REORDER-POINT MODELS WITH DISCRETE PROBABILITY DISTRIBUTIONS

This paper is concerned with the determination of reorder points and safety-stock levels for situations where both the demand and lead-time distributions are discrete and independent. Formulas are developed for computing exact probabilities for the lead-time demand distribution on the basis of empirical distributions. Practitioners can use the model to obtain exact probabilities for situations where the computational burden is justified, while academicians can use the model to evaluate heuristic approaches to the reorder-point problem.     

A STUDY OF THE PERFORMANCE OF SUBJECTIVE PROBABILITY ASSESSORS

Despite the key role that subjective probabilities play in decisions made under conditions of uncertainty, little is known about the ability of probability assessors in developing these estimates. A literature survey is followed by a review of results from a continuing series of experiments designed to investigate the external accuracy of subjectively assessed probability distributions. Initial findings confirm that probability assessments provided by untrained assessors are of questionable value in predicting the distribution of actual outcomes of uncertain events. Particular difficulty is encountered when subjects attempt to quantify the extremes of their subjective distributions. The impact of extended assessor training and hypotheses regarding the effects of variation in the assessor's information level and the complexity of the assessment task are explored. Implications for applied decision making are drawn, and directions for future investigations are suggested.     

PROCEDURES TO INCREASE THE VALIDITY OF SUBJECTIVE PROBABILITY ESTIMATES

A decision making model is often very sensitive to the subjective probability estimates that are used. To reduce this sensitivity, it is necessary to utilize elicitation procedures that yield more valid estimates and increase the decision maker's confidence in the estimates. This paper discusses an experiment in which the subjects were asked to estimate the areas of various squares. Two procedures were evaluated. In one procedure, the subjects were told that estimates were distributed typically around the true value in accordance with the normal probability distribution. In the other, the subjects were asked to estimate the length as a component that could be used to calculate the area. The results indicate that the normal error model is a reasonable representation of the estimation procedure. Both procedures provided estimates with significant validity. There is also an indication that the procedures reduce bias and that both procedures result in more consistent estimates when the sizes of the squares are varied.     

THE EFFECTIVE UNIT OF THE POISSON DISTRIBUTION AND DEMAND FORECASTING

This short paper deals with some of the difficulties which have been found in applying the effective unit concept of estimating the Poisson distribution in order to forecast demand in a major industry. It points to two special cases in which the common formulation produces misleading results, discusses the frequency with which these two special cases could be expected to occur based on this one major industry, and proposes some pragmatic solutions to the problems resulting.     

UNSUCCESSFUL IMPLEMENTATION THE CASE OF A COMPUTER-BASED ORDER ENTRY SYSTEM

This paper discusses results of a longitudinal field experiment to evaluate the implementation of a computer-based system. This new system includes the introduction of an optically scanned order input form and new computer programs. It is hypothesized that successful implementation would be affected by the quality of service and the personal costs and benefits to the users of the new system. The experimental results show a marked reduction in job satisfaction after implementation of the new system. The implications of the findings for the implementation of computer-based systems in general are discussed.     

TEACHING THE INDEPENDENCE OF X AND S2 IN APPLIED STATISTICS*

In this note, the independence of X and S² is proved without the prerequisite knowledge of differential calculus. The purpose is to compensate for the lack of a text in applied statistics that proves the independence of such statistics.     

SOME TESTS OF BINOMIAL PROBABILITY ASSESSMENTS

A replication of the Alpert-Raiffa probability assessment experiment is used to motivate the development of several tests for evaluating assessors. The tests permit an evaluation of an assessor's accuracy in estimating target quantities and in estimating his own uncertainty as well. Assumption of normal subjective distributions permits the determination of subjective variances. Data from trial assessments are employed to test models which assert that assessed quantities are equal to subjectively assessed error variances. Several tests of the latter type are compared using data from individual, as well as pooled, assessors.     

