Applications of Conditional Value at Risk to Full Truckload Pricing Under Demand and Service Time Uncertainties

Abstract

Problem statement: Pricing is one of the fundamental management decisions required by a truckload carrier. Traditional pricing based on an average all relevant costs including fixed and variable costs is not capable of providing adequate margins that prevent losses during operation uncertainties inherent in truckload operation including demand variability and variation in service times. Approach: This study utilizes Conditional Value at Risk (CVaR) as a measure of risk with significant advantage over Value at Risk (VaR), to full truckload pricing when conditions are unpredictable. It criterion focuses on the tail of the loss distribution and provides a measure of the expected loss exceeding Value-at-Risk. Therefore, it was applied to control the maximum loss or the minimum gain within a specified tolerance level to enable more flexible full truckload pricing. A simulation model is developed to capture the stochastic patterns inherent in the operation of full truckload network. Results: Price per trip from 95% CVaR is less than traditional pricing for delivery over short distances while extremely higher for delivery over long distances. We apply traditional prices back to the truckload operation and network imitated in the simulation model and find that even the traditional prices are set to include a certain percentage of profit over the average cost there is still a large chance that the carrier will be subjected to a loss. Conclusion: The numerical analysis for this study demonstrates a pricing method for transportation carriers who are risk averse. Transportation carriers in this group dislike risk and will stay away from high risk.