Knowledge that Transforms

This paper deals with the classical dynamic lot size problem without backlogging and capacity limitation. We derive worst case performance bounds for a class of lot sizing heuristics. When the considered methods are applied a decision whether to have a set-up or not in a certain period is taken without regarding the future demand. It is shown that 2 is a lower bound for the worst case performance ratio for such heuristics. The results illustrate circumstances under which the approximate techniques fail.

A persistent conceptual problem in the theory of risk accounting and risk analysis methodology is that of allocating or attributing a risk among the joint causes or “factors” producing it. When multiple factors interact, the especially difficult problem of “risk externalities” arises. Drawing on related work in the mathematical theory of games that seeks solutions to similar philosophical and conceptual problems, this paper proposes a method for solving the risk attribution problem. The proposed solution is justified on the grounds that it is the unique risk attribution function satisfying three reasonable principles, or “axioms,” of risk accounting. A mathematical framework for formulating risk attribution problems, and several possible applications, are also discussed.

In constrast to “ordinary” sensitivity analysis in linear programming, the tolerance approach considers simultaneous and independent changes in the objective function coefficients and in the right-hand side terms. This approach yields a maximum tolerance percentage such that, as long as selected coefficients or terms are accurate to within that percentage of their estimated values, the same basis is optimal. In particular, if the objective function coefficients are accurate to within the maximum tolerance percentage of their specified values, then the same solution is optimal.

This paper develops optimal order quantities for firms that are offered a one-time opportunity to delay payment for an order of a commodity. Such delayed payments result in a reduction of the effective purchase cost, which is a function of the return available on alternative investments, the number of units of the commodity ordered, and the length of the extended period. Optimal order quantities are developed for extended payment privileges that occur at a reorder point of between reorder points. Six suppliers' extended payment scenarios are evaluated. A simulation analysis is conducted to determine the sensitivity of derived models to changes in the various input parameters. The simulation with realistic parameter values reveals that the additional discounted order quantity is insensitive to large changes in the ordering cost and unit price; sensitive to changes in the carrying cost and return rate of funds, but without significantly affecting the total cost; and extremely sensitive to the annual demand. Simple analytic decision rules are provided to guide firms that are offered such extended payment privileges.

This paper attempts to relate the conditions that require different planning approaches. A theoretical planning framework is presented that considers the confidence of causal linkages coupled with the extent of environmental change. Prior planning research is synthesized to speculate on the appropriate leadership and decision-making styles for single-businesses, nondiversified firms, or divisions of diversified firms. Examples of computational, consensual, contingency, and conceptual planning systems are also provided.

In the pristine model of general economic equilibrium producers and consumers are assumed to take prices for their inputs and outputs as given. A market equilibrium solution is obtained when the prices of all products lead to equal amounts of supply and demand for each. The mathematical properties of this model provide a rich and powerful unifying foundation for much of modern microeconomic theory. However, in many practical applications it is difficult or impossible to develop the data, and formulate and solve the equations required to implement the model of general economic equilibrium in its most general form. In practice, generality of formulation is often sacrificed for ease of computation and interpretation. These tradeoffs allow the latest breakthroughs in optimization algorithms and computer technology to be applied in the analysis of important societal problems. A potential drawback associated with this otherwise desirable trend is that the analysis could become infatuated with the use of particular algorithms, and lose sight of the restrictive simplifying assumptions they imply. The present paper includes a comparison of the simplifying assumptions required in four of the most popular types of energy-economic models with respect to the model of general economic equilibrium. This comparison helps sharpen our appreciation for the tradeoffs between generalization of formulation and ease of computation and interpretation that are available. The concept of general economic equilibrium is employed to provide a common framework for four ostensibly different approaches to large-scale modeling: (1) variable-coefficient input-output theory, (2) process network methodology, (3) linear programming and (4) general nonlinear optimization. The similarities and the differences of the four approaches are isolated within this framework. This comparison makes both the absolute and the relative strengths and weaknesses of the models more transparent.

We analyze a duopoly through a differential game, in which the players set prices as functions of time. Under reasonable assumptions, we find that prices first decline, then increase. The market share of the biggest firm grows initially but decreases later. It is demonstrated that a firm may growth maximize early, but never late, in the product life cycle. Finally we show that only the low price firm will pay for informative advertising, whereas both firms will pay for persuasive advertising, though less if their market shares are very different.

Applications of reliability theory and some forms of chance-constrained programming need real-time, nonstationary estimates of regression quantiles to trigger preventive actions, thereby avoiding undesirable system states. We have designed the Quantile Estimation Procedure (QEP) for this purpose. QEP is a new adaptive filter that nonparametrica11y estimates time-varying parameters of multivariate regression quantiles. Results of Monte Carlo tests show that QEP provides accurate estimates for a range of stochastic processes. Falling within this range is the case study of this paper on monitoring compliance with short-term air quality standards.

In probabilistic linear programming models the decision maker is typically assumed to know the probability distribution of the random parameters. Here it is assumed that the distribution functions of the parameters have a specified functional form F(t, θ), where θ is an unknown (real) vector parameter. We suppose that the decision maker has the opportunity of observing a random sample drawn from F(t, θ). For a two-stage stochastic programming with recourse model the deterministic equivalent model is found using a Bayesian approach. Properties are presented for the deterministic equivalents in general and in the special case of the simple recourse model. Expressions for Expected Value of Sample Information (EVSI) and Expected Net Gain from Sampling (ENGS) are also derived. In the final section similar results are obtained for chance constrained programming models.

We develop an optimization procedure for assisting decision-makers in the allocation of resources for cleaning up a specific oil spill. The objective function is to minimize a weighted combination of spill-specific response and damage costs. Inputs to this problem include information about the outflow of oil, availability and performance of spill cleanup equipment, as well as costs of equipment transported and on-scene operation. A general (albeit separable) damage function is assumed. The algorithm is deterministic and is based on a dynamic program within which a series of 0-1 knapsack problems are solved repeatedly. Although this algorithm is approximate, its worst-case performance is quantified and we argue that under realistic inputs the procedure can be expected to produce solutions very close to optimality. Under prescribed conditions we prove that the algorithm produces optimal solutions. A realistic example based on the Argo Merchant oil spill is presented to provide insight into the structure of this problem. Finally, we discuss possible uses of this model within the existing and alternative operational and policy environments.