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To formulate a real-world optimization problem, it is sometimes necessary to adopt a set of non-linear terms in the mathematical formulation to capture specific operational characteristics of that decision problem. However, the use of non-linear terms generally increases computational complexity of the optimization model and the computational time required to solve it. This motivates the scientific community to develop efficient transformation and linearization approaches for the optimization models that have non-linear terms. Such transformations and linearizations are expected to decrease the computational complexity of the original non-linear optimization models and, ultimately, facilitate decision making. This study provides a detailed state-of-the-art review focusing on the existing transformation and linearization techniques that have been used for solving optimization models with non-linear terms within the objective functions and/or constraint sets. The existing transformation approaches are analyzed for a wide range of scenarios (multiplication of binary variables, multiplication of binary and continuous variables, multiplication of continuous variables, maximum/minimum operators, absolute value function, floor and ceiling functions, square root function, and multiple breakpoint function). Furthermore, a detailed review of piecewise approximating functions and log-linearization via Taylor series approximation is presented. Along with a review of the existing methods, this study proposes a new technique for linearizing the square root terms by means of transformation. The outcomes of this research are anticipated to reveal some important insights to researchers and practitioners, who are closely working with non-linear optimization models, and assist with effective decision making.

As the people are becoming conscious about protection of the environment from pollutant caused by human beings, businesses are adopting green technology to procure green products to save the environment from pollution. Consequently, it is a challenging task at the firm manager to capture the market providing best green quality at fair price in a given economy. The paper plans to discuss two situations in two models. In model 1, the optimal green quality and sales prices of the manufacturer and the retailer in both decentralize and centralize systems of a two-echelon supply chain system are investigated. The profit functions of the manufacturer and the retailer include procurement costs, selling prices and cost for green level development and then it is analyzed by calculus method to obtain the optimal values of the decision variables. The model 2 focuses on price competition of two substitute products where demand of the end customers depends on price and quality of green product. Both the firms of green and regular products manufacturer are corporate social responsible. In this model, profit functions of the firms 1 & 2 are formulated separately considering revenues from sales items, cost of green quality and contribution for activities of social responsibility. The main objective is to find out optimal prices and green quality in order to maximize the profit functions of individual and integrated systems. The proposed models are analyzed mathematically and numerical examples are illustrated to justify the feasibility of the model in reality.

Pharmaceutical supply chain (PSC) is one of the most important healthcare supply chains and the recent pandemic (COVID-19) has completely proved it. Also, the environmental and social impacts of PSCs are undeniable due to the daily entrance of a large amount of pharmaceutical waste into the environment. However, studies on closed-loop PSCs (CLPSC) are rarely considered real-world requirements such as competition among diverse brands of manufacturers, the dependency of customers’ demand on products’ price and quality, and diverse reverse flows of end-of-life medicines. In this study, a scenario-based Multi-Objective Mixed-Integer Linear Programming model is developed to design a sustainable CLPSC, which investigates the reverse flows of expired medicines as three classes (must be disposed of, can be remanufactured and can be recycled). To study the competitive market and deal with demand uncertainty, a novel scenario-based game theory model is proposed. The demand function for each brand depends on the price and quality provided. Then, a hybrid solution approach is provided by combining the LP-metrics method with a heuristic algorithm. Furthermore, a real case study is investigated to evaluate the application of the model. Finally, sensitivity analysis and managerial insights are provided. The numerical results show that the proposed classification of reverse flows leads to proper waste management, making money, and reducing both disposal costs and raw material usage. Moreover, competition increases PSCs performance and improves the supply of products to pharmacies.

In this paper, we consider a supply chain with a single manufacturer and two competing retailers. The manufacturer sells his digital goods, which may be pirated, to customers through a traditional and a digital retail channel. It is assumed that the manufacturer takes a leader role and the retailers follow it. We investigate the contracts that the manufacturer offers to the retailers and our goal is to find the optimal pricing and ordering decisions made by retailers and the best contract that includes maximum profit for the supply chain. Also, we study a numerical example and examine the proposed contracts. On the other hand, in the sensitivity analysis section, we analyze the impact of each parameter of the problem, in particular, the impact of piracy on the profit of supply chain members and decision variables.

The current study proposes a new DEA model to evaluate the efficiency of 39 Chinese commercial banks over the period 2010–2018. The paper also, in the second stage, investigates the inter-relationships between efficiency and some bank-specific variables (i.e. bank profitability, bank size, expenses management, traditional business and non-traditional business) under the Robust Endogenous Neural Network Analysis. The findings suggest that the sample of Chinese banks experiences a consistent increase in the level of bank efficiency up to 2015; the efficiency score is 0.915, after which the efficiency level declines and then experiences a slight volatility, while finally ending up with an efficiency score of 0.746 by the end of 2018. We also find that among different bank ownership types, the state-owned banks have the highest efficiency, the rural commercial banks are found to be least efficient and the foreign banks experience the strongest volatility over the examined period. The second-stage analysis shows that bank size exerts a positive influence on the development of non-traditional banking business and a proactive expense management, bank size and non-traditional businesses have a positive impact on efficiency levels, while bank profitability, traditional businesses and expenses management have negative influences on bank efficiency.

