Mathematical Modelling of an Inventory Transportation System To Optimize Cost of Inventory and Fuzzy Environmental Impact under Two Warehouse Storage System

Abstract

This thesis is divided into seven chapters. Chapter 1 is Introduction which deals with the basic concept, terminology and research objectives of the present work. Operations research is a branch of mathematics that deals with the issues involved in society. Mathematical modelling is an essential concept of Operations Research that helps resolve real-world issues systematically. A mathematical model is the most important key used in the Operation Research field for modelling the issues in mathematical languages. Various terms like inventory, types, classification, stocking, cost components, transportation system and impact on the environment, deterioration, shortages, back ordering, inflation, warehousing, two warehouse systems, and fuzzy environment have been discussed. Finally, the research objectives and methodology along with the organization of the thesis have been dealt with. Chapter 2 named Literature Review described the history of the development of the fuzzy inventory model by considering various parameters. It deals with the research gaps as per previous research and hence the motivation to do the present work by incorporating the present issues of energy and carbon emission during the inventory transportation system. Chapter 3 named Modelling of an Inventory System of Supply Chain in Fuzzy System presents an integrated supply chain model to optimize the total inventory cost of the supply chain in which retailer and supplier are involved. The deterioration rate for both is taken to be constant and the same. The demand of retailers varies depending upon the inventory level while per order demand is fixed. Deteriorating production system works with inventory model on a supply chain system for considering transportation cost depending upon quantity ordered and distance from supplier s production unit to retailer s warehouse. First a crisp model is developed and considering some parameters of fuzzy nature affecting inventory cost, a corresponding fuzzy model is developed. In an inventory modelling separate model has been developed for retailer as well as supplier and rarely transportation cost is taken into account. During production and storage, constant deterioration occurs at retailer s and supplier s warehouse. newline