USING RESIDUAL ANALYSIS TO SEARCH FOR SPECIFICATION ERRORS*

The author generated several residual patterns under controlled conditions in order to observe the effects of various specification errors. The results and their interpretation are presented in this article extending the work of Richards [3]. A list of conditions which affect the residual pattern resulting from the misspecifications is included.     

Notes and Communications ON SENSITIVITY ANALYSIS IN DECISION THEORY*

This note points out a crucial flaw in Evans's recent article [1] on decision sensitivity analysis which was published in this journal. This flaw leads to errors in the majority of his formulae and examples. Correct distance formulae in “probability space,” easily computed from the problem data, are provided. After a critical discussion of some of the concepts Evans employed, we bring to the reader's attention a body of prior work in this area that apparently was overlooked.     

USING CONJOINT ANALYSIS TO PREDICT TRIAL AND REPEAT-PURCHASE PATTERNS OF NEW FREQUENTLY PURCHASED PRODUCTS*

A new approach is proposed to evaluate new-product opportunities. This approach uses the distribution of brand-purchase probability of the new product over a population of potential customers and the outputs from conjoint analysis. The heterogeneous distribution of brand-purchase probability is expressed by a beta binomial brand-choice model compounded with a negative binomial product-class purchase-incidence model. The resulting model provides a way to predict trial and repeat-purchase patterns of new-product concepts. The paper discusses the development of the model. It also discusses issues of measurement, estimation, testing, and implementation of the proposed approach based on actual empirical data.     

USING AN UNCERTAINTY MODEL TO ASSESS SALES RESPONSE TO ADVERTISING*

Implications of a probabilistic “random walk” model of incremental sales response to advertising are developed for various timing patterns of advertising expenditures. Maximum likelihood procedures for assessing advertising effectiveness and for estimating a decay (forgetting) rate are developed and applied to artificial data of known configuration and are used to assess the impact over time of a brochure program on mail-order sales. Results are also compared to those from alternative models involving various lag patterns in advertising effects.     

A MATHEMATICAL PROGRAMMING APPROACH TO SENSITIVITY ANALYSIS IN SINGLE-STAGE DECISION MAKING

This paper presents sensitivity analyses for a single-stage decision problem where an action which will maximize the expected payoff must be chosen from a finite number of actions given the states of nature, their probabilities, and the payoffs corresponding to each action and state of nature. Three types of sensitivity analysis are developed: (1) sensitivity analysis on the probabilities keeping the payoff numbers fixed, (2) sensitivity analysis on the payoffs keeping the probabilities fixed, and (3) joint sensitivity analysis on the payoffs and the probabilities. The approach is illustrated with an example. Quite often the sensitivity analysis can be conducted by solving an appropriate linear or quadratic programming problem.     

SENSITIVITY ANALYSIS WITH INTERACTION EFFECTS

The purpose of this paper is to extend the sensitivity analysis methodology as it applies to linear programming. The methodology developed herein is concerned with those changes in a technological coefficient that cause simultaneous changes in the relevant cost coefficients of the objective function. By proceeding from the definitions of feasibility and optimality, the authors develop formulas for determining bounds on the extent to which a technological coefficient, which has a predetermined effect on the corresponding cost coefficient, can vary without changing the optimal set of activities. After the formulas are developed, their use is demonstrated on a product-mix problem. This technique is of interest because changes in the rate at which an input is utilized can be expected to change the cost per unit of a resulting product. This interdependence should be recognized whenever a sensitivity analysis is performed on a technological coefficient of either a cost minimization or a contribution margin maximization problem.     

SENSITIVITY ANALYSIS IN DECISION THEORY

This paper explores linear programming-like sensitivity analysis in decision theory. In particular, the paper considers the sensitivity of an optimal decision to changes in probabilities of the states of nature and the development of “confidence spheres” to bound arbitrary parametric changes in the probability vector. Such information can be used to assess the accuracy required in assigning probabilities and the confidence in the maximumutility decision.     

