Knowledge that Transforms

When a multiattribute utility function is only partially specified by prior preference statements, what can be said about the relative desirability of actual alternatives? This question is addressed for the cases of additively separable cardinal utility with unknown scaling constants; multiplicatively separable cardinal utility with unknown scaling constants; and additively separable ordinal utility. We review previous approaches, and treat issues of consistency (is the prior information consistent?), dominance (does the prior preference information imply that one outcome is preferred to another?) and potential optimality (are there utility functions of the given form, consistent with prior preference information, under which a particular outcome is preference optimal?). In the additive cases, a key relationship between dominance and potential optimality may be derived. The paper concludes by presenting an example application to a well known nuclear siting study.

We evaluate, by means of mathematical programming formulations, the relative technical and scale efficiencies of decision making units (DMUs) when some of the inputs or outputs are exogenously fixed and beyond the discretionary control of DMU managers. This approach further develops the work on efficiency evaluation and on estimation of efficient production frontiers known as data envelopment analysis (DEA). We also employ the model to provide efficient input and output targets for DMU managers in a way that specifically accounts for the fixed nature of some of the inputs or outputs. We illustrate the approach, using real data, for a network of fast food restaurants.

For an undirected network G = (V, E) whose arcs are subject to random failure, we present a relatively complete and comprehensive description of a general class of Monte Carlo sampling plans for estimating g = g(s, T), the probability that a specified node s is connected to all nodes in a node set T. We also provide procedures for implementing these plans. Each plan uses known lower and upper bounds [B, A] on g to produce an estimator of g that has a smaller variance (A − g)(g − B)/K on K independent replications than that obtained for crude Monte Carlo sampling (B = 0, A = 1). We describe worst-case bounds on sample sizes K, in terms of B and A, for meeting absolute and relative error criteria. We also give the worst-case bound on the amount of variance reduction that can be expected when compared with crude Monte Carlo sampling. Two plans arc studied in detail for the case T = t. An example illustrates the variance reductions achievable with these plans. We also show how to assess the credibility that a specified error criterion for g is met as the Monte Carlo experiment progresses, and show how confidence intervals can be computed for g. Lastly, we summarize the steps needed to implement the proposed technique.

This paper seeks to demonstrate that lower setup costs can benefit production systems by improving quality control. It does so by introducing a simple model that captures a significant relationship between quality and lot size: while producing a lot, the process can go "out of control" with a given probability each time it produces another item. Once out of control, the process produces defective units throughout its production of the current lot. The system incurs an extra cost for rework and related operations for each defective piece that it produces. Thus, there is an incentive to produce smaller lots, and have a smaller fraction of defective units. The paper also introduces three options for investing in quality improvements: (i) reducing the probability that the process moves out of control (which yields fewer defects, larger lot sizes, fewer setups, and larger holding costs); (ii) reducing setup costs (which yields smaller lot sizes, lower holding costs, and fewer defects); and (iii) simultaneously using the two previous options. By assuming a specific form of the investment cost function for each option, we explicitly obtain the optimal investment strategy. We also briefly discuss the sensitivity of these solutions to changes in underlying parameter values. A numerical example illustrates the results.