# Optimizing a Reverse Supply Chain Network for Electronic Waste under Risk and Uncertain Factors
## 3 A Developed Mathematical Model
\begin{tabular}{l l} \(B1_{cd}\) & distance \(c\)-\(d\); \\ \(B2_{ds}\) & distance \(d\)-\(s\); \\ \(B3_{dc}\) & distance \(d\)-\(e\); \\ \(B4_{dr}\) & distance \(d\)-\(r\); \\ \(B5_{dl}\) & distance \(d\)-\(l\); \\ \(B6_{cs}\) & distance \(e\)-\(s\); \\ \(B7_{m}\) & distance \(r\)-\(m\); \\ \(B8_{nl}\) & distance \(r\)-\(l\); \\ \(\widetilde{A}_{pc}\) & the amount of used product \(p\) at collection center \(c\); \\ \(\widetilde{c1}_{up}\) & the average unit of reused item \(u\) obtained from the used product \(p\); \\ \(\widetilde{c2}_{up}\) & the average unit of renewable item \(w\) obtained from the used product \(p\); \\ \(\widetilde{c3}_{ip}\) & the average unit of recycling material \(i\) obtained from the used product \(p\); \\ \(\widetilde{c4}_{lp}\) & the average unit of disposal item \(h\) obtained from the used product \(p\); \\ \(\widetilde{p}_{h}\) & the average fraction of disposal item \(h\) obtained from recycling center; \\ \(\widetilde{p}_{i}\) & the average fraction of recycling material \(i\) obtained at recycling center; \\ \(\widetilde{N}u_{ss}\) & maximum demand for reused item \(u\) at secondary market \(s\); \\ \(\widetilde{N}w_{ws}\) & maximum demand for renewable component \(w\) at secondary market \(s\); \\ \(\widetilde{N}lim\) & maximum demand for recycling material \(i\) at main market \(m\); \\ \(\widetilde{K}d_{pd}\) & maximum capacity of used product \(p\) at dismantling center \(d\); \\ \(\widetilde{K}e_{uv}\) & maximum capacity of renewable item \(w\) at repairing center \(e\); \\ \(\widetilde{K}r_{ir}\) & maximum capacity of recycling material \(i\) at recycling center \(r\); \\ \(\widetilde{K}l_{hl}\) & maximum capacity of disposal item \(h\) at landfill site \(l\); \\ \(\widetilde{P1}_{d}\) & the possibility of an unexpected event occurred at dismantling center \(d\); \\ \(\widetilde{P2}_{e}\) & the possibility of an unexpected event occurred at repairing center \(e\); \\ \(\widetilde{P3}_{r}\) & the possibility of an unexpected event occurred at recycling center \(r\); \\ \(\widetilde{P4}_{cd}\) & the possibility of an unexpected event occurred on the way \(c\)-\(d\); \\ \(\widetilde{P5}_{ds}\) & the possibility of an unexpected event occurred on the way \(d\)-\(s\); \\ \(\widetilde{P6}_{de}\) & the possibility of an unexpected event occurred on the way \(d\)-\(e\); \\ \(\widetilde{P7}_{du}\) & the possibility of an unexpected event occurred on the way \(d\)-\(r\); \\ \(\widetilde{P8}_{dl}\) & the possibility of an unexpected event occurred on the way \(d\)-\(l\); \\ \(\widetilde{P9}_{es}\) & the possibility of an unexpected event occurred at resampling center \(r\); \\ \(\widetilde{I1}_{d}\) & the impact of an unexpected event occurred at recycling center \(r\); \\ \(\widetilde{I2}_{e}\) & the impact of an unexpected event occurred at recycling center \(e\); \\ \(\widetilde{I3}_{r}\) & the impact of an unexpected event occurred at recycling center \(r\); \\ \(\widetilde{I4}_{cd}\) & the impact of an unexpected event occurred on the way \(c\)-\(d\); \\ \(\widetilde{I5}_{ds}\) & the impact of an unexpected event occurred on the way \(d\)-\(s\); \\ \(\widetilde{I6}_{de}\) & the impact of an unexpected event occurred on the way \(d\)-\(e\); \\ \(\widetilde{I7}_{dr}\) & the impact of an unexpected event occurred on the way \(d\)-\(r\); \\ \(\widetilde{I8}_{dl}\) & the impact of an unexpected event occurred on the way \(d\)-\(l\); \\ \(\widetilde{I9}_{es}\) & the impact of an unexpected event occurred on the way \(e\)-\(s\); \\ \(\widetilde{I10}_{rm}\) & the impact of an unexpected event occurred on the way \(r\)-\(m\); \\ \(\widetilde{I11}_{rl}\) & the impact of an unexpected event occurred on the way \(r\)-\(l\). \\ \end{tabular}   
Based on the four-tier RSC network, the main goal of the developed model is to suggest a mathematical model to minimize the overall cost through the entire RSC system.