The capacitated newsboy problem with random yield: The Gardener Problem

Abstract This publication is the third in a series of articles by Abdel-Malek et al. [2004. Exact, approximate, and generic iterative models for the multi-product newsboy with budget constraint. International Journal of Production Economics 91, 189–198] and Abdel-Malek and Montanari [2005. An analysis of multi-product newsboy problem with a budget constraint. International Journal of Production Economics 97, 296–307], which appeared in IJPE addressing issues regarding the newsboy models. In this paper, models are developed to extend the existing ones to cover random yield scenarios. We designate this type of models as the Gardener Problem. The models are based on the application of Lagrange multipliers, Leibniz's rule and Newton's method to obtain the optimum solution for the considered random yield and probabilistic demand situations. The developed methodologies are applicable to general probability distribution functions. Examples are given to show the applicability of the developed approach to different probability distributions for both the supply and the demand as well as for interdependent yield structures.

[1]  Amy Hing-Ling Lau,et al.  Demand uncertainty and returns policies for a seasonal product: An alternative model , 2000 .

[2]  Hau L. Lee,et al.  Lot Sizing with Random Yields: A Review , 1995, Oper. Res..

[3]  Yves Dallery,et al.  A comprehensive analysis of the Newsvendor model with unreliable supply , 2007, OR Spectr..

[4]  Yigal Gerchak,et al.  Manufacturing to Order with Random Yield and Costly Inspection , 2000, Oper. Res..

[5]  M. Khouja.  The single-period (news-vendor) problem: literature review and suggestions for future research , 1999 .

[6]  Julie A. Niederhoff,et al.  Production , Manufacturing and Logistics Using separable programming to solve the multi-product multiple ex-ante constraint newsvendor problem and extensions , 2006 .

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

[8]  Yigal Gerchak,et al.  The Structure of Periodic Review Policies in the Presence of Random Yield , 1990, Oper. Res..

[9]  Gerald Keller,et al.  One-Period Order Quantity Strategy With Uncertain Match Between The Amount Received And Quantity Requisitioned , 1986 .

[10]  Layek L. Abdel-Malek,et al.  Production , Manufacturing and Logistics A quadratic programming approach to the multi-product newsvendor problem with side constraints , 2006 .

[11]  Layek Abdel-Malek,et al.  Exact, approximate, and generic iterative models for the multi-product Newsboy problem with budget constraint , 2004 .

[12]  Steven J. Erlebacher.  OPTIMAL AND HEURISTIC SOLUTIONS FOR THE MULTI‐ITEM NEWSVENDOR PROBLEM WITH A SINGLE CAPACITY CONSTRAINT , 2000 .

[13]  E. Silver.  Establishing The Order Quantity When The Amount Received Is Uncertain , 1976 .

[14]  Eric V. DeNardo,et al.  The Science of Decision Making : A Problem-Based Approach Using Excel , 2001 .

[15]  Steven Nahmias,et al.  Production and operations analysis , 1992 .

[16]  Hau L. Lee,et al.  Production Control in Multistage Systems with Variable Yield Losses , 1988, Oper. Res..

[17]  Abdul Raouf,et al.  On the Constrained Multi‐item Single‐period Inventory Problem , 1993 .

[18]  Ruud H. Teunter,et al.  The distribution-free newsboy problem with resalable returns , 2003 .

[19]  Edward A. Silver,et al.  The multi-item newsvendor problem with a budget constraint and fixed ordering costs , 2000, J. Oper. Res. Soc..

[20]  Layek Abdel-Malek,et al.  An analysis of the multi-product newsboy problem with a budget constraint , 2005 .

[21]  A. Lau,et al.  The newsstand problem: A capacitated multiple-product single-period inventory problem , 1996 .

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

[23]  G. Gallego,et al.  The Distribution Free Newsboy Problem: Review and Extensions , 1993 .