A production inventory model with interval-valued carbon emission parameters under price-sensitive demand

Abstract

As environmental pollution has become a serious problem in recent years, production firms have now shifted their attention to lower the carbon emission level along with their financial goal. Now, one major drawback of the available models is that they consider the amount of carbon emission associated with various inventory processes like setup process, production process, inventory holding process, etc. as fixed numbers. However, these quantities may not be fixed in reality due to several factors, like the condition of the carbon filtrating apparatus in the production firm, machine breakdown, quality of the raw material, nature of the fuel or energy used, etc. The parameters may vary in between some certain ranges. This paper aims at developing an imperfect production inventory model under the various carbon emission regulatory policies where the various carbon emission parameters are interval numbers. The various inventory cost parameters are also represented as interval numbers to reflect the practical situation. The demand of the product is assumed to be a linearly decreasing function of the selling price of the product. Also, the idea of a new inventory cost component, referred to as the ‘development cost’ is introduced. Four different policies- simple tax policy, cap and purchase policy, cap and reward policy and strictly under permitted cap policy are discussed, and based on those policies four different inventory models are developed. The Quantum behaved Particle Swarm Optimization(QPSO) algorithm has been applied to find the optimal profit of the manufacturer. The optimal profit obtained here is also an interval number which is quite realistic. The traditional fuzzy or probabilistic approach to represent impreciseness fails to find such kind of solution. A numerical example for every case has been given to illustrate the applicability of the models. Finally, sensitivity analysis of the optimal feasible solution due to variation in some key parameters has been provided with the key managerial insights.