We now have an unprecedented opportunity to analyze and model complex systems with increasing accuracy and precision, due to dramatic growth in the availability of processing power, advances in software architectures, the availability of robust software libraries, increases in the availability of real time digital data and fast, high-bandwidth communications capability. Most importantly, companies now need to use analytic tools as they engage in ever more competitive e-business. The rapid proliferation of e-commerce provides extensive time sensitive data (demand, supply, prices) that has not yet been subject to significant analysis or optimization. The infrastructure and technology components required to support “continual optimization” are rapidly becoming available in most industries.
The challenges to realizing continual optimization fall into several categories. The first is definition, dissemination, maintenance and synchronization of mathematical models representing the underlying problems to be solved in the pervasive models of continual optimization. The second is managing the dataflows generated by the models as they collect and incorporate real time data into the modeling framework. The third is developing algorithms for maintaining a model state representing a high quality solution while cognizant of the constraints placed by data transfer limitations and the dynamic nature of the models themselves.
Examples of Incremental Optimization Applications:
Scheduling and Planning Models
Business operations plan the allocation of scarce resources so as to maximize capability or minimize cost. For example airlines schedule aircraft and personnel to minimize costs; airports allocate gates, runways and taxi ways to maximize on-time flights; delivery companies create shortest routes for their vehicles; call centers schedule their staff to provide adequate coverage at minimal cost. In all of these examples a resource allocation schedule is created in advance for a fixed time period, ranging from a month to a few days and regenerated some portion of the way through the planning period. A near-term application of real-time planning involves recovering, during operation, from disruptions to the plan. Traditional planning models and algorithms must be dramatically modified for use in operational recovery systems.
Time Tabling under Uncertainty
A mathematical programming model based solution for allocation of rooms, personnel, and other resources to classes associated with delivery windows and subject to future cancellations. The problem was formulated as a large-scale stochastic, (mixed) integer optimization model (maximize expected revenue subject to physical and business process constraints) and has resulted in improving the schedule quality by 10%. Further improvement is expected to come from taking advantage of the full range of capabilities (such as chaining, precedence requirements of classes) of the developed system. This solution approach is amenable to deal with similar problems arising in other service areas such as hotel room rentals and apartment rentals.
Service Operations
Since more than 60% of the US economy is in the service industry, applying optimization techniques to this industry has the potential for great benefits. It would allow the corporation to be more aggressive in setting service level agreements, pricing service contracts, planning and acquiring resources, and in increasing customer loyalty. Much of the data to support contract pricing models (failure rates, technician cost, inventory holding cost) is available, but analytic models that estimate the marginal cost of new contracts, or of new terms in existing contracts, are missing and are an area of current research.
Decentralized Allocation
A general setting for decentralized allocation is one where there are multiple agents with a utility function for the different resources and the allocation problem is to distribute the resource in an optimal way. A key difference from classical optimization is that the utility functions of the agents is private information and is not explicitly known to the decision maker. For example, an emerging application is in negotiations for electronic procurement where a buyer is looking to buy several items from a pool of suppliers. However, the cost function of the suppliers is private information and unknown to the buyer (www.research.ibm.com/auctions).
Deep Thunder
IBM Research has a project focused on applications of local, high-resolution, short-term weather forecasting. This effort, which has been dubbed, "Deep Thunder", is described in some detail on our web site, . In particular, we have built a prototype, operational system to provide 24-hour forecasts for the New York City area at 1 km resolution, which are updated twice daily. We also produce forecasts at 4 km resolution, which cover the greater Tri-State region and beyond, and then 16 km resolution for the northeast US. These model-based forecasts provide detailed information about temperature, winds, precipitation, etc. Our current meteorological modeling efforts are unique in the industry and the academic community.
COIN-OR
The COmputational INfrastructure for Operations Research (COIN-OR) is a broad initiative to advance open source for the operations research community. The main thrust of COIN-OR is to build an open-source repository of OR software analogous to what the open literature is for OR theory with the expectation of reaping analogous community benefits. A repository cannot be created and sustained without a community. To that end COIN-OR serves to educate, to promote awareness, to provoke discussions, to encourage developers and users, and to otherwise build an open-source community for OR.
Transportation planning
Researchers in IBM Tokyo Research Laboratory are developing an algorithm for planning transportation between facilities in a supply chain. The algorithm finds the best transportation modes --- trucks, trains, ships, and airplanes --- and the best cross-docking points for delivery orders, and also schedules movements of carriers between facilities. Technique used is a steepest descent method for an abstract solution space, which can efficiently reduce the search space and is easy to incorporate side constraints, such as time windows and inventory costs. The developed algorithm can be used for operational transportation planning and also in higher level simulations.