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.
Due to the combinatorial nature of the facility layout problem, current heuristic computer procedures do not always provide better solutions than visual methods. A new algorithm, FLAC (Facility Layout by Analysis of Clusters), is described which emulates the visual methods used by industrial engineers in solving facility layout problems. Initially side-stepping the combinatorial nature of the problem, FLAC is found to perform well in problems with high as well as low flow dominance, and in the presence and absence of line dominance. Computation time is attractive, especially on larger problems.
Social preferences for equity in the distribution of net benefits are not represented in a cost-benefit study by the sum of the individuals’ net present values. This paper presents two different decision analysts models for representing such an equity issue. For each model, conditions on the tradeoffs between different individuals are shown to imply that preferences can be represented by a special type of group value function. Procedures are presented by which such a group value function can be determined and used as part of a public policy evaluation.
We consider stochastic models for flow shops, job shops and open shops in which the work required by job j is the same at each machine, being a random variable W j . Because machines operate at different speeds, S i , the processing time of job j at machine i is W j /S i ,. It is the main result of this note that in a flow shop where the machine speeds increase (decrease) from the first to last machine and the workload distributions are ordered by a likelihood ratio criterion, then the makespan of the jobs is stochastically minimized by processing the jobs in the order of least to greatest (greatest to least) workload.
In this paper we consider a class of job shops with a dispatch area and a machine shop, where operational controls are exercised at the dispatch area as well as at the machine shop. For such dynamic job shops with these two levels of control, there are three categories of models. They are (1) pseudo-static, (2) pure dynamic, and (3) pseudo-dynamic. In this paper approximate queueing models are developed for pure dynamic and pseudo-dynamic job shops; open queueing network models and controlled arrival single stage queueing models, respectively. The accuracy of the open queueing network models and their use are illustrated. An example indicative of the possible accuracy of the controlled arrival single stage queueing models is also given.
Applying a relatively decentralised system of control which would keep state-owned enterprises (SOE) at arm's length from ministerial departments has been a stated policy for many governments around the world. However, the specific controls typically used for implementing this policy have seldom been successful. The purpose of this paper is to review and evaluate certain of these controls, drawing upon the British system of arm's length control of nationalised industries. In order to delimit the problem the paper cuts across the government-SOE relationship from the perspective of investment planning. Using primary information from the capital investment process in a particular nationalised industry, the paper searches for evidence on whether and in what ways existing controls have not been successful. Three types of controls are investigated: (1) The economic and financial groundrules, which are supposed to simulate a competitive, business-style efficiency. These rules are often assumed to act as an “invisible hand,” limiting direct government control. (2) The direct investment review, in the framework of the wider public sector expenditure survey. In discussing the nature of this review the paper examines whether government approval of investment conforms to an incrementalist or “muddling through” model. It further considers the role for incremental methods in controlling SOE investment. (3) The attempt to use corporate planning as a control instrument. Evidence from internal control processes within the enterprise and in particular the review of investment by a Central Executive is used in order to evaluate the above controls. This serves to show the diffuse character of the planning process and the possibilities and limitations of using similar controls at the government level. Suggestions are put forward for strengthening these forms of control by modifying or reinforcing certain elements within the existing arm's length framework. The paper would be useful for evaulating the difficulties involved in establishing some form of orderlines and formalisation in government-SOE relationships. It shows some of the weaknesses associated with certain “technocratic” rules and solutions to public policy problems in this environment.
We examine the firm's optimal advertising behavior under conditions of uncertainty. For the static one-period model, we show that the firm's attitude toward risk may be responsible for the potential divergence between advertising decisions under uncertainty and those under deterministic conditions. For the dynamic multi-period model, the ultimate impact of uncertainty on advertising is further complicated when the sales response function contains an unknown parameter, and the firm wishes to gain more information about it through experimentation. We demonstrate that whether it is optimal for the firm to experiment at an advertising rate higher, equal to, or lower than the myopic (one-period) level would depend on the specification of the response function. Finally, we offer some empirical evidence for our assumption of a quadratic sales response function, using time-series data of twelve major brands of cigarettes.
This paper considers the periodic review inventory problem for which one or more parameters of the demand distribution are unknown with a known prior distribution chosen from the natural conjugate family. The Bayesian formulation of this problem results in a dynamic program with a multi-dimensional state space. Two models are analysed: the depletive inventory model of consumable items and the nondepletive model of reparable items. For both models and for some specific demand distributions, it is shown that the solution of the Bayesian model can be reduced to that of solving another dynamic program with a one-dimensional state space. Moreover, an explicit form for the optimal Bayesian ordering policy is given in each case.