Separable programming/duality approach to solving the multi-product Newsboy/Gardener Problem with linear constraints

Layek L. Abdel-Malek, Mojisola Otegbeye

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

The Gardener Problem is an extension of the multi-product Newsboy Problem with constraints. It deals with situations where not only the demand is random but also the yield (the supply). Separable programming and duality approaches are utilized to solve the constrained Newsboy/Gardener Problem. The solution methodologies are developed for the common probability distribution functions for the demand, and uniform distribution for the supply, rendering exact and approximate solutions to the problem. Numerical examples are given and when applicable, the performance of the developed approach is compared to those of existing works in this arena. The results reveal that the developed solution methods efficiently converge to the optimal or near optimum solutions. Also, a salient feature of the proposed methodologies is that they can utilize readily available commercial software to solve the considered problems. This feature facilitates the portability of the developed models to the classroom environment.

Original languageEnglish (US)
Pages (from-to)4497-4508
Number of pages12
JournalApplied Mathematical Modelling
Volume37
Issue number6
DOIs
StatePublished - Mar 15 2013

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Applied Mathematics

Keywords

  • Inventory control
  • Mathematical programming
  • Newsboy Problem

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