The (σ, S) policy for uncertain multi-product newsboy problem

This paper derives an optimal (@s,S) policy for uncertain multi-product newsboy problem. Demands for the products are estimated by experts and assumed to be independent uncertain variables. Uncertainty theory, which is a new mathematical tool to deal with human uncertainty, is employed to model demand distributions. A fixed setup cost and a linear ordering cost are incurred if products are ordered. Setup cost is variant and depends on whether a joint order or an individual order is placed. A methodology is proposed for determining the optimal (@s,S) policy. Finally, a two-product example is provided to show how to design an optimal (@s,S) policy in realistic situation.

[1]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[2]  George L. Vairaktarakis,et al.  Robust multi-item newsboy models with a budget constraint , 2000 .

[3]  Baoding Liu.  Fuzzy Process, Hybrid Process and Uncertain Process , 2008 .

[4]  Roger M. Hill,et al.  Performance of approximations for compound Poisson distributed demand in the newsboy problem , 2004 .

[5]  Xiang Li,et al.  Uncertain Alternating Renewal Process and Its Application , 2012, IEEE Transactions on Fuzzy Systems.

[6]  Yuan Gao,et al.  On Liu's Inference Rule for Uncertain Systems , 2010, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[7]  Xiaowei Chen,et al.  A note on truth value in uncertain logic , 2011, Expert Syst. Appl..

[8]  Di Huang,et al.  A competitive multiple-product newsboy problem with partial product substitution , 2011 .

[9]  A. Lau,et al.  The multi-product multi-constraint newsboy problem: Applications, formulation and solution , 1995 .

[10]  Yigal Gerchak,et al.  On the Effect of Demand Randomness on Inventories and Costs , 1992, Oper. Res..

[11]  Baoding Liu,et al.  Theory and Practice of Uncertain Programming , 2003, Studies in Fuzziness and Soft Computing.

[12]  A. F. Veinott,et al.  Computing Optimal (s, S) Inventory Policies , 1965 .

[13]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[14]  Baoding Liu.  Some Research Problems in Uncertainty Theory , 2009 .

[15]  K. Arrow,et al.  Optimal Inventory Policy. , 1951 .

[16]  Herbert E. Scarf,et al.  A Min-Max Solution of an Inventory Problem , 1957 .

[17]  Yuan Gao,et al.  Shortest path problem with uncertain arc lengths , 2011, Comput. Math. Appl..

[18]  L. Abdel-Malek,et al.  Separable programming/duality approach to solving the multi-product Newsboy/Gardener Problem with linear constraints , 2013 .

[19]  A. Tversky,et al.  Prospect theory: an analysis of decision under risk — Source link , 2007 .

[20]  Samarjit Kar,et al.  Cross-entropy measure of uncertain variables , 2012, Inf. Sci..

[21]  Samarjit Kar,et al.  Single-period inventory problem under uncertain environment , 2013, Appl. Math. Comput..

[22]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[23]  B. D. Sivazlian,et al.  Probability of Shortage for Erlang Distributed Demand in a $(\sigma ,S)$ Inventory Problem , 1980 .

[24]  Arthur F. Veinott,et al.  Analysis of Inventory Systems , 1963 .

[25]  Baoding Liu.  Why is There a Need for Uncertainty Theory , 2012 .

[26]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[27]  Richard A. Levine,et al.  Production, Manufacturing and Logistics Bayesian demand updating in the lost sales newsvendor problem: A two-moment approximation q , 2007 .

[28]  Yuhan Liu,et al.  Expected Value of Function of Uncertain Variables , 2010 .