An integrated mixture of distribution model for environmental cost with fuzzy demand

The idea of encouraging collaboration as well as the sharing of information among supply chain participants to boost system efficiency has garnered a lot of attention as the supply chains have grown longer in recent years. In order to attain a higher level of collaboration and automation in the supply chain. The supply chain occasionally invests in lowering ordering costs in order to simplify and speed up transactions through the use of information technology. If the cost of ordering per order can be efficiently decreased, the total necessary expenses per unit time will immediately improve. To accommodate more practical aspects of fundamental inventory systems, we examine a continuous review model of inventory with a controllable lead time for mixtures of lead time demand distributions, subject to the service level constraint. In many inventory models, uncertainty is due to fuzziness, which is a closed possible approach to reality. In this paper, we propose a fuzzy inventory model with demand using a pentagonal fuzzy number in addition to environmental costs, such as carbon emissions during manufacturing and transportation, to obtain the fuzzy total cost. The signed distance method and the Graded mean integration method are used to defuzzi the cost function and an algorithmic procedure is proposed for determining the optimal decision variables. Moreover, a computational algorithm with the help of a computer code using the software MATLAB 7.0 is developed to solve the problem. Finally, numerical examples are provided to illustrate the algorithmic procedure and sensitivity analysis with respect to different associated parameters has been presented, some observations and managerial implications are presented.