A Probabilistic Inventory Problem for Imperfect Quality with Partial Shortage Backordering, Carbon Emission, and Its Computation Using Genetic Algorithm in Python

In this article, a multiplayer inventory model is discussed that explains the relationship between a single manufacturer and multiple retailers in a supply chain system.There are products with imperfect quality in the quantity of lots produced, resulting from the production and transportation processes.A partial shortage backorder policy is implemented to handle shortage conditions.The cost of greenhouse gas emissions from loading and transportation equipment is also considered in the total cost.The quantity of imperfect products can affect the quantity of products to be shipped.Classical optimization techniques with an integrated approach are used for analytical inventory model analysis.Due to the complexity of the model, the optimal solution is performed using a numerical computational approach.The computational and optimization procedures are implemented in a new algorithm based on the genetic algorithms, which are executed by Python programming.