UNDERSTANDING THE EVOLUTION OF THE US WAGE DISTRIBUTION: A THEORETICAL ANALYSIS

In this paper, we propose an analytically tractable overlapping‐generations model of human capital accumulation and study its implications for the evolution of the US wage distribution from 1970 to 2000. The key feature of the model, and the only source of heterogeneity, is that individuals differ in their ability to accumulate human capital. Therefore, wage inequality results only from differences in human capital accumulation. We examine the response of this model to skill‐biased technical change (SBTC) theoretically. We show that in response to SBTC, the model generates behavior consistent with some prominent trends observed in the US data including (i) a rise in overall wage inequality both in the short run and long run, (ii) an initial fall in the education premium followed by a strong recovery, leading to a higher premium in the long run, (iii) the fact that most of this fall and rise takes place among younger workers, (iv) a rise in within‐group inequality, (v) stagnation in median wage growth (and a slowdown in aggregate labor productivity), and (vi) a rise in consumption inequality that is much smaller than the rise in wage inequality. These results suggest that the heterogeneity in the ability to accumulate human capital is an important feature for understanding the effects of SBTC and interpreting the transformation of the US labor markets since the 1970s.     

AN EVALUATION OF ORDER PICKING POLICIES FOR MAIL ORDER COMPANIES

This paper is concerned with the problem of order picking in mail order companies. Order picking is the retrieval of items from their warehouse storage locations to satisfy customer orders. Five order picking policies, strict order, batch, sequential zone, batch zone, and wave, are evaluated using labor requirements, processing time, and customer service as performance measures. A simulation model was developed to investigate these picking policies in a mail order environment. Prior research has focused on the study of individual picking policies. This study extends the prior research by evaluating multiple picking policies under varying operating conditions. The results of the study seem to indicate that (1) wave picking and batch picking perform well across the range of operating conditions considered in this study, and (2) sequential zone and batch zone picking do not perform well, especially as the order volume increases. However, the benefits and drawbacks to each picking policy must be taken into account. The key to effective implementation of an order picking system is to match the firm's business strategy, capabilities, technology, and space requirements with an order picking policy that maximizes the benefits of order picking to the firm and its customers.     

AN EVALUATION OF TWO MODELS OF UNDERGRADUATE STATISTICS

The paper reports on a large scale evaluation of two alternative models of undergraduate statistics courses. The traditional course orientation was compared with a problem-solving orientation in which the emphasis was on real world problem-solving, during the winter and spring quarters of 1973–74. The evaluation battery included behavioral and problem-solving skill measures. The findings indicate that improvements in statistics programs can be made.     

MAXIMIZING THE PROBABILITY OF ACHIEVING A TARGET PROFIT IN A TWO-PRODUCT NEWSBOY PROBLEM*

This paper explores the two-product newsboy problem. Solution procedures are developed to find the optimal production quantities of each product that will maximize the probability of achieving a profit target. The problem is shown to be surprisingly challenging, and numerical results obtained for only the more restrictive cases exhibit interesting behavior with important decision implications. For example, the results suggest that, if a firm has two single-product divisions and each will receive a bonus for achieving a profit target, it is beneficial for the two divisions to cooperate if the targets are lax and the profit margins are high, but not if the targets are tight and the profit margins low. Also, between two products having different profit margins, one should produce more of the product with the lower profit margin if the target is sufficiently lax. This exploration motivates further efforts in solving the two-product problem for the more general cases and also in extending the problem to three or more products.     

THE MONOPOLY OF VIOLENCE: EVIDENCE FROM COLOMBIA

Many states in Latin America, Africa, and Asia lack the monopoly of violence, even though this was identified by Max Weber as the foundation of the state, and thus the capacity to govern effectively. In this paper we develop a new perspective on the establishment of the monopoly of violence. We build a model to explain the incentive of central states to eliminate nonstate armed actors (paramilitaries) in a democracy. The model is premised on the idea that paramilitaries may choose to and can influence elections. Since paramilitaries have preferences over policies, this reduces the incentives of the politicians they favor to eliminate them. We then investigate these ideas using data from Colombia between 1991 and 2006. We first present regression and case study evidence supporting our postulate that paramilitary groups can have significant effects on elections for the legislature and the executive. Next, we show that the evidence is also broadly consistent with the implication of the model that paramilitaries tend to persist to the extent that they deliver votes to candidates for the executive whose preferences are close to theirs and that this effect is larger in areas where the presidential candidate would have otherwise not done as well. Finally, we use roll‐call votes to illustrate a possible “quid pro quo” between the executive and paramilitaries in Colombia.     

