Summary: 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.