Quadratic Approximation of the Newsvendor Problem with Imperfect Quality
DOI:
https://doi.org/10.6000/1929-7092.2017.06.34Keywords:
Imperfect quality items, Newsvendor problem, Quadratic programmingAbstract
The paper presents a newsvendor problem in a fuzzy environment by introducing product quality as a fuzzy variable, and product demand as a probability distribution in an economic and supply chain management environment. In order to determine the optimal order quantity, a methodology is developed where the solution is achieved using a fuzzy ranking method combined with a quadratic programming problem approximation. Numerical examples are provided and compared in both situations, namely fuzzy and crisp. The results of these numerical examples show that the decision maker has to order a higher quantity when product quality is a fuzzy variable. The model can be useful for real world problems when historical data are not available.References
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https://doi.org/10.1016/j.ejor.2005.11.002
Abdel-Malek L., Montanari R., Diego M. (2008), The capacitated newsboy problem with random yield: The gardener, International Journal of Production Economics, 115, 113- 127.
https://doi.org/10.1016/j.ijpe.2008.05.003
Abdel-Malek L., Montanari R. (2004), An analysis of multi-product newsboy problem with a budget constraint, International Journal of Production Economics, 97(3), 296-307.
https://doi.org/10.1016/j.ijpe.2004.08.008
Areeratchakul N., Abdel-Malek L. (2006), An approach for solving the multi-product newsboy problem, International Journal of Operational Research, 3, 219-227.
Ben-Daya M., Raouf A. (1993), On the constrained multi-item single period inventory problem, International Journal of Operations & Production Management Bradford, 13, 104-112.
https://doi.org/10.1108/01443579310046472
Chen S. P., Ho Y. H. (2011), Analysis of the newsboy problem with fuzzy demands and incremental discounts. International Journal of Production Economics, 129, 169-177.
https://doi.org/10.1016/j.ijpe.2010.09.014
Choi. T. M. (2012), Handbook of Newsvendor Problems: Models, Extensions and Application. Springer, New York.
https://doi.org/10.1007/978-1-4614-3600-3
Dutta P., Chakraborty D. (2010), Incorporating one-way substitution policy into the newsboy problem with imprecise customer demand. European Journal of Operational Research, 200, 99-110.
https://doi.org/10.1016/j.ejor.2008.12.011
Dutta P., Chakraborty D., Roy A. R. (2005), A single-period inventory model with fuzzy random variable demand, Mathematical and Computer Modelling, 41, 915-922.
https://doi.org/10.1016/j.mcm.2004.08.007
Erlebacher S.J. (2000), Optimal and heuristic solutions for the multi-item newsvendor problem with a single capacity constraint, Production and Operations Management, 9(3), 303-318.
https://doi.org/10.1111/j.1937-5956.2000.tb00139.x
Ehrhardt R., Taube L. (1987), An inventory model with random replenishment quantities, Journal of Production Research, 25(12), 1795-1803.
Gerchak Y., Vickson R.G., Parlar M. (1988), Periodic review production models with variable yield and uncertain demand, IIE Transactions, 20(2), 144–150.
https://doi.org/10.1080/07408178808966163
Henig M., Gerchak Y. (1990), The structure of periodic review policies in the presence of variable yield, Operations Research, 38, 634–643.
https://doi.org/10.1287/opre.38.4.634
Ji Y. P., Guo C. Y. (2010), Supply chain coordination for fuzzy random newsboy problem with imperfect quality, International Journal of Approximate Reasoning, 51(7), 771-784.
Inderfurth K. (2004), Analytical solution for a single-period production-inventory problem with uniformly distributed yield and demand, Central European Journal of Operations Research, 12(2), 117-127.
Kao C., Hsu W. K. (2002), A single-period inventory model with fuzzy demand, Computer and Mathematics with Application, 42, 841-848.
https://doi.org/10.1016/S0898-1221(01)00325-X
Khouja M. (1999), The single-period (news-vendor) problem: Literature review and suggestions for future research, Omega International Journal of Management Science, 27, 537–553.
https://doi.org/10.1016/S0305-0483(99)00017-1
Lau H. S., Lau A. H. L. (1995), The multi-product multi-constraint Newsboy problem: Applications formulation and solution, Journal of Operations Management, 13, 153-162.
https://doi.org/10.1016/0272-6963(95)00019-O
Lau H. S., Lau A. H. L. (1996), The newsstand problem: A capacitated multiple-product single period inventory problem, European Journal of Operational Research, 94, 29-42.
