Some Inventory Models Approach to Decision Making in Fuzzy Environment

Mathematics, the king of all sciences, remains and will remain as a subject with great charm having an intrinsic value and beauty of its own. It plays very important role in sciences, engineering and other subjects as well. So, mathematical knowledge is essential for the growth of science and technology, and for any individual to shine well in the field of one's choice. In addition, a rigorous mathematical training gives one not only the knowledge of mathematics but also a disciplined thought process, an ability to analyze complicated problems. We need the power and prowess of mathematics to face and solve the ever increasing complex problems that we encounter in our life. Furthermore, mathematics is a supremely creative force and not just a problem solving tool. The learners will realize this fact to their immense satisfaction and advantage as they learn more and more of mathematics. Besides, a good mathematical training is very much essential to create a good work force for posterity. The rudiments of mathematics attained at the school level form the basis of higher studies in the field of mathematics and other sciences. Besides learning the basics of mathematics, it is also important to learn how to apply them in solving problems. The basic objective of an inventory model is to reduce total average cost, i.e., maximum profit and also ensuring that the production process does not suffer at the same time. In this book, we have developed some inventory models for finding total annual average cost and optimal ordering quantity in crisp and fuzzy environment. In the past researchers assumed the parameters involved in an inventory model such as the demand, holding cost, se-up cost, deteriorating cost, etc. as a crisp values or random variables. But in reality some uncertainty occurs. The demand and cost of the items change from day to day. Again, calculating these variables by the probability distribution is very hard due to lack of historical data. The cost parameters generally estimated based on previous experiment and managerial judgment. Therefore, in real life situation fuzzy set theory is more realistic than crisp set theory or traditional probability theory. Here we have used triangular fuzzy number (TFN) also used fuzzy grade-mean integration representation (GMIR) method. Optimal solution (OS) is obtained here by applying non-linear programming techniques (GP, SGP, Khun -Tucker necessary conditions) for a single item inventory model. But it is observed that the geometric programming (GP) technique minimizes the total annual average cost more than any usual non-linear technique. It is also analyzed that when fuzzification of the given inventory model is done the total average cost is minimized by satisfying the constraints under necessary conditions.