Recourse decisions

They show that all decisions, including recourse decisions, can be determined uniquely as a function of the first-period stocking factor. The stocking factor z is defined as follows ... 

The information about the scenario tree is introduced into the model by adding two indexes to the decision variables I and hi. As an example, variable associated with a decision that is made when solely the combination of events hi is known, however the decision will be materialized at period t when event I unveils. A subscript hi below a variable also indicates that is a (/ -I- l)-stage variable. For instance, a (/ -I-1)-stage variable such as would be related to a recourse decision... 

All previously discussed optimization problems are deterministic, that is, all the data required in those models is assumed to be perfectly known. In this section, we address stochastic programs in which some data may be considered imcertain. In this kind of problems, it is relevant to distinguish between two set of decisions (i.e., variables) the first stage decisions, and the recourse decisions. 

All those equations involving recourse decisions y are taken into account in Q. As it can be seen, 2 is a mathematical program that minimizes the second-stage cost for a given value of the uncertain parameter f. Then, the expected recourse function the mathematical expectation of Q, is defined by the expression (A. 18). 

The computation of mesopore size distribution is valid only if the isotherm is of Type IV. In view of the uncertainties inherent in the application of the Kelvin equation and the complexity of most pore systems, little is to be gained by recourse to an elaborate method of computation, and for most practical purposes the Roberts method (or an analogous procedure) is adequate—particularly in comparative studies. The decision as to which branch of the hysteresis loop to use in the calculation remains largely arbitrary. If the desorption branch is adopted (as appears to be favoured by most workers), it needs to be recognized that neither a Type B nor a Type E hysteresis loop is likely to yield a reliable estimate of pore size distribution, even for comparative purposes. 

It is evident that there is no simple, universally agreed-upon formula for solving this problem. For practical applications, then, if t is much different from t(., any one of the above equations will do, and if t is close to tc, or if high stakes are involved in a decision, more experiments (to achieve equality n = ri2) might be the best recourse. (See subcase b. )... 

For the reasons described, no specific test will be advanced here as being superior, but Huber s model and the classical one for z = 2 and z = 3 are incorporated into program HUBER the authors are of the opinion that the best recourse is to openly declare all values and do the analysis twice, once with the presumed outliers included, and once excluded from the statistical analysis in the latter case the excluded points should nonetheless be included in tables (in parentheses) and in graphs (different symbol). Outliers should not be labeled as such solely on the basis of a fixed (statistical) rule the decision should primarily reflect scientific experience. The justification must be explicitly stated in any report cf. Sections 4.18 and 4.19. If the circumstances demand that a mle be set down, it is best to use a robust model such as Huber s its sensitivity for the problem at hand, and the typical rate for false positives, should be investigated by, for example, a Monte... 

In a stochastic program with recourse, some corrective decisions or recourse actions can be taken after the uncertainty is disclosed. Each point in time where a decisions is made is called a stage. The two-stage stochastic program is the most... 

To ensure that the original information structure associated with the decision process sequence is honored, for each of the products whose demand is uncertain, the number of new constraints to be added to the stochastic model counterpart, replacing the original deterministic constraint, corresponds to the number of scenarios. Herein lies a demonstration of the fact that the size of a recourse model increases exponentially since the total number of scenarios grows exponentially with the number of random parameters. In general, the new constraints take the form ... 

Although increasing 02 with fixed value of 0 corresponds to decreasing expected profit, it generally leads to a reduction in expected production shortfalls and surpluses. Therefore, a suitable operating range of 02 values should be selected to achieve a proper trade-off between expected profit and expected production feasibility. Increasing 02 also reduces the expected deviation in the recourse penalty costs under different scenarios. This, in turn, translates to increased solution robustness. In that sense, the selection of 0j and 02 values depends primarily on the policy adopted by the decision maker. 

Stochastic Recourse Variables (Second-Stage Decision Variables)... 

The stochastic model with recourse in the previous section takes a decision merely based on first-stage and expected second-stage costs leading to an assumption that the decision-maker is risk-neutral (Sahinidis, 2004). In order to capture the concept of risk in stochastic programming, Mulvey, Vanderbei and Zenios (1995) proposed the following amendment to the objective function ... 

Recourse to the precautionary principle does not necessarily mean adopting final instruments designed to produce legal effects that are open to judicial review The decision to fund a research programme or even a decision to inform the public about possible adverse effects of a product or a procedure may themselves be inspired by the precautionary principle.40... 

Nitrocellulose of 11.8-12.3% N intended for celluloid manufacture is obtained in a way resembling the production of lacquer-grade material with the exception that the viscosity of the product is not of such decisive importance. Low viscosity of the nitrocellulose can cause the celluloid gel to be brittle, however. For this reason care should be taken to keep the viscosity above a certain limit. The essential stabilization can be carried out in boilers without recourse to autoclaves, but in order to shorten the stabilization process it is possible to carry out the kiering in autoclaves, the process then requiring only a few minutes. 

In a deterministic planning environment the most likely scenario, here scenario 2, would be considered the base case and the optimization model would be solved based on this scenario. The optimal decision would be to open facility 1 in period 1 and facility 3 in period 2 leading to a total profit of 2,590. To assess the robustness of this network to alternative demand scenarios the profit achievable with this configuration in case of the alternative demand scenarios can be assessed. In the example, for scenario 1 the overall profit would be 1,640 and for scenario 3, 2,765 respectively. Considered individually, the optimal decision for scenario 1 would be to open only facility 1 with a total profit of 1,880 and for scenario 3 to open both facilities 1 and 2 in period 1 with a total profit of 2,931. In order to explicitly incorporate the uncertainties caused by the different realization probabilities of the three demand scenarios, the optimization model can be extended into a two-stage decision with recourse ... 

The global (and European) financial system must urgently be reformed. Its deceleration, inter alia through controls, public presentation of externalized production costs, a tax on financial transactions (such as the Tobin tax), and the limitation of nonperformance-related benefits, are favored by more and more countries. The sustainability of the capital expenditure and its recourse to environmental compatibility must become the essential criterion of economic action. And it must be made accessible to journalistic thinking it must represent a motivation to reflect on interesting public-oriented forms of how to mutually agree, initiate, and implement the decisive steps. 

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