USING FISHBURN'S TECHNIQUES FOR ANALYSIS OF DECISION TREES: SOME EXAMPLES*

Techniques for the analysis of payoff matrices with “imprecise” assessment of state probabilities are applied to the analysis of decision trees in normal form. The analytical techniques, due to Peter Fishburn, are summarized and then illustrated by analyzing two decision trees. Problem I, a two state problem, provides geometrical analogs for the two most “imprecise” probability assessments and simple analytical and geometrical analogs for the least “imprecise” probability assessment. Problem II, a three state problem, illustrates the application of all four precision levels, from most “imprecise” through least “imprecise.”     

USING DUMMY VARIABLES TO CHECK FOR ROUNDING ERROR IN COMPUTERIZED REGRESSION PROGRAMS*

After a brief review of the role of dummy variables in regression analysis and the current state-of-the art in rounding/truncation error detection in computerized least squares programs, this paper presents a theorem that can be used to detect this type of error whenever an analyst is running a regression program that has one (or more) dummy variables as independent variables.     

USING A LATE-START RESOURCE-CONSTRAINED PROJECT SCHEDULE TO IMPROVE PROJECT NET PRESENT VALUE*

Although literature on the achievement of monetary objectives in a resource-constrained project environment is limited, the maximization of project net present value (NPV) is an important criterion of project success. This paper presents a procedure for developing a late-start resource-constrained project schedule using the critical path method-material requirements planning. Using an extensive set of problems from the literature, we show that this procedure yields a higher NPV and lower average duration than schedules derived with heuristics that schedule each activity as early as possible. In addition, while the late-start schedule on average was significantly longer than the optimal-duration resource-constrained schedule, no significant difference occurred in the average NPVs of the two scheduling methods.     

THE ANALYSIS OF OUTLYING DATA POINTS USING ROBUST REGRESSION: A MULTIVARIATE PROBLEM-BANK IDENTIFICATION MODEL*

Because the eight largest bank failures in United States history have occurred since 1973 [24], the development of early-warning problem-bank identification models is an important undertaking. It has been shown previously [3] [5] that M-estimator robust regression provides such a model. The present paper develops a similar model for the multivariate case using both a robustified Mahalanobis distance analysis [21] and principal components analysis [10]. In addition to providing a successful presumptive problem-bank identification model, combining the use of the M-estimator robust regression procedure and the robust Mahalanobis distance procedure with principal components analysis is also demonstrated to be a general method of outlier detection. The results from using these procedures are compared to some previously suggested procedures, and general conclusions are drawn.     

FOUR APPROACHES TO THE CLASSIFICATION PROBLEM IN DISCRIMINANT ANALYSIS: AN EXPERIMENTAL STUDY*

Four discriminant models were compared in a simulation study: Fisher's linear discriminant function [14], Smith's quadratic discriminant function [34], the logistic discriminant model, and a model based on linear programming [17]. The study was conducted to estimate expected rates of misclassification for these four procedures when observations were sampled from a variety of normal and nonnormal distributions. In contrast to previous research, data were taken from four types of Kurtotic population distributions. The results indicate the four discriminant procedures are robust toward data from many types of distributions. The misclassification rates for both the logistic discriminant model and the formulation based on linear programming consistently decreased as the kurtosis in the data increased. The decreases, however, were of small magnitude. None of these procedures yielded statistically significant lower rates of misclassification under nonnormality. The quadratic discriminant function produced significantly lower error rates when the variances across groups were heterogeneous.     