INFORMATION THROUGH SAMPLING FROM A BINOMIAL DISTRIBUTION*

Lindley's measure of experimental information is utilized to determine the optimal sample-size that is required to obtain a prescribed level of accuracy about the parameter of a binomial distribution. The measure is expressed through its approximate limiting relationship to the posterior variance of the parameter, and a simple application of the methodology is presented.     

AN EFFICIENT METHOD FOR DETERMINING THE WAITING TIME DISTRIBUTION OF QUEUES

This paper presents a practical method for determining the waiting time distribution of a single-stage queueing system for general distribution of inter-arrival/service times. The method requires the matrix solution of Lindley's equation for waiting time distribution by treating time in discrete units. Some important characteristics of the method are: a) it is easily programmable; b) it has high accuracy; c) it has modest CPU time and storage requirements; and, d) it requires no mathematical functional form for inter-arrival/service time distributions.     

PITFALLS OF ROUNDING IN DISCRETE MANAGEMENT DECISION PROBLEMS

A number of articles on managerial decision making have addressed the issue of whether or not to round a fractional solution to obtain a solution for a problem involving discrete alternatives. (An example is the problem in which the decision maker must select exactly one of several investment alternatives, but attaches no meaning to selecting two-thirds of one alternative and one-third of another.) Those articles which suggest that rounding can lead to undesirable answers are seemingly supported by the numerous “textbook examples” that purport to illustrate the dangers of rounding. However, the standard examples in which rounding fails to give a workable solution involve only a few rounding possibilities (usually two or four) and do not come from real world applications. Hence, it is questionable whether they provide any insight about what is likely to occur in a practical setting. This note fills a gap in previous discussions of rounding by providing two easily understood examples that dramatically portray the difficulties that rounding can encounter. The first example belongs to an important class of practical problems. We illustrate that rounding fails not only for this example, but also fails for all problems in its class. The second example is a unique “showcase” problem which can be summarized by a 5 times 5 cost matrix. This problem contains more than a million rounding alternatives, all of them infeasible! Following these examples, we present a “rounding paradox” and we show that its resolution gives analytical support to the conclusion that rounding will produce grave difficulties in a wide variety of practical situations.     

THE IMPACT OF IMMIGRATION ON THE STRUCTURE OF WAGES: THEORY AND EVIDENCE FROM BRITAIN

Immigration to the UK, particularly among more educated workers, has risen appreciably over the past 30 years and as such has raised labor supply. However studies of the impact of immigration have failed to find any significant effect on the wages of native‐born workers in the UK. This is potentially puzzling since there is evidence that changes in the supply of educated natives have had significant effects on their wages. Using a pooled time series of British cross‐sectional micro data on male wages and employment from the mid‐1970s to the mid‐2000s, this paper offers one possible resolution to this puzzle, namely that in the UK natives and foreign born workers are imperfect substitutes. We show that immigration has primarily reduced the wages of immigrants—and in particular of university educated immigrants—with little discernable effect on the wages of the native‐born.     

PLAYING THE BEER DISTRIBUTION GAME OVER THE INTERNET

This paper describes an Internet implementation of the Beer Distribution Game. Many teachers demonstrate the bullwhip effect that is often observed in supply chains by playing this game with their students. This implementation has the advantage of considerably reducing the time required to play the game.     

AN EXAMINATION OF THE INDIRECT PRODUCTIVITY GAINS FROM QUALITY IMPROVEMENT

Recent theoretical work suggests that quality-improvement activities can yield significant indirect effects through process improvements and reduced factory congestion and confusion, benefits that are overlooked or hidden in most management accounting or cost of quality systems. Using time series data from two consumer durables manufacturing plants, I estimate the indirect productivity gains from quality improvement. The evidence from the plants indicates that the indirect effects from improved quality are at least two to three times the direct benefits attributable to lower scrap, rework, and inventory holding costs. An important implication of these findings is that companies that justify investments and measure performance based only on the direct costs of poor quality will motivate managers to make suboptimal decisions regarding quality-improvement activities.