An EOQ Model For Time Dependent Weibull Deterioration with Linear Demand and Shortages

• Autorzy: Umakanta Mishra , C.K. Tripathy

Warianty tytułu

Model EOQ uszkodzeń Weibulla ze zmienną zależną czasu oraz liniowym popytem i brakami

• Języki publikacji: EN

Abstrakty

Wstęp: W ostatnim czasie coraz większego znaczenia nabierają prace badawcze z zakresu kontroli i utrzymania zapasów towarów łatwo psujących się. Problem psucia się towarów jest bardzo istotnym zagadnieniem w wielu systemach magazynowania. Psucie się definiowane jest jako obniżenie jakości lub uszkodzenia, które powodują, że dany towar nie może być użyty zgodnie z jego pierwotnym przeznaczeniem. Metody: W pracy opracowano model oparty na systemie poziomu zamówienia dla towarów łatwo psujących się, charakteryzujących się popytem liniowym oraz uszkodzeń Weibulla. Przy opracowaniu modelu założono, że wielkość produkcji i popytu jest zależną czasu. Jednostkowy koszt produkcji jest odwrotnie proporcjonalny do popytu. System produkcyjno-magazynowy obejmuje dwa parametry uszkodzeń Weibulla. Wyniki i wnioski: Zostały opracowane dwa modele, jeden przeznaczony dla sytuacji bez braków oraz drugi uwzględniający braki, które przyczyniają się do powstawania zaległości. Celem modelu było opracowanie optymalnego sposobu postępowania minimalizującego średni koszt całkowity. Przedstawiono analizę wrażliwości celem wykazania wpływu zmian parametrów na optymalny średni koszt całkowity. (abstrakt oryginalny)

EN

Background. The study of control and maintenance of production inventories of deteriorating items with and without shortages has grown in its importance recently. The effect of deterioration is very important in many inventory systems. Deterioration is defined as decay or damage such that the item cannot be used for its original purpose. Methods: In this article order level inventory models have been developed for deteriorating items with linear demand and Weibull deterioration. In developing the model we have assumed that the production rate and the demand rate are time dependent. The unit production cost is inversely proportional to demand. Inventory-production system has two parameters Weibull deterioration. Results and conclusions: Two models have been developed considering without shortage cases and with shortage case where the shortages are completely backlogged. The objective of the model is to develop an optimal policy that minimizes the total average cost. Sensitivity analysis has been carried out to show the effect of changes in the parameter on the optimum total average cost. (original abstract)

