On the Relativistic BGK-Boltzmann Model: Asymptotics and Hydrodynamics

The generalization of the BGK relaxation model to the special relativity setting is revisited here. We deal with several issues related to this relativistic kinetic model which seem to have been overlooked in the previous physical literature, including the unique determination of associated physical parameters, classical, ultra-relativistic and hydrodynamical limits, maximum entropy principles and the analysis of the linearized operator.     

Optimum service capacity and demand management with price incentives

Service firms periodically face fluctuating demand levels. They incur high costs to handle peak demand and pay for under-utilized capacity during low demand periods. In this paper, we develop a mixed integer programming (MIP) model based on the real life experience of a Brazilian telecommunications firm. The model determines the optimum staffing requirements with different seniority levels for employees, as well as the distribution and balancing of workload utilizing flexibility of some customers in their service completion day. The proposed MIP uses monetary incentives to smooth the workload by redistributing some of the peak demand, thereby increasing capacity utilization. Due to the intractable nature of optimizing the proposed MIP model, we present a heuristic solution approach. The MIP model is applied to the case of the examined Brazilian Telecommunications firm. The computational work on this base case and its extensions shows that the proposed MIP model is of merit, leading to approximately seventeen percent reduction in the base case operating costs. Extensive computational work demonstrates that our heuristic provides quality solutions in very short computational times. The model can also be used to select new customers based on the workload, the revenue potential of these new customers and their flexibility in accepting alternate service completion dates. The generic structure of the proposed approach allows for its application to a wide variety of service organizations facing similar capacity and demand management challenges. Such wide applicability enhances the value of our work and its expected benefits.