Thomas W. M. Vossen

Slot Trading Opportunities in Collaborative Ground Delay Programs

The Federal Aviation Administration (FAA) and the major airlines in the United States have embraced a new initiative to improve air traffic flow management. This initiative, called collaborative decision making (CDM), is based on the recognition that improved data exchange and communication between the FAA and the airlines will lead to better decision making. In particular, the CDM philosophy emphasizes that decisions with a potential economic impact on airlines should be decentralized and made in collaboration with the airlines whenever possible. The CDM paradigm has led to fundamental changes in the implementation of ground delay programs. A key component has been the introduction of the compression procedure, which allows for the exchange of arrival slots between airlines. In this paper, we consider opportunities for increased airline control by interpreting the compression procedure as a mediated slot trading mechanism. Based on this interpretation, we propose an extension that allows airlines to submit so-called at-least, at-most offers. We develop an efficient integer programming model to solve the mediators problem, and show that the resulting mechanism can substantially improve the ability of airlines to optimize their internal cost functions.

An LP-based heuristic for optimal planning

One of the most successful approaches in automated planning is to use heuristic state-space search. A popular heuristic that is used by a number of state-space planners is based on relaxing the planning task by ignoring the delete effects of the actions. In several planning domains, however, this relaxation produces rather weak estimates to guide search effectively. We present a relaxation using (integer) linear programming that respects delete effects but ignores action ordering, which in a number of problems provides better distance estimates. Moreover, our approach can be used as an admissible heuristic for optimal planning.

THE ONE-DIMENSIONAL CUTTING STOCK PROBLEM WITH DUE DATES

The one-dimensional cutting stock problem is the problem of cutting stock material into shorter lengths, in order to meet demand for these shorter lengths while minimizing waste. In industrial cutting operations, it may also be necessary to fill the orders for these shorter lengths before a given due date. We propose new optimization models and solution procedures which solve the cutting stock problem when orders have due dates. We evaluate our approach using data from a large manufacturer of reinforcement steel and show that we are able to solve industrial-size problems, while also addressing common cutting considerations such as aggregation of orders, multiple stock lengths and cutting different types of material on the same machine. In addition, we evaluate operational performance in terms of resulting waste and tardiness of orders using our model in a rolling horizon framework.

Research Note---Vertical Information Sharing in a Volatile Market

When demand is uncertain, manufacturers and retailers often have private information on future demand, and such information asymmetry impacts strategic interaction in distribution channels. In this paper, we investigate a channel consisting of a manufacturer and a downstream retailer facing a product market characterized by short product life, uncertain demand, and price rigidity. Assuming the firms have asymmetric information about the demand volatility, we examine the potential benefits of sharing information and contracts that facilitate such cooperation. We conclude that under a wholesale price regime, information sharing might not improve channel profits when the retailer underestimates the demand volatility but the manufacturer does not. Although information sharing is always beneficial under a two-part tariff regime, it is in general not sufficient to achieve sharing, and additional contractual arrangements are necessary. The contract types we consider to facilitate sharing are profit sharing and buyback contracts.

Air Traffic Flow Management

Air transportation systems are some of the most complex logistical systems imaginable. The world’s airlines transported over 2.2 billion passengers in 2008, and transported approximately 40% of world trade (measured by value). There are nearly 2,000 airlines worldwide, which have a total fleet of nearly 23,000 aircraft and serve some 3,750 airports through a route network of several million miles managed by around 160 air navigation service providers.

Reductions of Approximate Linear Programs for Network Revenue Management

The linear programming approach to approximate dynamic programming has received considerable attention in the recent network revenue management literature. A major challenge of the approach lies in solving the resulting approximate linear programs (ALPs), which often have a huge number of constraints and/or variables. We show that the ALPs can be dramatically reduced in size for both affine and separable piecewise linear approximations to network revenue management problems, under both independent and discrete choice models of demand. Our key result is the equivalence between each ALP and a corresponding reduced program, which is more compact in size and admits an intuitive probabilistic interpretation. For the affine approximation to network revenue management under an independent demand model, we recover an equivalence result known in the literature, but provide an alternative proof. Our other equivalence results are new. We test the numerical performance of solving the reduced programs directly using o...

Loosely coupled formulations for automated planning: an integer programming perspective

We represent planning as a set of loosely coupled network flow problems, where each network corresponds to one of the state variables in the planning domain. The network nodes correspond to the state variable values and the network arcs correspond to the value transitions. The planning problem is to find a path (a sequence of actions) in each network such that, when merged, they constitute a feasible plan. In this paper we present a number of integer programming formulations that model these loosely coupled networks with varying degrees of flexibility. Since merging may introduce exponentially many ordering constraints we implement a so-called branch-and-cut algorithm, in which these constraints are dynamically generated and added to the formulation when needed. Our results are very promising, they improve upon previous planning as integer programming approaches and lay the foundation for integer programming approaches for cost optimal planning.

Hierarchical Benders Decomposition for Open-Pit Mine Block Sequencing

The open-pit mine block sequencing problem (OPBS) models a deposit of ore and surrounding material near the Earth’s surface as a three-dimensional grid of blocks. A solution in discretized time identifies a profit-maximizing extraction (mining) schedule for the blocks. Our model variant, a mixed-integer program (MIP), presumes a predetermined destination for each extracted block, namely, processing plant or waste dump. The MIP incorporates standard constructs but also adds not-so-standard lower bounds on resource consumption in each time period and allows fractional block extraction in a novel fashion while still enforcing pit-wall slope restrictions. A new extension of nested Benders decomposition, “hierarchical” Benders decomposition (HBD), solves the MIP’s linear-programming relaxation. HBD exploits time-aggregated variables and can recursively decompose a model into a master problem and two subproblems rather than the usual single subproblem. A specialized branch-and-bound heuristic then produces high...