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Closing the loop of a global supply chain through a robust optimal decentralized decision support system

  • Recent Advances in Viable and Sustainable Supply Chain Management
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Abstract

This paper presents a novel decentralized decision support system to optimally design a general global closed-loop supply chain. This is done through an original risk-based robust mixed-integer linear programming that is formulated based on an initial uncertain bi-level programming. Addressing the decision-maker’s (DM’s) attitude toward risk, a scenario-based conditional value-at-risk is used to deal with demand and return uncertainty. Also, the Karush–Kuhn–Tucker (KKT) conditions are employed to transform the model into its single-level counterpart. The results obtained from solving a numerical example through the proposed framework are compared with those of the corresponding centralized system, which is formulated through deterministic multi-objective programming and solved by the Lp-metric method. The results show that the use of the proposed framework improves the robustness of profit, income, and cost by about 28%, 34%, and 36% on average. However, a more conservative DM faces a larger cost of robustness than an optimistic DM while experiencing a more significant improvement in the system responsiveness. Using the proposed framework, the manager can measure the advantages, disadvantages, and consequences of their decisions before their actual implementation. This is because the model is capable of establishing fundamental trade-offs among risk, cost, profit, income, robustness, and responsiveness according to the DM’s attitude toward risk.

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Abbreviations

RQ:

Research question

SC:

Supply chain

RO:

Robust optimization

CLSC:

Closed-loop supply chain

CLSCND:

Closed-loop supply chain network design

GCLSC:

Global closed-loop supply chain

DSS:

Decision support system

GCLSCND:

Global closed-loop supply chain network design

GSCN:

Global supply chain network

VaR:

Value-at-risk

CVaR:

Conditional value-at-risk

DM:

Decision-maker

MILP:

Mixed integer-linear programming

BLP:

Bi-level programming

KKT:

Karush–Kuhn–Tucker

\(s\in \left\{1,\cdots s,\cdots ,S\right\}\) :

Index of suppliers

\(p\in \left\{1,\cdots p,\cdots ,P\right\}\) :

Index of products

\(f\in \left\{1,\cdots f,\cdots ,F\right\}\) :

Index of manufacturers

\(b\in \left\{1,\cdots b,\cdots ,B\right\}\) :

Index of distribution centers

\(m\in \left\{1,\cdots m,\cdots ,M\right\}\) :

Index of markets

\(g\in \left\{1,\cdots g,\cdots ,G\right\}\) :

Index of collection centers

\(n\in \left\{1,\cdots n,\cdots ,N\right\}\) :

Index of countries

\(t\in \left\{1,\cdots t,\cdots ,T\right\}\) :

Index of times

\(o\in \left\{1,\cdots o,\cdots ,O\right\}\) :

Index of disposal centers

\(\tau \in \left\{1,\cdots o,6\right\}\) :

Index of cost functions

\({q}_{sfpt}^{(1)}\) :

Number of product p purchased for manufacturer f from supplier s at time t

\({q}_{fbpt}^{(2)}\) :

Number of product p produced by manufacturer f for distribution center b at time t

\({q}_{bmpt}^{(3)}\) :

Number of product p distributed from distribution center b to market m at time t

\({q}_{mgpt}^{(4)}\) :

Number of returned product p from market m to collection center g at time t

\({q}_{gopt}^{(5)}\) :

Number of returned product p from collection center g to disposal center o at time t

\({q}_{gfpt}^{(6)}\) :

Number of returned product p from collection center g to manufacturer f at time t

\({X}_{f}\) :

Binary variable to define whether manufacturer f is opened

\({Y}_{b}\) :

Binary variable to define whether distribution center b is opened

\({Z}_{g}\) :

Binary variable to define whether disposal center g is opened

Income:

System’s total income

\({\Psi }_{1}\) :

Facilities’ total opening cost

\({\Psi }_{2}\) :

Products’ total purchasing, transportation, and customs duties cost

\({\Psi }_{3}\) :

