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Advances in Operations Research
Volume 2014, Article ID 597626, 7 pages
Research Article

Lot Size Decisions for Vendor-Buyer System with Quantity Discount, Partial Backorder, and Stochastic Demand

Department of Industrial Engineering, Sebelas Maret University, Jl. Ir, Sutami 36 A, Surakarta 57126, Indonesia

Received 12 May 2014; Revised 3 October 2014; Accepted 14 October 2014; Published 11 November 2014

Academic Editor: Konstantina Skouri

Copyright © 2014 Wakhid Ahmad Jauhari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents production-inventory model for two-echelon system consisting of single vendor and single buyer. The proposed model contributes to the current inventory literature by incorporating quantity discount scheme into stochastic vendor-buyer model. Almost all vendor-buyer inventory models have discussed this scheme in single-echelon system and deterministic demand situation. Here, we assume that the demand of the buyer is normally distributed and the unmet demand is considered to be partially backordered. In addition, the lead time is variable and consists of production time and nonproductive time. The quantity discount is developed by using all-units quantity discounts. Finally, an iterative procedure is proposed to obtain all decision variables and numerical examples are provided to show the application of the proposed procedure.