We study uncertain linear complementarity problems (LCPs), i.e., problems in which the LCP vector q or the LCP matrix M may contain uncertain parameters. To this end, we use the concept of Gamma-robust optimization applied to the gap function formulation of the LCP. Thus, this work builds upon [16]. There, we studied Gamma-robustified LCPs for … Read more
With wind and solar becoming major contributors to electricity production in many systems, wholesale market operators have become increasingly aware of the need to address uncertainty when forming prices. While implementing theoretically ideal stochastic market clearing to address uncertainty may be impossible, the use of operating reserve demand curves allows market designers to inject an … Read more
This paper addresses the scheduling problem of coordinating train services and network maintenance windows for a railway system. We present model reformulations, for a mixed integer linear optimization model, which give a mathematically stronger model and substantial improvements in solving performance – as demonstrated with computational experiments on a set of synthetic test instances. As … Read more
Quantifying extra functions, herein referred to as outcome functions, over optimal solutions of an optimization problem can provide decision makers with additional information on a system. This bears more importance when the optimization problem is subject to uncertainty in input parameters. In this paper, we consider linear programming problems in which input parameters are described … Read more
We study the nurse staffing problem under random nurse demand and absenteeism. While the demand uncertainty is exogenous (stemming from the random patient census), the absenteeism uncertainty is endogenous, i.e., the number of nurses who show up for work partially depends on the nurse staffing level. For the quality of care, many hospitals have developed … Read more
This paper addresses the vehicle routing problem with time windows and multiple deliverymen (VRPTWMD) under uncertain demand as well as uncertain travel and service times. This variant is faced by logistics companies that deliver products to retailers located in congested urban areas, where service times are relatively long compared to travel times. In addition to … Read more
Electricity markets worldwide allow participants to bid non-convex production offers. While non-convex offers can more accurately reflect a resource’s capabilities, they create challenges for market clearing processes. For example, system operators may be required to execute side payments to participants whose costs are not covered through energy sales as determined via traditional locational marginal pricing … Read more
There are currently two broad strategies for optimal Multi-agent Pathfinding (MAPF): (1) search-based methods, which model and solve MAPF directly, and (2) compilation-based solvers, which reduce MAPF to instances of well-known combinatorial problems, and thus, can benefit from advances in solver techniques. In this work, we present an optimal algorithm, BCP, that hybridizes both approaches … Read more
Natural disasters, such as hurricanes, large wind and ice storms, typically require the repair of a large number of components in electricity distribution networks. Since power cannot be restored before the completion of repairs, optimally scheduling the available crews to minimize the cumulative duration of the customer interruptions reduces the harm done to the affected … Read more
We study order acceptance dynamics in same-day delivery systems by formulating the Dynamic Dispatch Waves Problem with Immediate Acceptance, which models integrated request management and order distribution for dynamically arriving requests. When a delivery request arrives, a decision is made immediately to accept (offer service) or reject (with a penalty). Accepted requests are not available … Read more