Inventory modeling has always been an innovative research topic for the researchers. It is concerned with minimization of the total inventory cost and maximization of the service level with minimum inventory. In the real world, the demand is always variable; and also the lead time of supply of an item cannot be always fixed due to some unavoidable circumstances. This chapter is focused on an inventory model with shortages where demand quantity and lead time are considered as variable and represented by triangular fuzzy numbers. An expression for optimum order size, reorder point, safety stock and fuzzy total safety stock cost is developed for a fixed customer service level. This model may help the manager to minimize the inventory cost with a maximum service level under the environment of uncertainty and vague information.
TopIntroduction
For any organization, both understocking and overstocking results in monetary loss; the inventory manager always tries to optimize the inventory size so that the monetary loss can be minimized. A shortage or not enough supply of an item can disrupt the entire production plan or inventory management. The main aim of the inventory management is making tradeoffs between the minimization of the total cost and maximization of the customer satisfaction (Tanthatemee & Phruksaphanrat, 2012).
The conventional inventory models incorporate the certain or uncertain demand and supply. However, in practice, both demand and supply are uncertain due to change of orders and some of the unpredictable events. Fuzzy theory gives a closer picture of the situations than the probabilistic theory. Fuzzy set theory, originally introduced by (Zadeh, 1965), provides a tool to consider imprecise or vague information or the information based on perception or belief of individuals. Inventory problems are very common in business operations. Often uncertainties may be associated with demand and various relevant costs like those of inventory carrying, shortage of items and set-up or ordering cost. In conventional inventory models, uncertainties are treated as randomness and probability theory is applied to solve the problem. However, in certain situations, uncertainties are due to fuzziness and in such cases the fuzzy set theory is more appropriate (Chakravarti et al., 2013).
The fuzzy set theory is developed for solving the phenomenon of vague, imprecise, and fuzziness prevalent in the real world. Up to this point, the fuzzy set theory has been widely applied and accepted in many fields, such as science, medicine and management (Ouyang et al., 2010). Kumar et al. (2008) used fuzzy linear programming in supplier selection. Kumar et al. (2011) used fuzzy quality function deployment and multi objective linear programming for supplier evaluation and quota allocation problem. Kumar et al. (2012) used fuzzy analytic hierarchy process and TOPSIS for 3PL evaluation. Thus, the applications of fuzzy set theory in the field of management have become very popular and useful. Fuzzy theory provides an alternate and flexible approach to handle the situations because it can incorporate various subject experts’ advice in developing critical parameter estimates (Zimmermann, 2001).
In this chapter, the authors have proposed an inventory model with fuzzy lead time and fuzzy demand for determining the economic order quantity and fuzzy total safety stock cost using a triangular fuzzy number. The rest of the chapter is organized as follows: Second section represents the background, i.e. literature review related to inventory models and fuzzy set theory. The third section discusses the model development and the fourth section shows a numerical illustration. Finally, fifth section represents the conclusion and the scope for future research.