This paper investigated a multistage sustainable production–inventory model for deteriorating items (i.e., raw materials and finished goods) with price-dependent demand and collaborative carbon reduction technology investment under carbon tax regulation. The model was developed by first defining the total profit of the supply chain members under carbon tax regulation and, second, considering a manufacturer (leader)–retailer (follower) Stackelberg game. The optimal equilibrium solutions that maximize the manufacturer’s and retailer’s total profits were determined through the method analysis. An algorithm complemented the model to determine the optimal equilibrium solutions, which were then treated with sensitivity analyses for the major parameters. Based on the numerical analysis, (a) carbon tax policies help reduce carbon emissions for both the manufacturer and retailer; (b) most carbon emissions from supply chain operations negatively impact the total profits of both members; (c) the retailer may increase the optimal equilibrium selling price to respond to an increase in carbon emissions from supply chain operations or carbon tax; and (d) autonomous consumption positively affects both members’ optimal equilibrium policies and total profits, whereas induced consumption does the opposite. These findings are very managerial and instructive for companies seeking profits and fulfilling environmental responsibility and governments.


  • Carbon emissions from supply chain logistics processes significantly contribute to climate deterioration

  • This study investigates a multistage sustainable production–inventory model for deteriorating items under carbon tax policy, where the cooperation form between the manufacturer and retailer follows the rules of the Stackelberg game and where demand rate is assumed to be a function of the selling price

  • The proposed model is innovative and unique due to the reasons: (1) Most of the previous production–inventory models only discussed the inventory of finished products, but did not consider the raw materials—the current model includes both materials and finished products inventory; (2) this model suggests that both the manufacturer and retailer can agree on a joint investment in carbon emission reduction technology and share the benefits of reduced emissions under the carbon tax collection policy; (3) unlike the integrated production–inventory model, the proposed model considers the roles of the manufacturer as the leader and the retailer as the follower from the perspective of the Stackelberg game, as well as the optimal ordering, selling price, shipping, and investment decisions of both parties as the equilibrium is reached

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A Multistage Sustainable Production–Inventory

Artificial Intelligence Development Center, Fu Jen Catholic University, New Taipei City 242, Taiwan.

Inventory Model Introducing Carbon Emissions Management
Inventory Model Based on Price-Dependent Demand
Inventory Model Applying Game Theory
Research Gap Analysis
Notations and Assumptions
Model Formulation and Solution
Retailer’s Total Profit with Carbon Tax
Manufacturer’s Total Profit with Carbon Tax
Stackelberg Equilibrium
Numerical Examples

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