Purchasing occupies a strategic role in supply chain management for a firm and is the driver of competitive advantage. Owing to the high purchase cost to revenue ratio, decisions such as evaluation, selection, and performance management of suppliers are of the matter of immense interest to firms. Multi-criteria decision making tools allow the purchasing managers to evaluate the suppliers holistically. One such tool, data envelopment analysis (DEA) has been used extensively for supplier evaluation and selection. This paper presents a comprehensive review of 161 articles published since 2000, on the application of DEA in supplier selection. These articles are located from the Scopus database. With little existing literature on a full-fledged review, this work envisages to be first of its kind, by aiding DEA practitioners in purchasing function. The analysis of the study indicates the emergence of the theme of green supply chain and sustainability in recent years as well as the adoption of hybrid approaches to solving the problem of supplier selection using DEA. The paper presents various classifications of DEA methods based on input criteria, sectors of application, and industry-wide case studies, which can be used as a quick reckoner by an academician or a purchasing manager.

The purpose of this paper is to explore the enablers for the implementation of electronic traceability in agri-food supply chain in India. In several agri-food supply chains, the lack of any form of traceability or the presence of paper-based traceability impacts the trade of the concerned food product. Electronic traceability (e-traceability) will assist agri-food firms in improving their performance, minimize food fraud activities, ensure efficient recall of the products and contribute in overall agri-food supply chain management. With the help of literature review and expert opinions, enablers of e-traceability are modelled and analyzed using Fuzzy ISM and FUZZY MICMAC. The combination of both these techniques helps in identifying the essential drivers in the implementation of e-traceability in agri-food supply chains. The proposed approach found that that electronic form of traceability is better than paper-based traceability in agri-food supply chains. The significant drivers in e-traceability implementation, particularly in agri-food supply chain are appropriate technology for e-traceability, competitive advantage, coordination and transparency and management support. The identified enablers would guide the managers or decision-makers in the adoption of e-traceability in their existing supply chains in the agri-food sector.

In the present era of the circular economy, sustainable service quality has become an order winning criteria for all logistics provider across the world. The selection of appropriate logistics service providers (LSPs) greatly influences the performance of supply chains in terms of sustainability indicators. Most of the previous studies have not considered sustainability measures in the evaluation of logistics service providers. Therefore, the uniqueness of this study is that we are proposing a framework for selecting the best logistics provider based on sustainable service quality. Total seventeen attributes related to sustainable service quality are finalized based on literature review and subsequent focused group discussions. Through a questionnaire-based survey, data from 150 customers of LSPs are collected. Data is analysed through factor analysis and seventeen attributes of sustainable service quality are categorized into five factors namely Commitment, Competence, Communication, Creativity & Customization, and Coordination and Collaboration. It is named as a 5C framework. This framework is further used to illustrate the selection of best LSP based on sustainable service quality. Listed attributes are evaluated through hybrid Fuzzy Analytic Hierarchy Process (AHP) and Fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) techniques. This decision-making framework is illustrated with the help of a real-life case study. Sensitivity analysis is also done to validate the robustness of the proposed framework. From this study, it has been observed that the development of competencies for the adoption of sustainable practices should be the thrust area for logistics service providers. Findings imply that the logistics providers should give more focus on sustainable network optimization, response time reduction, reliable green services, flexibility in green processes, and development of mutual trust with all stakeholders to become the first choice of their customers. Insights from the study will help LSPs to develop their strategies for ensuring sustainable service quality to customers.

The development of the sustainable economy has gradually become a consensus, and corporate social responsibility (CSR) is the key to achieving the sustainable development. However due to the implementation of CSR will increase the cost burden of enterprises, some companies are even unwilling to fulfill CSR. At this time, the government often encourages companies to fulfill CSR through subsidies, and consumers are willing to pay a higher price for CSR products. Therefore, this article focuses on the supply chain decision-making analysis problem in the sustainable supply chain. Based on consumer preference for CSR products, considering CSR and government subsidies, some relevant models are constructed to analyze decisions under different power structures and different subsidy situations, then the article compares them and finally draws relevant conclusions. The study found that the higher the consumer's preference, the higher the product sales and CSR level. In addition, government subsidies to manufacturers or consumers have the same effect. Among the three power structures, the overall benefit of supply chain is the highest in VN (Vertical Nash) power structure, so the government should play a leading role and try to narrow any possible gap of channel power.

Procurement of aid material such as vaccines by a humanitarian agency (HA) is often fraught with uncertainties. For example, an epidemic outbreak can increase the demand for materials (such as vaccines) in a very short period. Most of the HAs depend on external donations (funding) to procure necessary vaccines to meet this demand. Hence, it is financially infeasible and operationally inefficient for the HA to procure large quantities of aid material in anticipation of a demand spike during an epidemic outbreak. Thus, the procurement processes for aid materials such as vaccines need to be flexible enough to meet these demand fluctuations. HAs can achieve this flexibility by employing a procurement mechanism portfolio that includes upfront buying, capacity reservation, spot market purchase, etc. However, the challenge lies in identifying the optimal combination of multiple procurement mechanisms and how they can be utilized to coordinate the humanitarian supply chain. In this study, we explore the feasibility of quantity flexibility contracts along with discount incentives combined with spot market procurement in humanitarian supply chains for aid material procurement. We also derive the conditions under which the contract can achieve systemic coordination between the supplier and HA. Furthermore, we also illustrate that under optimal conditions, the procurement of aid material using multiple procurement mechanisms by HA can also reduce the humanitarian supply chain’s total cost.