Perfect information, expected value

This chapter addresses the planning, design and optimization of a network of petrochemical processes under uncertainty and robust considerations. Similar to the previous chapter, robustness is analyzed based on both model robustness and solution robustness. Parameter uncertainty includes process yield, raw material and product prices, and lower product market demand. The expected value of perfect information (EVPI) and the value of the stochastic solution (VSS) are also investigated to illustrate numerically the value of including the randomness of the different model parameters. 

Since stochastic programming adds computational burden to practical problems, it is desirable to quantify the benefits of considering uncertainty. In order to address this point, there are generally two values of interest. One is the expected value of perfect information (EVPI) which measures the maximum amount the decision maker is willing to pay in order to get accurate information on the future. The second is the value of stochastic solution (VSS) which is the difference in the objective function between the solutions of the mean value problem (replacing random events with their means) and the stochastic solution (SS) (Birge, 1982). 

A solution based on perfect information would yield optimal first stage decisions for each realization of the random parameter Then the expected value of these decisions, known as wait-and-see (WS) can be written as (Madansky, 1960) ... 

In the United Kingdom, the Department of Health asks NICE to evaluate health technologies that have a major impact on the National Health Service. Although not formally based on efficiency considerations, this approach is more consistent with obtaining the best value for money from the use of resources on economic evaluation. More recently, methods involving the estimation of the expected value of perfect information have been used in a pilot study to inform research priorities in the United Kingdom (Claxton et al. 2004). 

The profit impact of demand uncertainty is thus 15,000 — 11,700 = 3300, or 28.2% of expected profit. This example shows how demand uncertainty interacts with capacity to affect profit. It also shows the potential value of perfect information, obtained through sources such as market surveys, expert forecasts, and test markets. 

Perfect capital markets should see through the cycle and the reaction of valuations to purely cyclical fluctuations in the industry return on capital should be insignificant. To examine this, we again compared the actual valuation level to a fundamental predicted valuation level for commodity chemical companies. To pinpoint the effects of cyclicality, however, we used a slightly different approach. As we wanted to evaluate capital market expectations, we compared the actual valuation level with a fundamental valuation level based on perfect foresight , i.e., assuming that the capital market knew the actual development of the key value drivers for the next 8 years and evaluated this information in line with its implied fundamental value creation.4 Furthermore, we used a capital structure-adjusted market-to-book ratio instead of an earnings-based metric for the valuation level. 

As a further consequence of an advanced shareholder value orientation, a more targeted approach can be taken to investor relations. We feel that investor relations in many chemical companies today is predominantly aimed at providing timely, accurate, and exhaustive information to capital markets. Again, the assumption is that capital markets are perfectly efficient and will always evaluate this information correctly again, this does not match up with the real world. Behind the capital markets are investors with a wide variety of expectations and important specific investment preferences and institutional restrictions. In addition, it can be demonstrated that only a small number of investors with significant trading volume mainly influence stock prices in the short and medium term (Coyne, K. P. and Witter, J. W.). 

Although, in an ideal world, the network would give rise to either a 0 (absent) or 1 (present) for each output neuron (K), the observed values are somewhere in between. Figure 4 shows a typical outcome, the distribution of Y values for a single output neuron, the carboxyl group. As expected, the distribution curves of the output values for present and absent classes (solid and broken lines, respectively) do overlap, i.e., the network is not capable of perfect discrimination. This is true of most of the 85 structural features studied. Thus, to infer the presence of a structural feature, a high cutoff value of K is chosen if high prediction accuracy is required however, this accuracy is achieved at the expense of lower recovery of valid information. 

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