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European Journal of Operational Research, Volume 220, Issue 3, 1 August 2012, Pages 752-761
Robert F. Bordley, Stephen M. Pollock
Booz Allen Hamilton, 525 Choice Court, Troy, MI 48085, United States
University of Michigan, 1205 Beal Avenue, Ann Arbor 48109-2117, United States
Abstract
Each of an organization’s many activities transforms inputs into outputs. Managing these activities involves allocating input resources for some activities and assigning output targets for others. Making these decisions is especially difficult in the presence of uncertainty. In practice, many organizations address these problems by using a fairly simple “proportional allocation” heuristic (e.g., “allocate to each activity the same percentage increase (or decrease) in its resources or targets”). But proportional allocation does not consider the uncertainty inherent in the ability of each activity to make use of its resources (or meet its targets).
To address this limitation, this paper uses an approach that maximizes organizational utility which is assumed to be zero if any of the activities cannot meet its target (or resource allocation). This approach, utility-based probability maximization (UPM), is a variant of stochastic optimization without recourse. UPM solutions are compared to those obtained by using the more traditional approach, chance-constrained programming. Using realistic assumptions (UPM), results in allocations and targets that are power function generalizations of proportional allocation. Moreover, these allocations are equivalent to the CCP solutions but with the advantage that they are explicit functions of the organization’s risk-preferences.
Concrete numerical examples show how target and resource allocations produced by UPM can be significantly different than (and superior to) those recommended by proportional allocation and chance-constrained programming.
Additional Information:
“Product liability regulation requires that engineers always implement a safer design if it is only marginally more expensive than a substantially less safe solution. Engineers can violate that requirement if they simply choose that solution which maximizes some measure of goodness subject to the risk of being unsafe not exceeding some prespecified risk threshold. If the design causes someone injury, the engineer’s client can be held liable for damages. To avoid violating product liability regulations, this paper proposes that the engineer’s objective should be to maximize the joint probability that the design is safe and that the goodness measure exceeds some value threshold. This value threshold, which is typically a random variable, can be chosen to reflect any degree of risk-aversion on the part of the client. This paper shows that this approach to design — based on a threshold — is typically mathematically easier to implement than the alternate approach — based on a risk threshold.