Total production and logistics cost from manufacturers to distribution centers

\({\Psi }_{4}\) :

Returned products’ total cost of transportation to collection centers

\({\Psi }_{5}\) :

Products’ total disposal and the relative transportation cost

\({\Psi }_{6}\) :

Sum of saved and transportation costs of returned products to manufacturers

\(\begin{array}{c}{Z}^{leader}\\ {Z}^{lead{er}^{*}}\end{array}\) :

Leader’s objective function/optimal objective function value

\(\begin{array}{c}{Z}^{follower}\\ {Z}^{follow{er}^{*}}\end{array}\) :

Follower’s objective function/optimal objective function value

\(\begin{array}{c}{\gamma }_{leader}\\ {\gamma }_{follower}\end{array}\) :

Objectives’ importance weights

\(Z\) :

The objective function of the mono-objective model resulting from the initial bi-objective one

\({t}_{sfp}^{de}\) :

Delivery time of product p from supplier s to manufacturer f (Month)

\({\rho }_{p}^{se}\) :

The selling price of product p ($)

\({c}_{f}^{mnu}\) :

Opening cost of manufacturer f ($)

\({c}_{b}^{dis}\) :

Opening cost of distribution center b ($)

\({c}_{g}^{col}\) :

Opening cost of collection center g ($)

\({c}_{spn}^{pu}\) :

The unit purchasing cost of product p from supplier s in country n ($)

\({r}_{bspn}^{cd}\) :

Customs duty rate of product p from supplier s in country n

\({c}_{psfn}^{tr (1)}\) :

Unit transportation cost of product p from supplier s to manufacturer f in country n ($)

\({c}_{pfb}^{tr (2)}\) :

Unit transportation cost of product p from manufacturer f to distribution center b ($)

\({c}_{pbm}^{tr (3)}\) :

Unit transportation cost of product p from distribution center b to market center m ($)

\({c}_{pmg}^{tr (4)}\) :

Unit transportation cost of product p from market center m to collection center g ($)

\({c}_{pgo}^{tr (5)}\) :

Unit transportation cost of product p from collection center g to disposal center o ($)

\({c}_{pgf}^{tr (6)}\) :

Unit transportation cost of product p from collection center g to manufacturer f ($)

\({c}_{p}^{pr}\) :

The unit production cost of product p ($)

\({c}_{p}^{o}\) :

Unit disposal cost of product p ($)

\({d}_{sfn}^{(1)}\) :

Distance between supplier s and manufacturer f in country n (× 100 km)

\({d}_{fb}^{(2)}\) :

Distance between manufacturer f and distribution center b (× 100 km)

\({d}_{bm}^{(3)}\) :

Distance between distribution center b and market center m (× 100 km)

\({d}_{mg}^{(4)}\) :

Distance between market m and collection center g (× 100 km)

\({d}_{go}^{(5)}\) :

Distance between collection center g and disposal center o ( x 100 km)

\({d}_{gf}^{(6)}\) :

Distance between collection center g and manufacturer f (× 100 km)

\({a}_{p}\) :

Cost-saving of product p due to its recovery ($)

\({o}_{p}\) :

Minimum disposal fraction of product p

\({{\boldsymbol{v}}}_{fp}^{(1)}\) :

The capacity of manufacturer f for product p

\({{\boldsymbol{v}}}_{bp}^{(2)}\) :

The capacity of distribution center b for product p

\({{\boldsymbol{v}}}_{gp}^{(3)}\) :

The capacity of collection center g for product p

\({r}_{n}^{ex}\) :

Exchange rate of country n

\(\mathcal{X}\) :

Returned products ratio

\({\widetilde{\delta }}_{mpt}\) :

Uncertain demand of product p from market m at time t

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    Hêriş Golpîra

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Golpîra, H. Closing the loop of a global supply chain through a robust optimal decentralized decision support system. Environ Sci Pollut Res 30, 89975–90005 (2023). https://doi.org/10.1007/s11356-022-23176-5

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