The microbial growth in multi-substrate environments may be viewed as an optimal resources allocation problem. The optimization aims at maximizing some biological objective like the biomass growth. The models developed using this hypothesis are called "cybernetic" and they represent the complex cell structure as an optimizing function that regulates the intracellular enzymatic machinery. In this work, a cybernetic model was developed to represent the growth of two E. coli strains (JM 109 and BL 21 -DE3-) on a medium containing glucose and glycerol as carbon and energy sources. The model was able to accurately simulate the biomass growth, the substrates consumption and the growth-rate profiles.

The Shortest-path problem with time-windows and capacity constraints (SPPTWCC) is a problem used for solving vehicle-routing and crew-scheduling applications. The SPPTWCC occurs as a sub-problem used to implicitly generate the set of all feasible routes and schedules in the column-generation formulation of the vehicle routing problem with time windows (VRPTW) and its variations. The problem is NP-hard in the strong sense. Classical solution approaches are based on a non-elementary shortest-path problem with resource constraints using dynamic-programming labeling algorithms. In this way, numerous label-setting algorithms have been developed. Contrarily to this approach and with the aim to obtain elemental and optimal solutions, we propose a new mixed integer-linear formulation to the SPPTWCC. Some valid inequalities that can be used to strengthen the linear relaxation of the SPPTWCC are also proposed. Numerical experiments on some VRPTW instances taken from Solomon's benchmark problems show that (near) optimal solutions are easily obtained in spite of the considerable problem size. Also the number of generated columns is kept at a very low level.

A key issue in logistics is the efficient management of a vehicle fleet servicing a set of customers with known demands. Every vehicle route must start and finish at the assigned depot, each customer is to be visited by a single vehicle and vehicle capacities must not be exceeded. These are the constraints for the capacitated vehicle routing problem (VRP) whose objective is usually the minimization of the travel distance. When every customer has an associated time window, we are dealing with the vehicle routing problem with time windows (VRPTW), an NP-hard problem extensively studied. In the static VPRTW, all the problem data are given. A more challenging subject is the dynamic VRPTW (DRVPTW) where routes must be periodically updated because of new service requests. In DVRPTW, the information on the problem is time-dependent since the data are in part given a priori and in part dynamically updated. As a result, the best solution must be periodically revised. There are two classes of DVRPTW solution methodologies: the immediate assignment that updates vehicle routes as soon as a new service request is received, and the deferred assignment retaining the new service calls for a certain time period before dispatching them all at once. The latter type has been adopted in this paper. At the time of revising their routes, the vehicles are already on duty and some nodes have already been visited. The remaining old customers that have designated vehicles are either being serviced or awaiting service. The customers to be considered in the DVRPTW include not only old customers still to be serviced but also new visit requests. The DVRPTW is tackled by solving a series of static VRPTW problems, with each one being defined every time the input data is updated. The approach assumes that each vehicle will start its new route at the location where it is servicing or to which it is traveling.

This work describes an application of maximum likelihood identification and statistical detection techniques for determining the presence and nature of abnormal behaviors in batch fermentations. By appropriately organizing these established techniques, a novel algorithm that is able to detect and isolate faults in nonlinear and uncertain processes was developed. The technique processes residuals from a nonlinear filter based on the assumed model of fermentation. This information is combined with mass balances to conduct statistical tests that are used as the core of the detection procedure. The approach uses a sliding window to capture the present statistical properties of filtering and mass-balance residuals. In order to avoid divergence of the nonlinear monitor filter, the maximum likelihood states and parameters are periodically estimated. The maximum likelihood parameters are used to update the kinetic parameter values of the monitor filter. If the occurrence of a fault is detected, alternative faulty model structures are evaluated statistically through the use of log-likelihood function values and chi2 detection tests. Simulation obtained for xanthan gum batch fermentations are encouraging.

The vehicle routing problem (VRP) has become a crucial industrial issue for its impact on product distribution costs. Though quite important in practice, the time-constrained version of the VRP accounting for several types of vehicles and m- depots, called the extended VRP with time windows (m-VRPTW), has received less attention. Since it is an NP-hard problem, most of the current approaches to m-VRPTW are heuristic, thus providing good but not necessarily optimal solutions. This work presents a novel MILP mathematical framework for the m-depot heterogeneous-fleet VRPTW problem. The new optimization approach permits to find both the optimal vehicle route/schedule and the fleet size by choosing the best set of preceding nodes for each pick-up point. To get a significant reduction on the problem size to tackle larger m-VRPTW problems, some elimination rules have been embedded in the MILP framework. When applied to a pair of examples, it was observed a remarkable saving in computer costs with regards to prior VRPTW optimization methods.

The main aim of this work is the development of mathematical models of aerobic batch fermentations for its use in estimation and control algorithms. Most batch fermentation models are empirical and simple, and do not provide interrelationships between state variables and measurements. In this work such interrelationships are obtained from mass and energy balances of the fermentation components. Since aerobic fermentations with formation of a single metabolite exhibit three degrees of freedom, three independent kinetic equations are necessary to build the state space model. Test results on the batch fermentation of xanthan gum are presented.