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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 274713, 7 pages
Research Article

Determination of Optimal Shipping Quantity for Perishable Goods under Probabilistic Supply

Department of Industrial & Management Engineering, Hanyang University, Ansan, Gyeonggi-do 15588, Republic of Korea

Received 30 September 2015; Revised 28 November 2015; Accepted 6 December 2015

Academic Editor: Jei-Zheng Wu

Copyright © 2015 Si-Yeong Lim and Sun Hur. 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.


The problems of shipping and transporting perishable goods are commonly considered in the literature as significant topics, but rarely did researchers adopt a probabilistic point of view in their models. It is common in SCM environments that the participating entities’ behaviors are random and unpredictable and so can only be modeled in a probabilistic way. In this paper, we consider the shipping problem of determining the optimal quantity of perishable products with a limited time to be stored in the warehouse. The optimal quantity minimizes the overall operational costs including those of inventory and shipping. We develop a mathematical model, from which the probability distribution function, mean, and variance of the length of the build-up period are derived and we establish a cost function for determining the optimal shipping value.