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The purpose of this paper is to analyze the operational decisions of a manufacturer who produces multiple products and the government's selection of cap-and-trade and carbon tax regulations.

This paper explores the production decisions of a multi-product manufacturer under cap-and-trade and carbon tax regulations in a cap-dependent carbon trading price setting and compares carbon emission, the manufacturer's profits and social welfare under the two regulations. Game theory and extreme value theory are used to analyze our models.

First, the authors find that the optimal profit of the manufacturer (the optimal cap) increases and then decreases with the cap (the unit carbon emission of product). Second, if the environmental damage coefficient is moderate, the optimal cap of unit environmental damage coefficient is independent of the product carbon emission or other related product parameters. Ultimately, cap-and-trade regulation always generates more carbon emission than carbon tax regulation. And cap-and-trade regulation (carbon tax regulation) can generate more social welfare if the environmental damage coefficient is low (high), and the social welfare under the two regulations is equal to each other, or otherwise.

This paper contributes the prior literature by considering the inverse relationship of the allocated cap and the carbon trading price and discusses the social welfare under cap-and-trade and carbon tax regulations. Some important and new results are found, which can guide the government's implementation of the two regulations.

In the era of climate change, industrial organizations are under increasing pressure from consumers and regulators to reduce greenhouse gas emissions. The purpose of this paper is to examine the effectiveness of product mix as a strategy to deliver the low carbon supply chain under the cap-and-trade policy.

The authors incorporate the cap-and-trade policy into the green product mix decision models by using game-theoretic approach and compare these decisions in a decentralized model and a centralized model, respectively. The research explores potential behavioral changes under the cap-and-trade in the context of a two-echelon supply chain.

The analysis results show that the channel structure has significant impact on both economic and environmental performances. An integrated supply chain generates more profits. In contrast, a decentralized supply chain has lower carbon emissions. The cap-and-trade policy makes a different impact on the economic and environmental performances of the supply chain. Balancing the trade-offs is critical to ensure the long-term sustainability.

The research offers many interesting observations with respect to the effect of product mix strategy on operational decisions and the trade-offs between costs and carbon emissions under the cap-and-trade policy. The insights derived from the analysis not only help firms to make important operational and strategic decisions to reduce carbon emissions while maintaining their economic competitiveness, but also make meaningful contribution to governments’ policy making for carbon emissions control.

This paper aims to find optimal emission reduction investment strategies for the manufacturer and examine the effects of carbon cap-and-trade policy and uncertain low-carbon preferences on emission reduction investment strategies.

This paper studied a supply chain consisting of one manufacturer and one retailer, in which the manufacturer is responsible for emission reduction investment. The manufacturer has two emission reduction investment strategies: (1) invest in traditional emission reduction technologies only in the production process and (2) increase investment in smart supply chain technologies in the use process. Then, three different Stackelberg game models are developed to explore the benefits of the manufacturer in different cases. Finally, this paper coordinates between the manufacturer and the retailer by developing a revenue-sharing contract.

The manufacturer's optimal emission reduction strategy is dynamic. When consumers' low-carbon preferences are low and the government implements a carbon cap-and-trade policy, the manufacturer can obtain the highest profit by increasing the emission reduction investment in the use process. The carbon cap-and-trade policy can encourage the manufacturer to reduce emissions only when the initial carbon emission is low. The emission reduction, order quantity and the manufacturer's profit increase with the consumers' low-carbon preferences. And the manufacturer can adjust the emission reduction investment according to the emission reduction cost coefficient in two processes.

This paper considers the investment of emission reduction technologies in different processes and provides theoretical guidance for manufacturers to make a low-carbon transformation. Furthermore, the paper provides suggestions for governments to effectively implement carbon cap-and-trade policy.

The purpose of this study is to model a vehicle routing problem with integrated picking and delivery under carbon cap and trade policy. This study also provides sensitivity analyses of carbon cap and price to the total cost.

