Abstract. In this paper, a purchasing inventory model with an aim to minimize the total inventory cost and to find the optimal time interval is discussed. Here the retailers are given trade credit offer. In this model, supplier provides replacement, or price discount for damageable items. Shortages are allowed and backlogged. The results are illustrated with numerical example.Keywords: inventory control, permissible delay in payments, deteriorating items, trade credit period, price discount. AMS Mathematics Subject Classification (2010): 90B05 IntroductionAn important assumption in inventory models found in the existing literature is that the life time of an item is infinite while it is in storage. But the effect of deterioration plays an important role in the storage of some commonly used decaying items like, breakable items (glass, china clay, ceramic goods…etc). Due to the deterioration in stored products some of these items loses their quality and cannot complete the customer's need for ideal product. Deterioration in these items may be constant, continuous, time dependent or stock dependent. The economic order quantity model is based on the assumption that the retailer paid for the items immediately after the items are received. However, in practice, the supplier may provide the retailer many incentives such as a cash discount to motivate faster payment and stimulate sales, or a permissible delay in payment to attract new customer and increase the sales. Hence trade credit can play a major role in inventory control for both the supplier as well as retailer.

In this paper, we have developed a deterministic inventory model for deteriorating items in which demand rate and holding cost are quadratic and linear function of time. During deterioration period, deterioration rate can be controlled using preservation technology (PT). An exponential distribution is used to represent the distribution of time to deterioration. The derived model is illustrated by a numerical example.

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To meet the demands of every customer by supplying the products at the limited time by maximizing the profit is a dream for many companies. By choosing the best candidate among the other candidates and effectively reaching the optimal solution with a new modified approach using Best Candidate Method in Fuzzy assignment problems. In this paper the author solve Fuzzy assignment problem in which Triangular and Trapezoidal fuzzy numbers are used. Robust Ranking Technique is used for the ranking of fuzzy numbers.

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