Optimization in Fuzzy Economic Order Quantity (FEOQ) Model with Deteriorating Inventory and Units Lost

• Autorzy: Monalisha Pattnaik

Warianty tytułu

Optymizacja modelu zmiennej wielkości ekonomicznej zamówienia (FEOQ) dla produktów podlegających psuciu się oraz uwzględniający straty towaru

Optimalisierung des Modells der Variablen Wirtschaftlichen Grösse Einer Bestellung (FEOQ) für Verderbanfällige Produkte unter Berücksichtigung von Warenverusten

• Języki publikacji: EN

Abstrakty

EN

Background: This model presents the effect of deteriorating items in fuzzy optimal instantaneous replenishment for finite planning horizon. Accounting for holding cost per unit per unit time and ordering cost per order have traditionally been the case of modeling inventory systems in fuzzy environment. These imprecise parameters defined on a bounded interval on the axis of real numbers and the physical characteristics of stocked items dictate the nature of inventory policies implemented to manage and control in the production system. Methods: The modified fuzzy EOQ (FEOQ) model is introduced, it assumes that a percentage of the on-hand inventory is wasted due to deterioration and considered as an enhancement to EOQ model to determine the optimal replenishment quantity so that the net profit is maximized. In theoretical analysis, the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions are proved and further the concavity of the fuzzy net profit function is established. Computational algorithm using the software LINGO 13.0 version is developed to find the optimal solution. Results and conclusions: The results of the numerical analysis enable decision-makers to quantify the effect of units lost due to deterioration on optimizing the fuzzy net profit for the retailer. Finally, sensitivity analyses of the optimal solution with respect the major parameters are also carried out. Furthermore fuzzy decision making is shown to be superior then crisp decision making in terms of profit maximization. (original abstract)

Wstęp: Model ten prezentuje wpływ psucia się produktów w systemie ciągłego uzupełniania dla skończonego horyzontu planowania. Tradycyjnie zostały wyliczone w tym modelowym systemie koszty magazynowania na jednostkę artykułu, na jednostkę czasu oraz koszt zamówienia na zamówienie. Te nieprecyzyjne parametry zdefiniowane w określonych przedziałach osi dla rzeczywistych wartości i fizycznych charakterystyk magazynowanych produktów określają zasady zarządzania zapasami stosowanymi w danym systemie produkcyjnym. Metody: Zastosowano zmodyfikowany model zmiennej ekonomicznej wielkości zamówienia (FEOQ), zakładający, że pewien odsetek zapasów jest tracony w wyniku psucia się wyrobów. Model ten został tak zmieniony aby uzyskać optymalną wielkość zamówienia przy maksymalizacji zysku netto. W analizie teoretycznej, koniecznym i wystarczającym warunkiem istnienia i unikalności optymalnego rozwiązania jest znalezienie przegięcia funkcji zysku netto. Opracowano algorytm obliczeniowy w celu znalezienia optymalnego rozwiązania przy zastosowaniu oprogramowania LINGO 13.0. Wyniki i wnioski: Wyniki analizy matematycznej umożliwiają osobom podejmującym decyzję określenie wielkości wpływu psucia się zapasów na optymalizację zysku netto detalisty. Przeprowadzono również analizę wrażliwości dla optymalnego rozwiązania uwzględniając istotne parametry. Przedstawiono dowody, że podejmowanie decyzji na zasadzie prawdopodobieństwa jest istotniejsze w procesie maksymalizacji zysku od decyzji typu Crisp. (abstrakt oryginalny)

Słowa kluczowe

EN

Optimalization; Storage; Economic order quantity

PL

Optymalizacja; Magazynowanie; Ekonomiczna wielkość zamówienia

• Czasopismo: LogForum
• Rocznik: 2014
• Tom: 10
• Numer: nr 3
• Strony: 247--262