AN APPROACH TO COST—VOLUME—PROFIT ANALYSIS UNDER UNCERTAINTY*

Cost-Volume-Profit analysis is a tool of cost accountants aiding in the choice of an optimal course of action in the solution of a managerial problem. C-V-P is a limited analysis since all the needs of management in determining the optimal strategy are not fulfilled. Factors pertinent to the choice of the optimal strategy under uncertainty are variables, although traditional C-V-P treats these factors as constants. Hence, an approach to C-V-P where pertinent factors necessary for decision making are considered as variables is more desirable than traditional C-V-P. By introducing uncertainty, it is also beneficial to broaden C-V-P to fulfill the following desire of management. Should management choose a course of action based only on its own estimates of the decision parameters or is it advisable to postpone a terminal decision until additional research into the decision parameters is accomplished? Broadened C-V-P solves this problem with the aid of Bayesian Decision Theory for the choice of the optimal course of action in the face of uncertainty.     

ON THE SENSITIVITY OF BRAND-CHOICE SIMULATIONS TO ATTRIBUTE IMPORTANCE WEIGHTS

This paper critically reviews the report by Green, DeSarbo, and Kedia “on the insensitivity of brand-choice simulations to attribute importance weights”. The review suggests that results from two of their four weight distortion conditions should be viewed with suspicion and that their procedure for selecting brand scores biased the sensitivity analysis and inflated individual-level hit rates. The most unfortunate problem is that their simulation-experimental design precludes a global test of the main research issue. Results are presented from an alternative simulation approach that has the power to detect the sensitivity of brand shares to a wide range of conditions that affect the shape of attribute weight distributions. The results suggest that conclusions of Green, DeSarbo, and Kedia apply only to a limited domain and would not obtain in many likely market situations. Extensions to nonadditive decision structures are suggested and several unresolved issues are outlined.     

USING SPECTRAL ANALYSIS FOR FORECAST MODEL SELECTION

Spectral analysis can be used to determine the general class of forecasting models which should be considered for purposes of generating forecasts of a marketing time series. Power spectral estimates and cross-spectral estimates can aid in selecting the most appropriate model when several variations of the predetermined class are under consideration.     

JOB RELEASE CONTROL USING A CYCLIC SCHEDULE*

In just‐in‐time inventory management in any manufacturing setting, the general idea has been to release jobs as late as possible (to reduce inventory costs) while still having them arrive at bottleneck machines in time to maintain the desired throughput (by not starving a bottleneck machine). When a cyclic schedule is employed, the throughput is determined by a cyclic sequence of operations known as the cyclic critical path. These operations are not, in general, all performed on a single bottleneck machine. We present an algorithm for releasing jobs that treats this cyclic critical path as the bottleneck. Although this algorithm has the somewhat complex task of not delaying any of these operations on the cyclic critical path, it is greatly simplified by being able to take advantage of the fixed sequence of the cyclic schedule. The result is that the algorithm is relatively simple to implement. Although it uses a simulation‐based analysis, this analysis can all be done and the necessary results stored in advance of its use. We test the algorithm in a job shop environment with stochastic operation times. This algorithm is shown to be effective at reducing inventory while avoiding decreases in throughput.     

SPECTRAL ANALYSIS IN BUSINESS FORECASTING*

Although spectral analysis has previously been discussed in a number of business journals, the discussion has not been detailed enough for non-mathematicians. The objective of this paper is to review in detail the concepts and to go over the computations of spectral analysis as they pertain to forecasting. To gain insight into the model building technique of spectral analysis, a passing comparison with a familiar model–regression–is made. Regression analysis attempts to find a set of independent variables that shed some light on the dependent variable to be forecasted. In other words, if the independent variables have some functional relationship with the dependent variable, a reliable forecast of the dependent variable can then be made. Forecasting using spectral analysis, on the other hand, is based on the assumption that the variation of a time series can be explained by some mixture of sine and cosine waves. Model parameters can then be estimated for these waves and forecasts be made. These parameters have the same property of least squares as in ordinary regression analysis. A transformation of these parameters gives the spectra of the time series. The spectra are related to the explained variation present in regression analysis. An extension of the spectra gives a set of coefficients of an autoregressive forecasting model. This latter model is referred to as the Wiener-Kolmogorov forecasting model.