Słowa kluczowe

PL

Popyt; Koszty produkcji; Koszty jednostkowe

EN

Demand; Production costs; Unit cost

• Czasopismo: LogForum
• Rocznik: 2012
• Tom: 8
• Numer: nr 2
• Strony: 123-136

Twórcy

autor

Umakanta Mishra

• P.K.A.College of Engg. Chakarkend,

autor

C.K. Tripathy

• Sambalpur University, Sambalpur, India

Bibliografia

• Aggarwal S.P., 1978. A note on an order-level inventory model for a system with constant rate of deterioration, Opsearch, 15, 184-187.
• Bahari-Kashani H., 1989. Replenishment schedule for deteriorating items with time-proportional demand, Journal of the Operational Research Society, 40, 75-81.
• Berrotoni J.N., 1962. Practical applications of Weibull distribution. ASQC Technical Conference Transactions, 303-323.
• Chuang J.P.C., 2012, Inventory model with stock dependent selling rate. African Journal of Business Management, 6(3), 780-786.
• Covert R.P., Philip G.C., 1973. An EOQ model for items with Weibull distribution deterioration, AIIE Transaction, 5, 323-326.
• Dave U., 1986. An order-level inventory model for deteriorating items with variable instantaneous demand and discrete opportunities for replenishment, Opsearch, 23, 244-249.
• Dave U., Patel L.K., 1981. (T,Si) policy inventory model for deteriorating items with time proportional demand", Journal of the Operational Research Society, 32, 137-142.
• Deb M., Chaudhuri K.S., 1986. An EOQ Model for items with finite rate of production and variable rate of deterioration, Opsearch, 23, 175-181.
• Ghare P.M., Schrader G.P., 1963. A model for exponentially decaying inventories, Journal of Industrial Engineering, 14, 238-243.
• Ghosh S. K., Goyal S. K., Chaudhuri K. S. 2006. An inventory model with Weibull demand rate, finite rate of production and shortages, International Journal of Systems Science, Vol. 37, No. 14, 15 November, 1003-1009.
• Giri B.C., Jalan A.K., Chaudhuri K.S. 2003. Economic order quantity model with Weibull deteriorating distribution, shortage and ramp-type demand, International Journal of Systems Science, 34, 237-243.
• Goswami A., Chaudhuri K.S., 1991. An EOQ model for deteriorating items with shortages and a linear trend in demand, Journal of the Operational Research Society, 42, 1105-1110.
• Goswami A., Chaudhuri K.S., 1992. Variations of order-level inventory models for deteriorating items, International Journal of Production Economics, 27, 111-117.
• Goyal S.K., Giri B.C., 2001. Recent trends in modelling of deteriorating inventory, European Journal of Operational Research, 134, 1-26.
• He Y., Wang S., Lai K.K., 2010, An optimal production-inventory model for deteriorating items with multiple-market demand. European Journal of Operational Research, 203, 3, 593-600.
• Jalan A.K., and Chaudhuri K.S., 1999. Structural properties of an inventory system with deterioration and trended demand, International J. of Systems Science, 30, 627-633.
• Meher M.K., Panda G.Ch., Sahu S.K., 2012, An inventory model with Wiebull deterioration rate under the dealy in payment in demand decling market. Applied Mathematical Sciences, 6, 23, 1121-1133.
• Mishra R.B., 1975. Optimum production lot-size model for a system with deteriorating inventory, International Journal of Production Research, 13, 495-505.
• Nahmias S., 1982. Perishable inventory theory: A review, Operations Research, 30, 680- 708.
• Papachristos S., and Skouri K., 2000. An optimal replenishment policy for deteriorating items with time varying demand and partial exponential type-backlogging, Operations Research Letter 27, 4, 175-184.
• Philip G.C., 1974. A generalized EOQ model for items with Weibull distribution deterioration, AIIE Transaction, 6, 159-162.
• Rafaat F., 1991. Survey of literature on continuously deteriorating inventory model, Journal of the Operational Research Society, 42, 27-37.
• Roy T., Chaudhuri K. S., 2009. A production-inventory model under stock-dependent demand, Weibull distribution deterioration and shortage, Intl. Trans. in Op. Res, 16 325-346.
• Shah Y. K. Jaiswal M. C. 1977. An order-level inventory model for a system with constant rate of deterioration, Opsearch, 14, 174-184.
• Tripathy C. K., Mishra U., 2010, An EOQ model for linear deteriorating rates with shortage and permissible delay in payment. The IUP Journal of Operations Management, IX, 4, 7-20.
• Tripathy C. K., Mishra U., 2011. An EOQ model with time dependent Weibull deterioration and ramp type demand, International Journal of Industrial Engineering Computations, 2, 307-318.
• Tripathy C. K., Pradhan L.M., 2010a, An EOQ model for three parameter Weibull deterioration with permissible delay in payments and associated salvage value. International Journal of Industrial Engineering Computations 3, 2012, 115-122.
• Tripathy C. K., Pradhan L.M., 2010b, An EOQ model for Weibull deteriorating items with power demand and partial backlogging. Int.J.Contemp.Math.Sciences, 5, 38, 1895-1904.
• Tripathy R.P., Kumar M., 2011, An EOQ model with time-dependent demand rate under trade credits, Int.J.of Mathematical Sciences and Applications, 1, 3.
• Tripathy R.P., 2011, EOQ model with time dependent demand rate and time dependent holding cost function. International Journal of Operations Research and Information Systems, 2(3), 79-92.
• Whitin T.M., 1957, Theory of Inventory Management, Princeton University Press, Princeton, NJ.