Joel S. Sokol

Optimal Protein Structure Alignment Using Maximum Cliques

In biology, the protein structure alignment problem answers the question of how similar two proteins are. Proteins with strong physical similarities in their tertiary (folded) structure often have similar functions, so understanding physical similarity could be a key to developing protein-based medical treatments. One of the models for protein structure alignment is the maximum contact map overlap (CMO) model. The CMO model of protein structure alignment can be cast as a maximum clique problem on an appropriately defined graph. We exploit properties of these protein-based maximum clique problems to develop specialized preprocessing techniques and show how they can be used to more quickly solve contact map overlap instances to optimality.

Designing Mechanisms for the Management of Carrier Alliances

When cargo carriers form an alliance, sharing network capacity in order to improve profitability, a key issue is how to provide incentive for carriers to make decisions that are optimal for the alliance as a whole. We propose a mechanism that allocates both alliance resources and profits by appropriately setting resource prices. Clearly, it is important to understand the impact of these prices on the behavior of an individual carrier. We analyze the performance of our mechanism using a modeling approach that makes use of realistic control parameters, investigating theoretical and practical properties of profit allocations obtained. Experimental results confirm that our proposed mechanism is robust with respect to variability in alliance composition and cargo demand, yielding solutions that retain a high proportion of optimal profit and achieve a stable distribution of revenue across members of the alliance. We also study an alternative modeling approach in which we assume that each carrier can make load selection decisions for other carriers. We find that changing assumptions about the degree of carrier control can significantly impact the feasibility of routing decisions made by individual carriers when operating under our mechanism, as well as the properties of the profit allocations.

MIRPLib – A library of maritime inventory routing problem instances: Survey, core model, and benchmark results

This paper presents a detailed description of a particular class of deterministic single product Maritime Inventory Routing Problems (MIRPs), which we call deep-sea MIRPs with inventory tracking at every port. This class involves vessel travel times between ports that are significantly longer than the time spent in port and require inventory levels at all ports to be monitored throughout the planning horizon. After providing a comprehensive literature survey of this class, we introduce a core model for it cast as a mixed-integer linear program. This formulation is quite general and incorporates assumptions and families of constraints that are most prevalent in practice. We also discuss other modeling features commonly found in the literature and how they can be incorporated into the core model. We then offer a unified discussion of some of the most common advanced techniques used for improving the bounds of these problems. Finally, we present a library, called MIRPLib, of publicly available test problem instances for MIRPs with inventory tracking at every port. Despite a growing interest in combined routing and inventory management problems in a maritime setting, no data sets are publicly available, which represents a significant “barrier to entry” for those interested in related research. Our main goal for MIRPLib is to help maritime inventory routing gain maturity as an important and interesting class of planning problems. As a means to this end, we (1) make available benchmark instances for this particular class of MIRPs; (2) provide the mixed-integer linear programming community with a set of optimization problem instances from the maritime transportation domain in LP and MPS format; and (3) provide a template for other researchers when specifying characteristics of MIRPs arising in other settings. Best known computational results are reported for each instance.

An optimization approach for planning daily drayage operations

Daily drayage operations involve moving loaded or empty equipment between customer locations and rail ramps. Our goal is to minimize the cost of daily drayage operations in a region on a given day. Drayage orders are generally pickup and delivery requests with time windows. The repositioning of empty equipment may also be required in order to facilitate loaded movements. The drayage orders are satisfied by a heterogeneous fleet of drivers. Driver routes must satisfy various operational constraints. We present an optimization methodology for finding cost-effective schedules for regional daily drayage operations. The core of the formulation is a set partitioning model whose columns represent routes. Routes are added to the formulation by column generation. We present numerical results for real-world data which demonstrate that our methodology produces low cost solutions in a reasonably short time.

Short-term booking of air cargo space

This paper proposes a stochastic dynamic programming model for a short-term capacity planning model for air cargo space. Long-term cargo space is usually acquired by freight forwarders or shippers many months ahead on a contract basis, and usually the forecasted demand is unreliable. A re-planning of cargo space is needed when the date draws nearer to the flight departure time. Hence, for a given amount of long-term contract space, the decision for each stage is the quantity of additional space required for the next stage and the decision planning model evaluates the optimal cost policy based on the economic trade-off between the cost of backlogged shipment and the cost of acquiring additional cargo space. Under certain conditions, we show that the return function is convex with respect to the additional space acquired for a given state and the optimal expected cost for the remaining stages is an increasing convex function with respect to the state variables. These two properties can be carried backward recursively and therefore the optimal cost policy can be determined efficiently.

