,0,0,-0.013,15.868,0)"><path id="g113-50" d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"/></g><g transform="matrix(.013,0,0,-0.013,22.166,0)"><path id="g113-94" d="M226 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H226Z"/></g></svg>), under a breakthrough scenario (in which a fraction of the initial production loss reaches a focal company downstream as opposed to containment upstream or at the originating point). Furthermore, we obtain a closed-form solution for a supply chain network with a <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063999pt" id="M2" height="9.49473pt" version="1.1" viewBox="-0.0498162 -9.28833 6.66314 9.49473" width="6.66314pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-108" d="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z"/></g></svg>-ary tree topology; a numerical study is performed for a scale-free network and a random network. Our proposed approach enables the evaluation of potential losses for a focal company considering its supply chain network structure, which may help the company to plan or redesign a robust and resilient network in response to different types of disruptions.