A sustainable two-echelon green supply chain coordination model under fuzziness incorporating carbon pricing policies

Noxious effect on environmental due to carbon emissions is being addressed worldwide by governments through carbon pricing instruments. Two of prevalent instruments adopted by governments are simple carbon tax and cap-and-trade policy. Effectiveness of carbon pricing instruments towards achieving reduction in carbon emissions is a matter of study on one hand. Whereas, the planning of supply chain operations under imposition of such financial instruments is a challenge for small and medium scale business enterprises. Addressing this situation, the present study develops a supply chain model for coordinated planning of production and inventory replenishment schedules along with decision on economic amounts of expenditure for green resources. This decision model is formulated separately under the enforcement of each of two carbon pricing policies. The study focuses a manufacturer-retailer duo which works by adopting certain sustainability and conservation practices. Manufacturer reworks on rectifiable proportion of defective units, while retailer launches discounts-based sales of partially damaged units. The decision-making model developed in this study incorporates such activities. Furthermore, practical aspects like a slowdown in production due to unforeseeable disruptions and the effect of the quality of product and advertisement campaigns on demand rates are included in the proposed model. Under the purview of each carbon pricing policy, decision-making model is formulated as a nonlinear constrained optimization problem with objective towards profit maximization. A novel conception of fuzziness has been suggested for tackling imprecision in the assessment of certain parameters involved in the model. A numerical study on an appropriate case of a manufacturer-retailer duo system is presented. Empirical results of numerical study evince that a substantial reduction in carbon emission is achieved, even with an escalation in the profit through appropriate green expenditure. This trend is observed under the imposition of each of the carbon pricing policies, thereby substantiating an encouragement to supply chain partners for making expenditures on green resources. Thereby, the hypothesis of getting desired response on curbing emissions by incentivization through carbon pricing is satisfied in the studied case. Furthermore, a sensitivity analysis concludes the stability of formulated model against most of the parameters involved.