Twórcy

autor

Monalisha Pattnaik

• Utkal University, Bhubaneswar, India

Bibliografia

• Bose S., Goswami A., Chaudhuri K.S., 1995. An EOQ model for deteriorating items with linear time-dependent demand rate and shortages under inflation and time discounting. Journal of Operational Research Society, 46: 775-782.
• Goyal S.K., Giri B.C., 2001. Recent trends in modeling of deteriorating inventory. European Journal of Operational Research, 134: 1-16.
• Goyal S.K., Gunasekaran A., 1995. An integrated production-inventory-marketing model for deteriorating items. Computers and Industrial Engineering, 28: 755-762.
• Gupta D., Gerchak Y., 1995. Joint product durability and lot sizing models. European Journal of Operational Research, 84: 371-384.
• Hariga M., 1995. An EOQ model for deteriorating items with shortages and timevarying demand. Journal of Operational Research Society, 46: 398-404.
• Hariga M., 1996. An EOQ model for deteriorating items with time-varying demand. Journal of Operational Research Society, 47: 1228-1246.
• Hariga M., 1994. Economic analysis of dynamic inventory models with nonstationary costs and demand. International Journal of Production Economics, 36: 255-266.
• Jain K., Silver E., 1994. A lot sizing for a product subject to obsolescence or perishability. European Journal of Operational Research, 75: 287-295.
• Mahata G.C., Goswami A., 2006. Production lot size model with fuzzy production rate and fuzzy demand rate for deteriorating item under permissible delay in payments. Journal of Operational Research Society India, 43: 359-375.
• Osteryoung J.S., Mc Carty D.E., Reinhart W.L., 1986. Use of EOQ models for inventory analysis. Production and Inventory Management, 3rd Qtr: 39-45.
• Padmanabhan G., Vrat P., 1995. EOQ models for perishable items under stock dependent selling rate. European Journal of Operational Research, 86: 281-292.
• Pattnaik M., 2013. A Framework of Dynamic Ordering Cost with Units Lost due to Deterioration in an Instantaneous Economic Order Quantity Model. Journal of Supply Chain and Operations Management, in press.
• Pattnaik M., 2012. A Note on Non Linear Profit-Maximization Entropic Order Quantity (EnOQ) Model for Deteriorating Items with Stock Dependent Demand Rate. Operations and Supply Chain Management, 5(2): 97-102.
• Pattnaik M., 2011. A note on optimal inventory policy involving instant deterioration of perishable items with price discounts. The Journal of Mathematics and Computer Science, 3(2): 145-155.
• Pattnaik M., 2013. A note on profitMaximization Fuzzy EOQ Models for Deteriorating Items with Two Dimension Sensitive Demand. International Journal of Management Science and Engineering Management, in press.
• Pattnaik M., 2010. An entropic order quantity (EnOQ) model under instant deterioration of perishable items with price discounts, International Mathematical Forum, 5(52): 2581-2590.
• Pattnaik M., 2011. An entropic order quantity (EnOQ) model with post deterioration cash discounts. International Journal of Contemporary and Mathematical Sciences, 6(19): 931-939.
• Pattnaik M., 2012. An EOQ model for perishable items with constant demand and instant Deterioration. Decision, 39(1): 55-61.
• Pattnaik M., 2011. Entropic order quantity (EnOQ) model under cash discounts. Thailand Statistician Journal, 9(2): 129-141.
• Pattnaik M., 2013. Fuzzy Multi-objective Linear Programming Problems: A Sensitivity Analysis. The Journal of Mathematics and Computer Sciences, 7(2): 131-137.
• Pattnaik M., 2013. Fuzzy NLP for a Single Item EOQ Model with Demand - Dependent Unit Price and Variable Setup Cost. World Journal of Modeling and Simulations, 9(1): 74-80.
• Pattnaik M., 2013. Fuzzy Supplier Selection Strategies in Supply Chain Management. International Journal of Supply Chain Management, 2(1): 30-39.
• Pattnaik M., 2013. Linear Programming Problems in Fuzzy Environment: The Post Optimal Analyses. Journal of Uncertain Systems, in press.
• Pattnaik M., 2012. Models of inventory control. Lambart Academic Publishing, Germany.
• Pattnaik M., 2013. Optimal Decision-Making in Fuzzy Economic Order Quantity (EOQ) Model under Restricted Space: A NonLinear Programming Approach. International Journal of Analysis and Applications, 2(2): 147-161.