https://doi.org/10.1016/0377-2217(95)00192-1
Lee H.L., Yano C.A. (1988), Production control in multistage systems with variable yield losses. Operations Research, 36(2), 269–278.
https://doi.org/10.1287/opre.36.2.269
Nahmias S., Moinzadeh K. (1997), Lot sizing with randomly graded yields, Operations Research, 974-989.
https://doi.org/10.1287/opre.45.6.974
Niederhoff J. (2007), Using separable programming to solve the multi constraints newsvendor problem and extension, European Journal of Operational Research, 176(2), 941-955.
https://doi.org/10.1016/j.ejor.2005.09.046
Noori A.H., Keller G. (1986), One-period order quantity strategy with uncertain match between the amount received and quantity requisitioned, INFORM, 24(1), 1-11.
https://doi.org/10.1080/03155986.1986.11731980
Ryu K., Yucesan E. (2010), A fuzzy newsvendor approach to supply chain coordination, European Journal of Operational Research, 200, 421-428.
https://doi.org/10.1016/j.ejor.2009.01.011
Taleizadeh A. A., Barzinpour F., Wee H. M. (2010), Meta-heuristic algorithms for solving a fuzzy single-period problem, Mathematical and Computer Modelling, 54, 1273-1285.
https://doi.org/10.1016/j.mcm.2011.03.038
Xu Y., Hu J. (2012), Random fuzzy demand newsboy problem, Physics Procedia, 25, 924-931.
https://doi.org/10.1016/j.phpro.2012.03.179
Xu R., Zhai X. (2008), Optimal models for single-period supply chain problems with fuzzy demand, Information Sciences, 178, 3374-3381.
https://doi.org/10.1016/j.ins.2008.05.012
Yao J. S., Chen M.S., Lu H. F. (2006), A fuzzy stochastic single-period model for cash management, European Journal of Operational Research, 170, 72-90.
https://doi.org/10.1016/j.ejor.2004.06.017
Yager R.R. (1981), A procedure for ordering fuzzy subsets of the unit interval, Information Sciences, 24, 143-161.
https://doi.org/10.1016/0020-0255(81)90017-7
Yu Y., Zhu J., Wang C. (2013), A newsvendor model with fuzzy price-dependent demand. Applied Mathematical Modelling, 37, 2644-2661.
https://doi.org/10.1016/j.apm.2012.06.008
https://doi.org/10.1016/j.ejor.2005.11.002
Abdel-Malek L., Montanari R., Diego M. (2008), The capacitated newsboy problem with random yield: The gardener, International Journal of Production Economics, 115, 113- 127.
https://doi.org/10.1016/j.ijpe.2008.05.003
Abdel-Malek L., Montanari R. (2004), An analysis of multi-product newsboy problem with a budget constraint, International Journal of Production Economics, 97(3), 296-307.
https://doi.org/10.1016/j.ijpe.2004.08.008
Areeratchakul N., Abdel-Malek L. (2006), An approach for solving the multi-product newsboy problem, International Journal of Operational Research, 3, 219-227.
Ben-Daya M., Raouf A. (1993), On the constrained multi-item single period inventory problem, International Journal of Operations & Production Management Bradford, 13, 104-112.
https://doi.org/10.1108/01443579310046472
Chen S. P., Ho Y. H. (2011), Analysis of the newsboy problem with fuzzy demands and incremental discounts. International Journal of Production Economics, 129, 169-177.
https://doi.org/10.1016/j.ijpe.2010.09.014
Choi. T. M. (2012), Handbook of Newsvendor Problems: Models, Extensions and Application. Springer, New York.
https://doi.org/10.1007/978-1-4614-3600-3
Dutta P., Chakraborty D. (2010), Incorporating one-way substitution policy into the newsboy problem with imprecise customer demand. European Journal of Operational Research, 200, 99-110.
https://doi.org/10.1016/j.ejor.2008.12.011
Dutta P., Chakraborty D., Roy A. R. (2005), A single-period inventory model with fuzzy random variable demand, Mathematical and Computer Modelling, 41, 915-922.
https://doi.org/10.1016/j.mcm.2004.08.007
Erlebacher S.J. (2000), Optimal and heuristic solutions for the multi-item newsvendor problem with a single capacity constraint, Production and Operations Management, 9(3), 303-318.
https://doi.org/10.1111/j.1937-5956.2000.tb00139.x
Ehrhardt R., Taube L. (1987), An inventory model with random replenishment quantities, Journal of Production Research, 25(12), 1795-1803.