A mixed integer linear programming (MILP) model is formulated to model the vehicle routing with integrated order picking and delivery constraints. The model is then solved by using the CPLEX solver. Carbon footprint is estimated by a fuel consumption function that is dependent on two factors, distance and vehicle speed. The model is analyzed by considering 10 suppliers and 20 customers. The distance and vehicle speed data are generated using simulation with random numbers.

Significant amount of carbon footprint can be reduced through the adoption of eco-efficient vehicle routing with a marginal increase in total transportation cost. Sensitivity analysis indicates that compared to carbon cap, carbon price has more influence on the total cost.

The model considers mid-sized problem instances. To analyze large size problems, heuristics and meta-heuristics may be used.

This study provides an analysis of carbon cap and price model that would assist practitioners and policymakers in formulating their policy in the context of carbon emissions.

This study provides two significant contributions to low carbon supply chain management. First, it provides a vehicle routing model under carbon cap and trade policy. Second, it provides a sensitivity analysis of carbon cap and price in the model.

The purpose of this paper is to analyze manufacturers' production decisions and governments' low-carbon policies in the context of influencer spillover effects.

This paper investigates the impact of the social influencer spillover effect on manufacturers' production decisions when they collaborate with intermediary platforms to sell products through marketplace or reseller modes. Game theory and static numerical comparison are used to analyze our models.

Firstly, under low-carbon policies, the spillover effect does not always benefit manufacturer profits and changes non-monotonically with an increasing spillover effect. Secondly, in cases where there are both a carbon emission constraint and a spillover effect present, if either the manufacturer or intermediary platform holds a strong position, then marketplace mode benefits manufacturer profits. Thirdly, regardless of business mode used when environmental damage coefficient is high for products; government should implement cap-and-trade regulation to optimize social welfare while reducing manufacturers’ carbon emissions.

This study offers theoretical and practical research support to assist manufacturers in optimizing production decisions for compliance with carbon emission limits, enhancing profits through the development of effective influencer marketing strategies, and providing strategies to mitigate carbon emissions and enhance social welfare while sustaining manufacturing activities.

This paper addresses the limitations of prior research by examining how the social influencer spillover effect influences manufacturers' business mode choices under government low-carbon policies and analyzing the social welfare of different carbon emission restrictions when such spillovers occur. Our findings provide valuable insights for manufacturers in selecting optimal marketing strategies and business modes and decision-makers in implementing effective regulations.

This paper aims to minimize the total carbon emissions and costs and also maximize the total social benefits.

The present study develops a mathematical model for a closed-loop supply chain network of perishable products so that considers the vital aspects of sustainability across the life cycle of the supply chain network. To evaluate carbon emissions, two different regulating policies are studied.

According to the obtained results, increasing the lifetime of the perishable products improves the incorporated objective function (IOF) in both the carbon cap-and-trade model and the model with a strict cap on carbon emission while the solving time increases in both models. Moreover, the computational efficiency of the carbon cap-and-trade model is higher than that of the model with a strict cap, but its value of the IOF is worse. Results indicate that efficient policies for carbon management will support planners to achieve sustainability in a cost-effectively manner.

This research proposes a mathematical model for the sustainable closed-loop supply chain of perishable products that applies the significant aspects of sustainability across the life cycle of the supply chain network. Regional economic value, regional development, unemployment rate and the number of job opportunities created in the regions are considered as the social dimension.

Within a framework of supply chain (SC) coordination, this paper analyzes a green SC consisting of a retailer and a manufacturer, under government incentives and legislations and the consumer environmental awareness. To mitigate carbon emissions and promote the sustainability of the SC, a customized carbon emission trading mechanism is developed.

A game-theoretical decision model formulated determines the optimal sustainability level and the optimal quota of carbon credit from the ceiling capacity set by the government. In order to coordinate the SC and optimize environmental decisions, a novel combination of consignment and zero wholesale price contracts is proposed.

