EPL models with fuzzy imperfect production system including carbon emission: a fuzzy differential equation approach
- 21 Downloads
The paper outlines the production policies for maximum profit of a firm producing imperfect economic lot size with time-dependent fuzzy defective rate under the respective country’s carbon emission rules. Generally in economic production lot-size models, defective production starts after the passage of some time from production commencement. So the starting time of producing defective units is normally uncertain and imprecise. Thus, produced defective units are fuzzy, partially reworked instantly and sold as fresh units. As a result, the inventory level at any time becomes fuzzy and the relation between the production, demand and inventory level becomes a fuzzy differential equation (FDE). Nowadays, different governments have made environmental regulations following the United Nations Framework Convention on Climate Change to reduce carbon emission. Some governments use cape and trade policy on emission. Due to this, firms are in fix how to optimize the production. If the firms produce more, the profit increases along with more emission and corresponding tax. Here, models are formulated as profit maximization problems using FDE, and the corresponding inventory and environmental costs are calculated using fuzzy Riemann integration. An \(\alpha \)-cut of average profits is obtained and the reduced multi-objective crisp problems are solved using intuitionistic fuzzy optimization technique. The models are illustrated numerically and results are presented graphically. Considering different carbon regulations, an algorithm for a firm management is presented to achieve the maximum profit. Real-life production problems for the firms in Annex I and developing countries are solved.
KeywordsFuzzy imperfect production Carbon emission Fuzzy differential equation Intuitionistic fuzzy optimization technique
Average carbon emission cost
Average carbon emission reward
Average total profit
Carbon emission cost
Carbon emission reward
Economic order quantity
Economic production lot size
Economic production quantity
Fuzzy differential equation
Fuzzy Riemann integration
Intuitionistic fuzzy number
Intuitionistic fuzzy optimization technique
Intuitionistic fuzzy set
Multi-objective optimization problem
Triangular fuzzy number
Unit production cost
The authors are greatly indebted to the referees for their valuable observations and suggestions for improving the presentation of the paper.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
- He P, Zhang W, Xu X, Bian Y (2015) Production lot-sizing and carbon emissions under cap-and-trade and carbon tax regulations. J Clean Prod 103:241–248. https://doi.org/10.1016/j.jclepro.2014.08.102 (Carbon emissions reduction: policies, technologies, monitoring, assessment and modeling)Google Scholar
- Jana B, Roy TK (2007) Multi-objective intuitionistic fuzzy linear programming and its application in transportation model. Notes Intuit Fuzzy Sets 13(1):34–51Google Scholar
- Manna A, Das B, Dey J, Mondal S (2016) An EPQ model with promotional demand in random planning horizon: population varying genetic algorithm approach. J Intell Manuf 27(1):1–17Google Scholar