Gerchak Y., Vickson R.G., Parlar M. (1988), Periodic review production models with variable yield and uncertain demand, IIE Transactions, 20(2), 144–150.
https://doi.org/10.1080/07408178808966163
Henig M., Gerchak Y. (1990), The structure of periodic review policies in the presence of variable yield, Operations Research, 38, 634–643.
https://doi.org/10.1287/opre.38.4.634
Ji Y. P., Guo C. Y. (2010), Supply chain coordination for fuzzy random newsboy problem with imperfect quality, International Journal of Approximate Reasoning, 51(7), 771-784.
Inderfurth K. (2004), Analytical solution for a single-period production-inventory problem with uniformly distributed yield and demand, Central European Journal of Operations Research, 12(2), 117-127.
Kao C., Hsu W. K. (2002), A single-period inventory model with fuzzy demand, Computer and Mathematics with Application, 42, 841-848.
https://doi.org/10.1016/S0898-1221(01)00325-X
Khouja M. (1999), The single-period (news-vendor) problem: Literature review and suggestions for future research, Omega International Journal of Management Science, 27, 537–553.
https://doi.org/10.1016/S0305-0483(99)00017-1
Lau H. S., Lau A. H. L. (1995), The multi-product multi-constraint Newsboy problem: Applications formulation and solution, Journal of Operations Management, 13, 153-162.
https://doi.org/10.1016/0272-6963(95)00019-O
Lau H. S., Lau A. H. L. (1996), The newsstand problem: A capacitated multiple-product single period inventory problem, European Journal of Operational Research, 94, 29-42.
https://doi.org/10.1016/0377-2217(95)00192-1
Lee H.L., Yano C.A. (1988), Production control in multistage systems with variable yield losses. Operations Research, 36(2), 269–278.
https://doi.org/10.1287/opre.36.2.269
Nahmias S., Moinzadeh K. (1997), Lot sizing with randomly graded yields, Operations Research, 974-989.
https://doi.org/10.1287/opre.45.6.974
Niederhoff J. (2007), Using separable programming to solve the multi constraints newsvendor problem and extension, European Journal of Operational Research, 176(2), 941-955.
https://doi.org/10.1016/j.ejor.2005.09.046
Noori A.H., Keller G. (1986), One-period order quantity strategy with uncertain match between the amount received and quantity requisitioned, INFORM, 24(1), 1-11.
https://doi.org/10.1080/03155986.1986.11731980
Ryu K., Yucesan E. (2010), A fuzzy newsvendor approach to supply chain coordination, European Journal of Operational Research, 200, 421-428.
https://doi.org/10.1016/j.ejor.2009.01.011
Taleizadeh A. A., Barzinpour F., Wee H. M. (2010), Meta-heuristic algorithms for solving a fuzzy single-period problem, Mathematical and Computer Modelling, 54, 1273-1285.
https://doi.org/10.1016/j.mcm.2011.03.038
Xu Y., Hu J. (2012), Random fuzzy demand newsboy problem, Physics Procedia, 25, 924-931.
https://doi.org/10.1016/j.phpro.2012.03.179
Xu R., Zhai X. (2008), Optimal models for single-period supply chain problems with fuzzy demand, Information Sciences, 178, 3374-3381.
https://doi.org/10.1016/j.ins.2008.05.012
Yao J. S., Chen M.S., Lu H. F. (2006), A fuzzy stochastic single-period model for cash management, European Journal of Operational Research, 170, 72-90.
https://doi.org/10.1016/j.ejor.2004.06.017
Yager R.R. (1981), A procedure for ordering fuzzy subsets of the unit interval, Information Sciences, 24, 143-161.
https://doi.org/10.1016/0020-0255(81)90017-7
Yu Y., Zhu J., Wang C. (2013), A newsvendor model with fuzzy price-dependent demand. Applied Mathematical Modelling, 37, 2644-2661.
https://doi.org/10.1016/j.apm.2012.06.008
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Published
2017-06-09
How to Cite
Areerakulkan, N. (2017). Quadratic Approximation of the Newsvendor Problem with Imperfect Quality. Journal of Reviews on Global Economics, 6, 335–341. https://doi.org/10.6000/1929-7092.2017.06.34
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Special Issue - Recent Topical Research on Global, Energy, Health & Medical, and Tourism Economics, and Global Software
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