Closing the loop: Forging high-quality agile virtual enterprises in a reverse supply chain via solution portfolios

Abstract

Reverse supply chains are receiving increased attention for business and sustainability opportunities. As few organizations are adept at both forward and reverse supply chains, subcontracting various activities is imperative. Vendor selection that best achieves combined expertise for reverse supply chains, while quickly forming virtual enterprises to seize market opportunities, is an emerging issue. We formulate a novel 0-1 integer nonlinear optimization model, subsequently linearized to enable efficient computational performance, to select vendors that minimize the maximum formation time for creating agile virtual reverse supply chains. We then generate a portfolio of diverse, high-quality vendor assignments by adapting a recent algorithmic technique, thereby allowing industrial managers to address intangible factors into their final decisions. Computational experiments on simulated data demonstrate the model’s efficiency for generating sets of high-quality and diverse solutions in reasonable timeframes.

Keywords:

• Virtual enterprise
• reverse supply chain
• agile enterprise
• sustainability
• integer programming
• diversity

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 At optimality, $y_s^{*}$ by construction assumes the exact value of the maximum cycle time for each stage $s\in \mathcal{S}.$ This is likely very valuable for practical analysis purposes, such as for examining the largest per-stage cycle times, and especially when comparing multiple high-quality solutions. If this precision in $y_s^{*}$ is not necessary, then constraint sets (19)(19) $$y_s\le t_{\mathit{rsp}}{x}_{\mathit{rsp}}+{\overline{t}}_s\left(1-d_{\mathit{rsp}}\right),\mathrm{}\forall r\in \mathcal{R},s\in \mathcal{S},p\in {\mathcal{P}}_{rs},$$(19) , (20)(20) $$\sum _{r\in \mathcal{R}}\mathrm{\hspace{0.17em}}\sum _{p\in {\mathcal{P}}_{rs}}\mathrm{\hspace{0.17em}}{d}_{\mathit{rsp}}=1,\mathrm{}\forall \mathrm{}s\in \mathcal{S},$$(20) , and the binary $d$ variables may be omitted without impacting the correctness of the model with respect to the optimal assignment decisions $x^{*}$ and minimized maximum formation time $v^{*}.$

2 This information is derived from actual industry sources for cell phones. Canalys. Smart phones overtake client PCs in 2011. Available from: https://www.canalys.com/newsroom/smart-phones-overtake-client-pcs-2011 [cited 2019 July 5].

3 Environmental Protection Agency. Electronics Waste Management in the United States through 2009; May 2011. Available from https://nepis.epa.gov/Exe/ZyPURL.cgi?Dockey=P100BKKL.TXT [cited 2019 July 5].