In the existing literature of inventory modeling under the conditions of permissible delay in payments, researchers have assumed that the retailers have to settle their accounts at the end of credit period i.e. supplier accept only full amount at the end of the credit period. However in reality, supplier may either accept the partial amount at the end of the credit period and unpaid balance subsequently or the full amount at a fix point of time after the expiry of the credit period, if the retailer finances the inventory from the supplier itself. Further, in the classical deteriorating inventory models, the common unrealistic assumption is that all the items start to deteriorate as soon as they arrive in the system. However, in realistic environment, it is observed that there are several non-instantaneous deteriorating items that have a shelf life and start to deteriorate after a time lag, like dry fruits, potatoes, yams and even some fruits and vegetables etc. Considering the importance of above mentioned facts, the present study formulates a fuzzy inventory model for non-instantaneous deteriorating items under conditions of permissible delay in payments. The paper discusses all the possible cases which may arise and yet not considered in the previous inventory models under permissible delay in payments. Further, this paper also considers price-dependent demand and the possibility of higher interest earn rate than interest payable rate. The objective of this study is to determine the optimal decision policies for the retailer which maximizes the total profit. Finally, the numerical examples are solved by using the proposed algorithm to show the validity of the model followed by the sensitivity analysis.

A systematic approach to the inventory control and classification may have a significant influence on company competitiveness. In practice, all inventories cannot be controlled with equal attention. In order to efficiently control the inventory items and to determine the suitable ordering policies for them, multi-criteria inventory classification is used. In this paper, fuzzy analytic hierarchy process for multiple criteria ABC inventory classification has been proposed. Fuzzy Analytic Hierarchy process (Fuzzy AHP) is used to determine the relative weights of the attributes or criteria, and to classify inventories into different categories. To accredit the proposed model, it is implemented for the 351 raw materials of switch gear section of Energypac Engineering Limited (EEL), a large power engineering company of Bangladesh. In this approach, at first, related criteria have been selected (Unit price, last year consumption or annual demand, last use date, supplier, criticality, durability) and the weights of these criteria was determined using Fuzzy AHP. Then a score to each item was assigned for each criterion as triangular fuzzy number and the final normalized weighted score of each item using fuzzy set theory is calculate. Finally, Chang’s extent analysis was used for the comparison of fuzzy numbers and the final scores are compared with each other. Then all items were classified into three classes according to their final score.

Decision making problem is the process of finding the best option from all of the feasible alternatives. One of the most important concepts in decision making process is to identify the weights of criteria. In real-world situation, because of incomplete or non-obtainable information, the data (attributes) are often not deterministic and can be treated in forms of fuzzy numbers. This paper investigates a method for deriving the weights of criteria from the pair-wise comparison matrix with fuzzy elements. Finding the weights of criteria has been one of the most important issues in the field of decision-making and the present method uses goal programming to solve the resulted model. In addition, using a ranking function we convert each obtained fuzzy weight to a crisp one, which makes it possible to compare the criteria. The proposed model of this paper is supported by several examples and a case study.