Analytical and numerical analyses conducted highlight that the proposed contract generates a Pareto improvement for both channel members, boosts the profit of the green SC, enhances the sustainability level of the channel and contributes to a reduction in the requested carbon emission credit by the manufacturer.

With the proposed mechanism, governments can protect their industries and, more importantly, comply with European Union (EU) rules on annually reducing emission ceilings allocated to industries.

Different from previous studies on cap-and-trade strategies, the proposed mechanism enables companies to select lower emission quota/allowances than the maximum amount set by the government, and in return, companies can benefit from several incentive strategies of the government.

This paper investigates to find whether it is possible to align the interests of a small and medium manufacturing enterprise (SMME) with its raw material supplier in a manufacturing supply chain (MSC) to achieve a sustainable solution. To this end, current study examines the coordination of an MSC under cap and trade consisting of a raw material supplier and a carbon-emitting SMME confronting a stochastic demand.

The model is developed under both the decentralized and centralized decision-making scenarios. Under the investigated model, the SMME decides on both production quantity and sustainability level simultaneously. To achieve coordination and align the interests of both MSC members toward sustainable economic development goals, a customized revenue-sharing contract is developed.

Although the centralized model is profitable for the MSC, it makes a loss for the SMME compared to the decentralized scenario. The revenue-sharing agreement is able to create coordination among the MSC members and optimize profitability and sustainability. The established revenue-sharing guarantees a Pareto-improving situation for both members. Applying the established contract not only reduces shortage occasions but also results in more sustainability levels, which in turn means movement toward attaining sustainable economic development goals.

Unlike previous studies, carbon emission is assumed as a nonlinear decreasing function of the sustainability level which is a more realistic case. In accordance with SMMEs business environments, the market demand is also assumed uncertain. In addition, instead of assuming an investment cost for sustainability, the authors assumed unit production/purchasing costs as functions of product sustainability level.

The purpose of this paper is to investigate whether truthful information sharing can be achieved via informal cheap talk in a competitive setting, and how carbon emission constraint and information-sharing modes (no information sharing, partial information sharing and public information sharing) interact with each other under cap-and-trade regulation.

This paper establishes an emission-dependent supply chain consisting of a manufacturer, an incumbent retailer who has superior demand information and a new entrant retailer. The manufacturer abates carbon emissions under the pressures of government environmental regulation and consumers’ eco-friendly concern. The research formulates a multistage game to explore every party’s decision and the implications of information-sharing modes.

The results show that truthful information sharing can be achieved when the manufacturer decides both the wholesale price and carbon emission abatement. The results also show that the incumbent retailer’s information-sharing decision highly depends on the manufacturer’s capacity in abating carbon emissions and the demand uncertainty.

The research adds value to information management and sustainable production literature. This work emphasizes the interaction between the information flow and material flow. Not only it investigates the factors that affect information-sharing modes from a new point of view when considering carbon emission constraint, but also provides operational strategies for manufacturers to make more profit when facing asymmetric information and emission regulation.

Strict carbon-cap policy is one of the basic policies proposed by the regulatory bodies to reduce the anthropogenic greenhouse gas emission. The purpose of this paper is to examine whether it is beneficial for a company to invest in green technology or not under the strict carbon-cap policy and for that a two echelon supply chain model is developed. This paper gives insight about judicious decision about investment on green technology.

Mathematical modeling approach has been adopted to understand the effect of investment on green technology. All the cost and emissions parameters have been derived and the total cost (TC) and total emission equations have been formulated mathematically. Two constrained mixed-integer nonlinear programming (MINLP) problems have been formulated and solved considering with or without green investment. Further, supply chain cost is optimized without carbon constraint to understand the effect of carbon constraint.

The investment in green technology can reduce the total supply chain cost. The study reveals that handling different parameters optimally can reduce both cost and emissions.

This paper tries to assess the effectiveness of green investment on technology under strict carbon-cap policy on a supply chain and, thereby, added value to the existing work. It examines the role played by various parameters under strict carbon-cap policy to draw insights, which will be beneficial for the academic community and managers.