Profit, expected value

Example 12 Expected Value of Net Profit Let iis consider a contractor who stands to make a net profit of 100,000 on a contract. The cost of preparing the bid on the contract is 10,000. There are four competing contractors, each with a probability pi = 0.25 of obtaining the contract. Thus, each contractor has a probability p2 = 0.75 of not obtaining the contract. Therefore, the expected value of the project is... 

We leave it as an exercise for the reader to find the condition under which the expected value of the profit is maximum i.e., maximize ... 

One-phase optimization Maximize expected profit across one or multiple price scenarios. This approach corresponds to the classical expect value maximization known from decision theory. 

If the chain letter is successful, the end result is a profitable company valued on the basis of conventional investment criteria, i.e., price/eamings ratio. During the 15 to 20 years after formding that is typically required to achieve profitability, a biotech company will have had a constantly changing shareholder list. With the exception of a few visionary formders, these investors expect to make their money over relatively short hme frames. 

Consideration of the expected value of profit alone as the objective function, which is characteristic of the classical stochastic linear programs introduced by Dantzig (1955) and Beale (1955), is obviously inappropriate for moderate and high-risk decisions under uncertainty since most decision makers are risk averse in facing important decisions. The expected value objective ignores both the risk attribute of the decision maker and the distribution of the objective values. Hence, variance of each of the random price coefficients can be adopted as a viable risk measure of the objective function, which is the second major component of the MV approach adopted in Risk Model I. 

From Table 6.7 and the corresponding efficient frontier plot in Figure 6.4, similar trends to Risk Model II (and also the expected value models) are observed in which decreasing values of 0 correspond to higher expected profit until a certain constant profit value is attained ( 81 770). The converse is also true in which a constant profit of 59330 is reached in the initially declining expected profit for increasing values of 0i. 

Suppose your marginal cost is 10. Based on the least squares regression, compute a 95% confidence interval for the expected value of the profit maximizing output. 

Technology Product flexibility Levelised cost [ /kg] Expected profit [M ] Expected value of flexibility [M ]... 

It is worthwhile to make tables or plot curves that show the effect of variations in costs and prices on profitabihty. This procedure is called sensitivity analysis. Its purpose is to determine to which factors the profitability of a project is most sensitive. Sensitivity analysis should always be carried out to observe the effect of departures from expected values. 

At the end of this stage, variance of the mature costs will be rather high. However, the expected value of this cost has been determined. If this cost is too high to offer adequate hope of profit (i.e., to offer hope that the technology will be commercialized) or if the cost necessary to commercialize lies within the variance but at an inadequately low probability, then the technology is not commercial. The project is dropped or perhaps the Invention stage is reentered. 

Principles that depend on determination of expected values by the mathematics of probability theory are frequently criticized on the grounds that the theory holds only when trials are repeated many times. It is argued that, for certain types of decisions—for example, whether to finance a major expansion—expectation is meaningless since this type of decision is not made very often. According to the counterargument, even if the firm is not faced with a large number of repetitive decisions, it should apply the principle to many different decisions and thus realize the long-run effects. Moreover, even if the decision is unique, the only way to approach decisions for which probabilities are known is to behave as if the decision were a repetitive one and thus minimize expected cost or maximize expected revenue or profit. 

The coefficient jS > 0 represents the weight given to the conservative part of the decision. If /3 is large, then the above optimization problem tries to find a solution with minimtil profit variance, while if /3 = 0, then problem (8) coincides with problem (4). Note that since the variance Var[G(x , D)] = E[(G(x, D) — E[G(x, D)]) ] is itself an expected vrilue, from a mathematical point of view, problem (8) is similar to the expected value problem (4). Thus, the problem of optimizing the expected value of an objective function G(x, D) is very genertil—it could include the means, variances, qtrantiles, and almost any other aspects of random variables of interest. 

One may need to optimize a function of the expected value function g x). This happened, for example, in problem (8), where the manager wanted to optimize a linear combination of the expected value and the variance of the profit. Although important from a modeling point of view, such an extension usually does not introduce additional technical difficulties into the problem. 

For instance, one may be interested in maximizing the expected value of a profit given (Albritton et al. 1999) ... 

To be an effective management tool, productivity management should be linked to a data-information decision-making model. Figure 16.7 proposes an eHealth data-driven model that identifies customer/patient value expectations (value proposition), the availability of resource requirements and their deployment, and the relationship between an acceptable (viable) value proposition and organizational profitability, productivity, and competitive advantage. 

Based on the hypothesis that pfio t) and w so(t) are random variables independent mutually, the stochastic expected value programming model for supply chain logistics planning, which aims at the maximum profit of the entire supply chain in planning period T is ... 

Since the size of the orders that has to be request is chosen between three values, and, in addition, there are four time instants in which an order has to be placed, there are 81 possible combinations for simulating in each scenario. For each one of these configurations, taking into account each scenario, the expected values of the profit (Eiprofit)) has been calculated and the one with the largest expected profit is picked. In the deterministic case the values for the demand have been chosen in 7 units of product A each five simulations steps and 3 units of B with the same frequency. Moreover, the value for the safety inventory level has been set in 50 units for all the entities except in SIP and PI where the selected value has been 100 units. In the first case below described, a variance of 3 and 2 has been added to both deterministic values of the demand size. In the second case, a variance of 30 has been added to the deterministic value of the safety inventory level. 

Under the old policy of ordering the expected value, the buyers would have ordered 1,000 parkas. However, demand is uncertain, and Table 13-1 shows that there is a 51 percent probability that demand wiU be 1,000 or less. Thus, a policy of ordering a thousand parkas results in a cycle service level of 51 percent at L. L. Bean. The buying conunittee must decide on an order size and cycle service level that maximize the profits from the sale of parkas at L. L. Bean. 

This is more than an 8 percent increase in profitability relative to the policy of ordering the expected value of 1,000 parkas. 

The expected profit from ordering 350 pairs of skis can be evaluated as 45,718. Thus, ordering 468 pairs results in an expected profit that is almost 8 percent higher than the profit obtained from ordering the expected value of 350 pairs. 

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