Robust goal programming for multi-objective optimization of data-driven problems: A use case for the United States transportation command's liner rate setting problem

Abstract

Robust goal programming (RGP) is a recently developed, powerful new optimization modeling technique that conjoins two widely accepted operations research disciplines: robust optimization (RO) and goal programming (GP). In lieu of applying a probability distribution over possible outcomes, an approach considered by stochastic programming, RO utilizes uncertainty sets to account for data uncertainty. This characteristic of RO is an important attribute because identifying such a probability distribution is challenging, at best. Given this RO context, RGP additionally incorporates GP, traditionally a deterministic procedure, to address optimization problems having multiple objectives. As such, RGP has potential to help address a wide array of data-driven applications, ranging from financial management to engineering design.As a motivating use case for the utility of an RGP approach, this paper demonstrates the applicability of RGP by way of the data-driven United States Transportation Command (USTRANSCOM) liner rate setting problem. USTRANSCOM is responsible for the technical direction and supervision of over $7 billion [1] of annual passenger, cargo, mobility, and personal property movements in support of the Department of Defense (DoD). Transporting people and material with both organic and contracted assets, USTRANSCOM supports DoD organizations and agencies on a reimbursable basis, annually setting and charging rates for air and liner (i.e., sea) transport for their customers and reimbursing the transportation providers accordingly. The Cost Recovery Branch within TCJ8, the Financial Management and Program Analysis staff organization for USTRANSCOM, annually sets liner shipping rates specific to each combination of origin, destination, commodity type, booking terms, and container size for the upcoming fiscal year (FY). As a government entity, USTRANSCOM seeks to neither make a profit nor operate at a loss in any given FY. The current rate setting methodology assumes existing data is deterministic, resulting in process inaccuracies that contribute to unexpected surpluses or deficits each FY. Moreover, the current method fails to consider an additional USTRANSCOM objective: meeting customer's expectations that liner rates will change annually in accordance with industry-specific inflation. Considering the different goals and inherent parametric variance, the use case herein incorporates a decision maker's risk preference regarding parametric variability via a priori analysis to inform RGP techniques and improve the USTRANSCOM liner rate setting process.