Impact of Bimodal and Lognormal Distributions in Ocean Transportation Transit Time on Logistics Costs

Abstract

This paper shows that ignoring bimodality and lognormality in transit time distributions can cause large increases in the logistic costs of maritime transportation. Bimodal and lognormal transit time distributions are observed to be of moderate frequency (approximately 17%) but high impact in the volume of shipment carried (approximately 85%) in these lanes. Ignoring and assuming incorrect distribution of transit time can have dramatic implications on the safety stock levels and reorder points and hence inventory cost incurred by the shipper. To display the incorrectness of such assumptions, the paper compares the typical approach of using a deterministic value (Case 1) for transit time and Hadley–Whitin (1963) with normal approximation (Case 2) to the authors’ simulation and empirical analysis on bimodal and lognormal transit time distributions (Case 3). This paper further explores how the shipper should optimally manage inventory in the parameters of transit time distribution and critical ratio (or the service level of the shipper). Specifically, different regions are defined by the transit time distribution parameters and critical ratios that determine the magnitude of relative cost differences when the three cases are compared.