Journal:Informatica
Volume 5, Issues 1-2 (1994), pp. 167–174
Abstract
We consider here the optimization problems of simple competitive model. There are two servers providing the some service. Each server fix the price and the rate of service. The rate of service defines the customer losses waiting in line for the service. The customer go to the server with lesser total service cost. The total cost includes the service price plus waiting losses. A customer goes away, if the total cost exceeds some critical level. The flow of customers and the service time both are stochastic. There is no known analytical solution for this model. We get the results by Monte Carlo simulation. We get the analytical solution of the simplyfied model.
We use the model as an illustration to show the possibilities and limitations of optimization theory and numerical techniques in the competitive models.
We consider optimization in two different mathematical frameworks: the fixed point and the Lagrange multipliers. We consider two different economic and social objectives, too: the equilibrium and the social cost minimization.
We use the model teaching Operations Research. The simple model may help to design more realistic models describing the processes of competition.
Journal:Informatica
Volume 5, Issues 1-2 (1994), pp. 123–166
Abstract
We consider here the average deviation as the most important objective when designing numerical techniques and algorithms. We call that a Bayesian approach.
We start by describing the Bayesian approach to the continuous global optimization. Then we show how to apply the results to the adaptation of parameters of randomized techniques of optimization. We assume that there exists a simple function which roughly predicts the consequences of decisions. We call it heuristics. We define the probability of a decision by a randomized decision function depending on heuristics. We fix this decision function, except for some parameters that we call the decision parameters.
We repeat the randomized decision procedure several times given the decision parameters and regard the best outcome as a result. We optimize the decision parameters to make the search more efficient. Thus we replace the original optimization problem by an auxiliary problem of continuous stochastic optimization. We solve the auxiliary problem by the Bayesian methods of global optimization. Therefore we call the approach as the Bayesian one.
We discuss the advantages and disadvantages of the Bayesian approach. We describe the applications to some of discrete programming problems, such as optimization of mixed Boolean bilinear functions including the scheduling of batch operations and the optimization of neural networks.