An inventory model to study the effect of the probabilistic rate of carbon emission on the profit earned by a supplier

The inventory of suppliers providing raw materials to industries producing green products faces two challenging problems. The first one is that raw materials are usually deteriorating items and the second one that they emit carbon-based gases during deterioration. Moreover, each item has its unique carbon emission rate and composition, called the pattern of carbon emission, which is a function of the rate of carbon emission. In this present research, we attempt to develop a stochastic inventory model with price, stock, and pattern of carbon emission-dependent demand to maximise the profit of a supplier selling a single product. The rate of deterioration is a function of the rate of carbon emission and effective investment in preservation. The cost of carbon emission is a function of green investment and the pattern of carbon emission. Holding costs and purchase costs are constant. We consider three patterns of carbon emission, and each pattern is defined by a negative exponential function. The rate of carbon emission is assumed to be probabilistic and follows one of the three probabilistic distributions: Uniform, Triangular, and Beta. Numerical validation is provided together with sensitivity analysis of the parameters for managerial insights. Analysis of the effect of carbon emission on the profit earned is made and results are interpreted. Particle swarm optimisation (PSO) and genetic algorithm (GA) are applied to solve the model, while statistical analysis and sensitivity analysis of the parameters of the algorithm are provided along with the graphical representation of convergence.