LCM Seminar

Developing specific staffing schedules in service systems such as call centers can be difficult, since implementations must take
into account complex scheduling constraints. Good schedules must also reflect the economic tradeoffs that arise from shift-pay
differentials, part-time pay, and overtime. A fundamental requirement is that there be enough staff on duty at all times to meet
targeted service levels.

Staffing requirements are typically determined by first dividing the workday or workweek into planning periods such as shifts,
hours, quarter-hours, etc.. Then, a series of stationary queueuing models, most often M/M/s type models, is constructed, one
model for each planning period. Each of these models is independently solved for the minimum number of servers needed to
meet the service target in that period.

We will review our own research developments in this area and will identify emerging problems. We will also present some of
our current developments in working with one of the major call center companies in Portugal.

15:00 - 15:30	Staffing of nonstationary Markovian service systems
	João Luís Soares
15:30 - 16:00	Derivative-Free Optimization and Applications
	Luís Nunes Vicente,
16:00 - 16:30	Large Scale Network Problems
	José Luís Santos
16.30- 16.50	Coffee Break
16.50-17.20	Mathematical Analysis of Piezoelectric Problems
	Isabel Narra de Figueiredo
17.20 - 17.50	Simulation of the Hydrodynamic Behaviour of a Biological Packed Bed
	Adérito Araújo
17.50- 18.20	Simulation of a Moving Bed Reactor used in the Pulp and Paper Industry
	Paula de Oliveira

João Luís Soares	Staffing of nonstationary Markovian service systems
	Developing specific staffing schedules in service systems such as call centers can be difficult, since implementations must take into account complex scheduling constraints. Good schedules must also reflect the economic tradeoffs that arise from shift-pay differentials, part-time pay, and overtime. A fundamental requirement is that there be enough staff on duty at all times to meet targeted service levels. Staffing requirements are typically determined by first dividing the workday or workweek into planning periods such as shifts, hours, quarter-hours, etc.. Then, a series of stationary queueuing models, most often M/M/s type models, is constructed, one model for each planning period. Each of these models is independently solved for the minimum number of servers needed to meet the service target in that period. We will review our own research developments in this area and will identify emerging problems. We will also present some of our current developments in working with one of the major call center companies in Portugal.
Luís Nunes Vicente	Derivative-Free Optimization and Applications
	Optimization problems defined by functions for which derivatives are unavailable or available at a prohibitive cost are appearing more and more frequently in computational science and engineering. Increasing complexity in mathematical modeling and higher sophistication of scientific computing are two reasons why derivative-free optimization is currently an area of impact. We have identified a number of applications involving complex simulations and/or physical experimentations, resulting from joint research with engineering colleagues, including molecular geometry optimization, analysis of mechanical systems with contact, and parameter estimation in astrophysics. On a different but related level, this project involves the development, analysis, and implementation of new algorithms for derivative-free optimization, by bringing together different geometrical concepts (like positive generators and poisedness) and different sampling strategies (like directional sampling and surrogate modeling). The goal is to exchange ideas from different methodologies (for instance, using simplex gradients to poll more efficiently in pattern search, or using heuristics to improve the search phase of pattern search towards global optimization). We will present numerical results for application problems and benchmarking test sets.
José Luís Santos	Large Scale Network Problems
	tba
Isabel N. Figueiredo	Mathematical Analysis of Piezoelectric Problems
	Piezoelectricity can be defined as an interaction between two phenomena: the direct piezoelectric effect (a mechanical deformation generates an electric field in the material) and the inverse piezoelectric effect (the application to the material of an electric field or of a potential difference generates a deformation), cf. T. Ikeda, Fundamentals of Piezoelectricity, Oxford University Press, Oxford, 1990. Therefore, a single piezoelectric device is both an actuator and a sensor, and consequently, piezoelectric materials belong to a class of smart or intelligent materials, that are very important in many applications as, for example, biomechanics, biomedicine, structural mechanics, etc.. The scope of this project is essentially to acquire a better mathematical knowledge of some particular piezoelectric models, as adaptive rod models and composite laminated plate models. This research project will lead to a better understanding of the mechanical and electric behavior of these problems and, consequently, to an improvement of real-life applications.
Adérito Araújo	Simulation of the Hydrodynamic Behaviour of a Biological Packed Bed
	The hydraulic characteristics of a laboratory submerged packed bed, filled with a volcanic stone, pozzuolana, have been experimentally investigated through tracer tests. Sets of essays at flow rates from 1 to 2.5 l/h in clean conditions were performed. The results showed a considerable amount of dispersion through the filter as the hydraulic loading was changed, indicating a multiplicity of hydrodynamic states, approaching its behavior to plug flow. An analytical solution for the advection-dispersion equation model has been developed for a semi-infinite system and we have considered an appropriate physical boundary condition. A numerical simulation using finite difference schemes is done taking into account this particular boundary condition that changes according to the flow rates. Proper formulation of boundary conditions for analysis of column displacements experiments in the laboratory is critically important to the interpretation of observed data, as well as for subsequent extrapolation of the experimental results to transport problems in the field.
Paula de Oliveira	Simulation of a Moving Bed Reactor used in the Pulp and Paper Industry
	The development of mathematical models that describe industrial processes is playing an increasing role in industrial context, because such models can replace, in some cases, experimental simulation, in a cheaper and more flexible way. In this talk a transient model of a continuous moving bed reactor - the digester - used in the pulp and paper industry is studied. In this complex and heterogeneous digester a moving bed of wood chips, containing cellulose, hemicellulose and lignin, reacts with sodium hydroxide and sodium sulfide -- in a liquid phase -- to remove the lignin from the cellulose fibers. The model is derived from the fundamental principles of mass and energy balance and is represented by a system of 15 partial differential equations (P.D.E's) of convection - reaction type. The numerical methods used in the discretization of this P.D.E's system is based on operator splitting which essentially consists in considering separately convection and reaction phenomena. This approach allows the use of methods with different properties - explicitness, implicitness and order - for each subprocess. The final global class of methods represents in some sense a "patching of tailored methods" well adapted to the feature of individual phenomena. Numerical simulations of the concentrations of organics and inorganics are presented.