A robust fuzzy optimization model for carbon-efficient closed-loop supply chain network design problem: a numerical illustration in electronics industry

Highlights

• A novel bi-objective facility location-allocation model for CLGSC network design problem.

• All the sources that may emit carbon dioxide are used to the CLGSC network.

• The inherent uncertainty of input data is taken into account by a robust and fuzzy programming.

• A case study of Copiers Industry is used to show the applicability of the proposed model.

• Sensitivity analysis with regards to key parameters is performed in the case study.

Abstract

Environmentalism has become an important global issue in the present century. During the recent years, the closed-loop green supply chain management has been increasingly a center of attention as a result of governmental laws and legislations (regarding the environmental effects of any activity) and the soaring consumers' expectations. In this study, effort has been made to investigate a facility location/allocation model for a multi-product closed-loop green supply chain network consisting of manufacturing/remanufacturing and collection/inspection centers as well as disposal center and markets. To design the network, we have proposed a mixed-integer linear programming model capable of reducing the network total costs. The model has been so developed as to consider such environmental objectives as reducing the rate of carbon dioxide emission in the environment throughout the network in question. Moreover, the model has been developed using a robust fuzzy programming approach to investigate the effects of uncertainties of the variable costs, as well as the demand rate, on the network design. To solve the bi-objective programming model, use has been made of the ε-constraint approach and a numerical illustration of Copiers Industry is used to show the applicability of the proposed optimization model. Results have revealed that the model is capable of controlling the network uncertainties as a result of which a robustness price will be imposed on the system.

Introduction

In supply chain management, to meet customers' demands and improve the general performance of a supply chain (SC), effort should be made to integrate its organizational units and coordinate material, information, and financial flows through proper management (Stadtler, 2005). In general, SC network flows are either forward (FSC) or reverse (RSC); the former encompasses all activities due to which raw materials turn into final products and managers try to improve its performance through demand management, procurement, and order fulfillment, but the latter on the other hand, deals with such activities as the collection and recycling of the returned products (Abdallah et al., 2012). The literature devoted to the RSC networks can be divided into problems that completely concentrate on the reverse flow (i.e. recovery logistics) and those in which the reverse flow is integrated with the forward flow (i.e. closed-loop logistics). Economic aspects, governmental laws and legislations such as the waste electrical and electronic equipment (WEEE) and end-of life vehicles (ELV) directives of the EU (European Union, 2008), and consumers' expectances are the three important factors in the recovery and closed-loop logistics (Melo et al., 2009).

Expansion of the frontiers of knowledge from Forward SC Networks to Reverse, Closed-Loop, and Green has caused Companies and Agencies to gain considerable and desirable economical and environmental achievements. Undoubtedly, this trend has had a significant role in the creation and formation of the sustainable SC management paradigm. In addition to economical and environmental issues, social aspects too are subjects of the sustainable SC network studies and studying the related literature can be of great help to the researchers of this domain (Brandenburg, 2015, Brandenburg and Rebs, 2015).

According to a research carried out in this area, the electric and electronic equipment waste is the third biggest source of environmental pollutant (after transportation and food consumption) and closed-loop supply chain network (CLSC) management can minimize, through remanufacturing process, the amount of the waste materials (Quariguasi Frota Neto et al., 2010). On the other hand, globalization of the supply chain has considerably increased the number of network nodes and its inter-nodal transportation which has caused the emission of an increased volume of greenhouse gases especially CO₂. Therefore, design of closed-loop and green SC networks can be an effective step in the future improvements of the environment situation. Most traditional closed-loop SCND (supply chain network design) problems' optimization models have a single objective of minimizing costs through meeting the customers' demands; however, in recent decades, researchers have been trying to add other objectives of minimizing the negative environmental and social effects (e.g. Zhu et al., 2007; Hutchins and Sutherland, 2008; Brandenburg et al., 2014, Eskandarpour et al., 2015).

Controlling uncertain parameters is another serious problem in the closed-loop green SCND; uncertainties in supply (delays in sending raw materials or products), in production and distribution processes, in demand estimation and, especially, in quality and quantity of the returned products are only some samples in CLSC network design problems. Hence, the complex and dynamic nature of the supply chain impose high degrees of uncertainty on the supply chain decisions and considerably affect the performance of the entire network (Özkır and Başlıgil, 2013).

SC decisions are strategic, tactical, or operational. Short term decisions are usually operational and their time intervals vary from approximately 1 h to 1 or 2 days (e.g. order fulfillment and truck scheduling). Medium term decisions are often tactical and their time intervals vary from approximately 1 week to a few months. Long term decisions are strategic and require a time interval of 3–5 years (e.g. facility location). Obviously, the effects of uncertainties on long-term decisions are by far more than on the short-term ones (Pishvaee et al., 2010). Hence, not considering uncertainties at operational levels incurs costs, but not much because the system corrects itself in a short period of time (the cost is incurred in a short duration). But, if uncertainties are ignored at strategic (long term) levels, the damage to the system (cost incurred) is irrecoverable; therefore, designing a reliable supply chain network that can properly function, even when some parameters change, seems necessary.

According to the existing literature, such different mathematical programming approaches as the stochastic, fuzzy and robust optimization models have been utilized to tackle the closed-loop green SCND related uncertainties and researchers have been recently attempting to combine them to attain more efficient models. In this paper, we have proposed a robust fuzzy optimization model for carbon-efficient CLSC network under uncertain conditions which can minimize the total cost in the first objective and carbon dioxide emission in the second.

The remainder of this paper has been organized as follows: the literature related to the CLSC under certain/uncertain conditions has been reviewed in Section 2, the proposed problem has been fully explained and modeled in Section 3, the research methodology including model formulation, uncertainty modeling, solution method, and application has been thoroughly presented in Section 4, the model results and computational performance are analyzed in Section 5, and the paper conclusions are provided in Section 6.