Optimal supplier choice with discounting

Abstract

This paper investigates a model for pricing the demand for a set of goods when suppliers operate discount schedules based on total business value. We formulate the buyers's decision problem as a mixed binary integer program, which is a generalization of the capacitated facility location problem (CFLP). A branch and bound (BnB) procedure using Lagrangean relaxation and subgradient optimization is developed for solving large-scale problems that can arise when suppliers’ discount schedules contain multiple price breaks. Results of computer trials on specially adapted large benchmark instances of the CFLP confirm that a sub-gradient optimization procedure based on Shor and Zhurbenko's r-algorithm, which employs a space dilation in the direction of the difference between two successive subgradients, can be used efficiently for solving the dual problem at any node of the BnB tree.

Keywords:

• allocation
• decision support systems
• integer programming
• location

Acknowledgements

Thanks are due to the two anonymous referees whose perceptive comments led to a substantially improved manuscript. We also gratefully acknowledge the assistance provided by the Manchester Institute for the Mathematical Sciences (MIMS) in providing financial support to allow visits of the first and the third authors (BG, VK) to the University of Manchester in 2004 and 2006.