Quadratic Approximation of the Newsvendor Problem with Imperfect Quality


  • Natapat Areerakulkan Department of Engineering Management, College of Innovative Technology and Engineering, Dhurakij Pundit University, Bangkok, Thailand




Imperfect quality items, Newsvendor problem, Quadratic programming


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.


Abdel-Malek L., Areeratchakul N. (2007), A quadratic programming approach to the multi-product newsvendor problem with side constraints, European Journal of Operational Research, 176(3), 1607- 1619.
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.
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.
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.
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.
Choi. T. M. (2012), Handbook of Newsvendor Problems: Models, Extensions and Application. Springer, New York.
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.

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.
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.
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.
Henig M., Gerchak Y. (1990), The structure of periodic review policies in the presence of variable yield, Operations Research, 38, 634–643.
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.
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.
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.
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.
Lee H.L., Yano C.A. (1988), Production control in multistage systems with variable yield losses. Operations Research, 36(2), 269–278.
Nahmias S., Moinzadeh K. (1997), Lot sizing with randomly graded yields, Operations Research, 974-989.
Niederhoff J. (2007), Using separable programming to solve the multi constraints newsvendor problem and extension, European Journal of Operational Research, 176(2), 941-955.
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.
Ryu K., Yucesan E. (2010), A fuzzy newsvendor approach to supply chain coordination, European Journal of Operational Research, 200, 421-428.
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.
Xu Y., Hu J. (2012), Random fuzzy demand newsboy problem, Physics Procedia, 25, 924-931.
Xu R., Zhai X. (2008), Optimal models for single-period supply chain problems with fuzzy demand, Information Sciences, 178, 3374-3381.
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.
Yager R.R. (1981), A procedure for ordering fuzzy subsets of the unit interval, Information Sciences, 24, 143-161.
Yu Y., Zhu J., Wang C. (2013), A newsvendor model with fuzzy price-dependent demand. Applied Mathematical Modelling, 37, 2644-2661.




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



Special Issue - Recent Topical Research on Global, Energy, Health & Medical, and Tourism Economics, and Global Software