Inventory and Production Dynamics in a Discrete-Time Vendor-Managed Inventory Supply Chain System

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/ddns/volume-2018/6091946/figures/6091946.fig.003a.svgz" name="6091946.fig.003a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Production and order dynamics when <svg height="11.7782pt" id="M235" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 28.3196 11.7782" width="28.3196pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M516 277C516 378 460 448 376 448C335 448 288 434 240 401C158 345 127 277 107 159C53 -161 38 -221 23 -247L28 -261C43 -260 95 -250 114 -226C122 -216 129 -199 146 -75C152 -29 157 0 164 31C182 9 206 -12 237 -12C267 -12 325 8 376 46C451 102 516 179 516 277ZM432 259C432 134 366 40 259 40C236 40 204 48 171 76L195 203C219 327 253 400 326 400C398 400 432 336 432 259Z" id="g113-239"></path></g><g transform="matrix(.013,0,0,-0.013,10.642,0)"><path d="M512 -3V55L134 254V256L512 456V514L75 281V230L512 -3Z" id="g117-91"></path></g><g transform="matrix(.013,0,0,-0.013,21.905,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path></g></svg></td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/ddns/volume-2018/6091946/figures/6091946.fig.003b.svgz" name="6091946.fig.003b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Inventory dynamics when <svg height="11.7782pt" id="M236" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 28.3196 11.7782" width="28.3196pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M516 277C516 378 460 448 376 448C335 448 288 434 240 401C158 345 127 277 107 159C53 -161 38 -221 23 -247L28 -261C43 -260 95 -250 114 -226C122 -216 129 -199 146 -75C152 -29 157 0 164 31C182 9 206 -12 237 -12C267 -12 325 8 376 46C451 102 516 179 516 277ZM432 259C432 134 366 40 259 40C236 40 204 48 171 76L195 203C219 327 253 400 326 400C398 400 432 336 432 259Z" id="g113-239"></path></g><g transform="matrix(.013,0,0,-0.013,10.642,0)"><path d="M512 -3V55L134 254V256L512 456V514L75 281V230L512 -3Z" id="g117-91"></path></g><g transform="matrix(.013,0,0,-0.013,21.905,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path></g></svg></td></tr><tr class="fig-image" id="c"><td><object data="https://static.hindawi.com/articles/ddns/volume-2018/6091946/figures/6091946.fig.003c.svgz" name="6091946.fig.003c" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(c) </b>Production and order dynamics when <svg height="11.7782pt" id="M237" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 28.3196 11.7782" width="28.3196pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M516 277C516 378 460 448 376 448C335 448 288 434 240 401C158 345 127 277 107 159C53 -161 38 -221 23 -247L28 -261C43 -260 95 -250 114 -226C122 -216 129 -199 146 -75C152 -29 157 0 164 31C182 9 206 -12 237 -12C267 -12 325 8 376 46C451 102 516 179 516 277ZM432 259C432 134 366 40 259 40C236 40 204 48 171 76L195 203C219 327 253 400 326 400C398 400 432 336 432 259Z" id="g113-239"></path></g><g transform="matrix(.013,0,0,-0.013,10.642,0)"><path d="M512 230V281L75 514V456L453 256V254L75 55V-3L512 230Z" id="g117-92"></path></g><g transform="matrix(.013,0,0,-0.013,21.905,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path></g></svg></td></tr><tr class="fig-image" id="d"><td><object data="https://static.hindawi.com/articles/ddns/volume-2018/6091946/figures/6091946.fig.003d.svgz" name="6091946.fig.003d" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(d) </b>Inventory dynamics when <svg height="11.7782pt" id="M238" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 28.3196 11.7782" width="28.3196pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M516 277C516 378 460 448 376 448C335 448 288 434 240 401C158 345 127 277 107 159C53 -161 38 -221 23 -247L28 -261C43 -260 95 -250 114 -226C122 -216 129 -199 146 -75C152 -29 157 0 164 31C182 9 206 -12 237 -12C267 -12 325 8 376 46C451 102 516 179 516 277ZM432 259C432 134 366 40 259 40C236 40 204 48 171 76L195 203C219 327 253 400 326 400C398 400 432 336 432 259Z" id="g113-239"></path></g><g transform="matrix(.013,0,0,-0.013,10.642,0)"><path d="M512 230V281L75 514V456L453 256V254L75 55V-3L512 230Z" id="g117-92"></path></g><g transform="matrix(.013,0,0,-0.013,21.905,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path></g></svg></td></tr></table>

<div>The inventory and production dynamics for the VMI supply chain system.</div>

Discrete Dynamics in Nature and Society

fig3

Figure 3

Figure 3: Inventory and Production Dynamics in a Discrete-Time Vendor-Managed Inventory Supply Chain System 