Green Probabilistic Inventory Model with Shortage Backodering, Carbon Emission Cost, and Imperfect Quality Items : A Newton - Raphson Method Approach using Python
Rubono Setiawan

Mathematics Education Department
Universitas Sebelas Maret

Abstract

In this paper, a green inventory model has been developed to explain the relationship between a single manufacturer and many retailers in a multiplayer supply chain system. It is assumed that there exist some imperfect items in a quantity lot. In green inventory, one of the important issues is carbon emission with its cost to inventory management. Some troubles in the transportation process yield imperfect quality items. This trouble is the potential to increase the amount of carbon emission and some imperfect quality items. It also affects the cost of the inventory. Therefore, these two aspects will be analyzed under the shortage backorder policy. The classical optimum techniques have been used to obtain the optimum solution. Due to the complexity of the model, the formulation optimization is predominantly conducted using a numerical approach for finding partial derivatives and Newton Raphson^s method for finding the optimal solution. These methods are assisted by the Python programming language, operated within the Google Colab environment and Spyder (Python 3.8) using Anaconda environment.

Keywords: manufacturer, carbon emission, inventory, imperfect quality, Python

Topic: Mathematics and Statistics