• Pattnaik M., 2013. Optimization in an Instantaneous Economic Order Quantity (EOQ) Model Incorporated with Promotional Effort Cost, Variable Ordering Cost and Units Lost due to Deterioration. Uncertain Supply Chain Management, 1(2): 57-66.
• Pattnaik M., 2013. Skilled Manpower Selection for Micro, Small and Medium enterprises: A Fuzzy Decision Making Approach. Operations and Supply Chain Management, 6(2): 64-74.
• Pattnaik M., 2011. Supplier Selection Strategies on Fuzzy Decision Space. General Mathematics Notes, 4(1): 49-69.
• Pattnaik M., 2012. The effect of promotion in fuzzy optimal replenishment model with units lost due to deterioration. International Journal of Management Science and Engineering Management, 7(4): 303-311.
• Pattnaik M., The Effect of Units Lost due to Deterioration in Fuzzy Economic Order Quantity (FEOQ) Model, International Journal of Analysis and Applications, 1(2): 128-146.
• Pattnaik M., 2013. Wasting of Percentage Onhand Inventory of an Instantaneous Economic Order Quantity Model due to Deterioration. The Journal of Mathematics and Computer Sciences, 7(3): 154-159.
• Raafat F., 1991. Survey of literature on continuously deteriorating inventory models. Journal of Operational Research Society, 42: 89-94.
• Sahoo P.K., Pattnaik M., 2013. An article "Decision Making Approach to Fuzzy Linear Programming (FLP) Problems with Post Optimal Analysis. International Journal of Operations Research and Information Systems, in press.
• Sahoo P.K., Pattnaik M., 2013. Linear Programming Problem and Post Optimality Analyses in Fuzzy Space: A Case Study of a Bakery Industry. Journal of Business and Management Sciences, 1(3): 36-43.
• Salameh M.K., Jaber M.Y., Noueihed N., 1993. Effect of deteriorating items on the instantaneous replenishment model. Production Planning and Control, 10(2): 175-180.
• Shah N., 2000. Literature survey on inventory models for deteriorating items. Economics Annals, 44: 221-237, 2000.
• Tripathy P.K., Pattnaik M., 2011. A fuzzy arithmetic approach for perishable items in discounted entropic order quantity model. International Journal of Scientific Statistical Compunting, 1(2): 7-19.
• Tripathy P.K., Pattnaik M., 2011. A nonrandom optimization approach to a disposal mechanism under flexibility and reliability criteria. The Open Operational Research Journal, 5: 1-18.
• Tripathy P.K. and Pattnaik, M. "An entropic order quantity model with fuzzy holding cost and fuzzy disposal cost for perishable items under two component demand and discounted selling price". Pakistan Journal of Statistics and Operations Research, 4(2): 93-110, 2008.
• Tripathy P.K., Pattnaik M., 2013. Fuzzy Supplier Selection Strategies in Supply Chain Management. International Journal of Supply Chain Management, 2(1): 30-39.
• Tripathy P.K., Pattnaik M., 2007. Optimal disposal mechanism with fuzzy system cost under flexibility & Reliability criteria in non-random optimization environment. Appllied Mathematical Sciences, 3(37): 1823-1847.
• Tripathy P.K., Pattnaik M., 2011. Optimal inventory policy with reliability consideration and instantaneous receipt under imperfect production process. International Journal of Management Sciences and Engineering Management, 6(6): 412-420.
• Tripathy P.K., Pattnaik M., Tripathy P., 2012. Optimal EOQ Model for Deteriorating Items with Promotional Effort Cost. American Journal of Operations Research, 2(2): 260-265.
• Tripathy P.K., Tripathy P., Pattnaik M., 2011. A Fuzzy EOQ Model with Reliability and Demand-dependent Unit Cost. International Journal of Contemporary Mathematical Sciences, 6(30): 1467-1482.
• Tsao Y.C., Sheen G.J., 2008. Dynamic pricing, promotion and replenishment policies for a deteriorating item under permissible delay in payment. Computers and Operations Research, 35: 3562-3580.
• Vujosevic M., Petrovic D., Petrovic R., 1996. EOQ formula when inventory cost is fuzzy. International Journal of Production Economics, 45: 499-504.
• Waters C.D.J., 1994. Inventory Control and Management. Chichester: Wiley.
• Wee H.M., 1993. Economic Production lot size model for deteriorating items with partial back-ordering. Computers and Industrial Engineering, 24: 449-458.