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1

Inventory model for deteriorating items with negative exponential demand, probabilistic deterioration and fuzzy lead time under partial back logging

Sen Nabendu, Saha Sumit

Operations Research and Decisions

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2020

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Vol. 30, No. 3

97--112

EN

The effect of lead time plays an important role in inventory management. It is also important to study the optimal strategies when the lead time is not precisely known to the decision-makers. This paper aimed to examine the inventory model for deteriorating items with fuzzy lead time, negative exponential demand, and partially backlogged shortages. This model is unique in its nature due to probabilistic deterioration along with fuzzy lead time. The fuzzy lead time was assumed to be triangular, parabolic, trapezoidal numbers. The graded mean integration representation method was used for the defuzzification purpose. Three different types of probability distributions, namely uniform, triangular and beta were used for rate of deterioration to find optimal time and associated total inventory cost. The developed model was validated numerically, and values of optimal time and total inventory cost are given in a tabular form, corresponding to different probability distributions and fuzzy lead-time. The sensitivity analysis was performed on the variation of key parameters to observe its effect on the developed model.

2

Two-storage inventory model for deteriorating items with price dependent demand and shortages under partial backlogged in fuzzy approach

Indrajitsingha Susanta Kumar, Samanta Padmanava, Raju Lakshmi Kanta, Misra Umakanta

LogForum

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2019

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Vol. 15, no. 4

487--499

EN

Background: In this paper we developed a fuzzy two-warehouse (one is OW, the own warehouse and other is RW, the rented warehouse) inventory model of deteriorating items with price dependent demand rate and allowed shortages under partially backlogged conditions. Since the capacity of any warehouse is limited, the supplier has to rent a warehouse for keeping the excess units over the fixed capacity W of the own warehouse in practice. The rented warehouse owed higher holding cost than the own warehouse. In this paper we considered holding cost, deterioration rate, shortages cost and lost sales as triangular fuzzy numbers. Methods: Graded Mean Integration Representation is used to defuzzify the total cost function. The result obtained by this method is compared with crisp model with the help of a numerical example. Sensitivity analysis is accomplished to changing one parameter at a time and keeping others at their archetypal. Results and conclusions: It has been proved that graded mean integration representation method gives more accurate result as compare to crisp model.

PL

Wstęp: W pracy zaprezentowano rozmyty model układu dwumagazynowego, składającego się z własnego magazynu (OW) oraz magazyny wynajmowanego (RW) dla asortymentów podlegających psuciu oraz o popycie zależnym od ceny przy dopuszczenia częściowych braków. Ze względu na ograniczoną powierzchnię własną magazynu, dostawca był zmuszony wynająć drugi magazyn w celu magazynowania nadwyżki. Koszt magazynu wynajmowanego jest wyższy niż koszt magazynu własnego. W pracy uwzględniono koszt utrzymywania obiektu, współczynnik psucia, koszt ubytków oraz koszt utraty sprzedaży jak liczby rozmyte. Metody: W celu odwrócenia rozmycia funkcji całkowitego kosztu użyto metody Graded Mean Integration Representation. Otrzymane wyniki porównano z modelem Crisp przy pomocy przykładu liczbowego. Następnie wykonano analizę wrażliwości zmieniają jeden z parametrów przy utrzymaniu niezmienionych pozostałych. Wyniki i wnioski: Wykazano, że wyniki uzyskane przy zastosowaniu metody Graded Mean Integration Representation są dokładniejsze aniżeli przy zastosowaniu modelu Crisp.

3

Inventory models with multiple production and remanufacturing batches under shortages

Singh S. R., Sharma S., Kumar M.

Control and Cybernetics

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2016

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Vol. 45, no. 3

385--416

EN

Owing to the ecological requirements and regulations, an enormous concern is being paid to the product re-processing. In the established literature, researchers considered that the remanufactured items are as good as the new ones. Yet, such an assumption is not convenient, as in many real situations the recycled products are considered by the customers to be of secondary quality. Further, the classical studies mainly addressed the inventory models without shortages, and this is not applicable in many practical business situations. This paper extends the reverse logistics inventory models with ﬁnite production and remanufacturing rate along with the assumption that newly produced and repaired (remanufactured) objects are not of same characteristics. Shortages are allowed and numerous stock-out cases are discussed. The collected used items are remanufactured (repaired) and non-repaired products are disposed oﬀ. The proposed models are illustrated with some numerical examples and their results are discussed.

4

Impact of inﬂation and trade credit policy in an inventory model for imperfect quality items with allowable shortages

Khanna A., Kishore A., Jaggi C. K.

Control and Cybernetics

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2016

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Vol. 45, no. 1

37--82

EN

Retail businesses must constantly evolve with new strategies introduced in order to meet and even to exceed customers’ expectations. This eﬀort can be enhanced by incorporating inspection processes in business routines that will maximize the eﬀectiveness of attempts to sell quality products. Further, permissible delay in payments has certainly been a prominent strategy in today’s business transactions, helping in gaining the ﬁnancial advantage for both the retailers and the suppliers. Moreover, in order to recognize the proper and exact timing of cash ﬂows associated with an inventory system, inﬂation and time value of money should also be incorporated. Considering all the above described real life aspects and problems, a model is formulated here to study the combined eﬀect of imperfect quality items, trade credit, shortages, inﬂation and time value of money on an inventory system. An analytical method is employed to jointly optimize the order quantity and the shortages. To study the behavior and application of the proposed model, a numerical example, including sensitivity analysis, has been analyzed. The potential applications, improving the decision making process of the model introduced can be found in industries like textile, footwear, plastics, electronics, etc.