Spare-Capacity Assignment For Line Restoration Using a Single-Facility Type

The network restoration problem is a specialized capacitated network design problem requiring the installation of spare capacity to fully restore disrupted network flows if any edge in a telecommunications network fails. We present a new mixed-integer programming formulation for a line restoration version of the problem using a single type of capacitated facility. We examine two different models, for distinct and integrated spare-capacity systems, reflecting technologies used in synchronous transfer mode (STM) and asynchronous transfer mode (ATM) networks. The problem is NP-complete in the strong sense. We study the problems polyhedral structure to identify strong valid inequalities that tighten the problem formulation. Our computational results on several real and randomly generated problems show that these inequalities considerably reduce the integrality gap from an average of 10% to an average of under 1%. These results indicate that strong cutting planes combined with branch-and-bound can provide efficient algorithms for solving a class of real-world problems in the telecommunications industry.

Telecommunication Link Restoration Planning with Multiple Facility Types

To ensure uninterrupted service, telecommunication networks contain excess (spare) capacity for rerouting (restoring) traffic in the event of a link failure. We study the NP-hard capacity planning problem of economically installing spare capacity on a network to permit link restoration of steady-state traffic. We present a planning model that incorporates multiple facility types, and develop optimization-based heuristic solution methods based on solving a linear programming relaxation and minimum cost network flow subproblems. We establish bounds on the performance of the algorithms, and discuss problem instances that nearly achieve these worst-case bounds. In tests on three real-world problems and numerous randomly-generated problems containing up to 50 nodes and 150 edges, the heuristics provide good solutions (often within 0.5% of optimality) to problems with single facility type, in equivalent or less time than methods from the literature. For multi-facility problems, the gap between our heuristic solution values and the linear programming bounds are larger. However, for small graphs, we show that the optimal linear programming value does not provide a tight bound on the optimal integer value, and our heuristic solutions are closer to optimality than implied by the gaps.

Planning the Supply Chain Network for New Products: A Case Study

Abstract: Planning a supply chain for a new product requires addressing demand and cost uncertainty as well as changes in market conditions over time. We developed an approach to supply chain planning to determine production capacities, distribution locations, and material flows for a new product launch. The model finds an overall solution for all identified potential scenarios of demand growth. This model also addresses the financial viability of the company during a new product launch by considering initial investments and cash flow. We demonstrate this approach with a case study of a Fortune 200 companys experience launching a new product line.

New approach for optimal electricity planning and dispatching with hourly time-scale air quality and health considerations.

Significance The production of electricity from coal, natural gas, petroleum, and biomass releases air pollutants with significant impacts on ecosystems and human health. Pollutant exposure depends not only on the pollutant source emissions rate and the relative location of the power plant to population centers but also on temperature, wind velocity, and other atmospheric conditions, all of which vary by hour, day, and season. We have developed a method to evaluate fluctuating pollutant formation from source emissions, which we integrate within an electricity production model. In a case study of the state of Georgia from 2004 to 2011, we show how to reduce air pollutants and health impacts by shifting production among plants during a select number of hourly periods. Integrating accurate air quality modeling with decision making is hampered by complex atmospheric physics and chemistry and its coupling with atmospheric transport. Existing approaches to model the physics and chemistry accurately lead to significant computational burdens in computing the response of atmospheric concentrations to changes in emissions profiles. By integrating a reduced form of a fully coupled atmospheric model within a unit commitment optimization model, we allow, for the first time to our knowledge, a fully dynamical approach toward electricity planning that accurately and rapidly minimizes both cost and health impacts. The reduced-form model captures the response of spatially resolved air pollutant concentrations to changes in electricity-generating plant emissions on an hourly basis with accuracy comparable to a comprehensive air quality model. The integrated model allows for the inclusion of human health impacts into cost-based decisions for power plant operation. We use the new capability in a case study of the state of Georgia over the years of 2004–2011, and show that a shift in utilization among existing power plants during selected hourly periods could have provided a health cost savings of

A Robust Heuristic for Batting Order Optimization Under Uncertainty

175.9 million dollars for an additional electricity generation cost of