The impact of transportation constraints in commodity markets has become increasingly relevant as many markets experience demand and supply growth that continues to outpace the growth in transportation infrastructure. In “Spatial Price Integration in Commodity Markets with Capacitated Transportation Networks,” Birge, Chan, Pavlin, and Zhu examine the relationship between the spatial distribution of commodity prices and the underlying transportation network that supports the flow of these commodities. The authors show that under mild assumptions, the prices between all locations must be bounded when there are no bottlenecks in the network. Conversely, a bottleneck can cause different locations to incur a congestion surcharge that pushes prices out of these bounds. The authors propose a time series analysis technique using mixed integer optimization that estimates the value of these surcharges from commodity prices and then apply the technique to study how gasoline prices changed after a series of well-documented supply chain disruptions in the Southeastern U.S. gasoline market.
Inverse optimization describes a process that is the "reverse" of traditional mathematical optimization. Unlike traditional optimization, which seeks to compute optimal decisions given an objective and constraints, inverse optimization takes decisions as input and determines an objective and/or constraints that render these decisions approximately or exactly optimal. In recent years, there has been an explosion of interest in the mathematics and applications of inverse optimization. This paper provides a comprehensive review of both the methodological and application-oriented literature in inverse optimization.
Inverse optimization—determining parameters of an optimization problem that render a given solution optimal—has received increasing attention in recent years. Although significant inverse optimization literature exists for convex optimization problems, there have been few advances for discrete problems, despite the ubiquity of applications that fundamentally rely on discrete decision making. In this paper, we present a new set of theoretical insights and algorithms for the general class of inverse mixed integer linear optimization problems. Specifically, a general characterization of optimality conditions is established and leveraged to design new cutting plane solution algorithms. Through an extensive set of computational experiments, we show that our methods provide substantial improvements over existing methods in solving the largest and most difficult instances to date.
Inverse optimization -determining parameters of an optimization problem that render a given solution optimal -has received increasing attention in recent years. While significant inverse optimization literature exists for convex optimization problems, there have been few advances for discrete problems, despite the ubiquity of applications that fundamentally rely on discrete decision-making. In this paper, we present a new set of theoretical insights and algorithms for the general class of inverse mixed integer linear optimization problems. Our theoretical results establish a new characterization of optimality conditions, defined as certificate sets, which are leveraged to design new types of cutting plane algorithms using trust regions. Through an extensive set of computational experiments, we show that our methods provide substantial improvements over existing methods in solving the largest and most difficult instances to date.
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