INSIGHTS ON SERVICE SYSTEM DESIGN FROM A NORMAL APPROXIMATION TO ERLANG'S DELAY FORMULA

We show how a simple normal approximation to Erlang's delay formula can be used to analyze capacity and staffing problems in service systems that can be modeled as M/M/s queues. The numbers of servers, s, needed in an M/M/s queueing system to assure a probability of delay of, at most, p can be well approximated by s ≅ p + z_***I-p+, where z_1-p, is the (1 - p)th percentile of the standard normal distribution and ρ, the presented load on the system, is the ratio of Λ, the customer arrival rate, to μ, the service rate. We examine the accuracy of this approximation over a set of parameters typical of service operations ranging from police patrol, through telemarketing to automatic teller machines, and we demonstrate that it tends to slightly underestimate the number of servers actually needed to hit the delay probability target—adding one server to the number suggested by the above formula typically gives the exact result. More importantly, the structure of the approximation promotes operational insight by explicitly linking the number of servers with server utilization and the customer service level. Using a scenario based on an actual teleservicing operation, we show how operations managers and designers can quickly obtain insights about the trade-offs between system size, system utilization and customer service. We argue that this little used approach deserves a prominent role in the operations analyst's and operations manager's toolbags.     

THE PERILS OF EXCELLENCE: BARRIERS TO EFFECTIVE PROCESS IMPROVEMENT IN PRODUCT-DRIVEN FIRMS

Several authors have suggested that a focus on manufacturing capability and on continued process improvement may be a powerful source of competitive advantage, yet many firms appear to have encountered great difficulties in taking advantage of this insight. This paper reports on the results of five these conducted under the auspices of the MIT Leaders for Manufacturing program at the Microwave Technology Division of the Hewlett-Packard Company. We found considerable evidence that the marginal returns to process development within the division were probably considerably higher than the division's cost of capital, suggesting that process improvement probably was underfunded despite the fact that improving manufacturing capability had been identified as a key strategic priority. We found no evidence that this “underfunding” reflected either a failure to recognize the problem or an overly hierarchical or rigid organization. Rather it appeared to flow from the historical strengths of the division. A devotion to leading-edge technical solutions and to immediate customer service at almost any price had created barriers to the effective funding of process improvement that were deeply rooted in the organizational structures, information systems, and formal and informal incentive structures that had evolved to support the division's historical emphasis on excellence on product design. Our results highlight the problems that very successful product-driven companies may encounter in attempting to make continual process improvement central to their strategic mission.     

DOES THE RIVER SPILL OVER? ESTIMATING THE ECONOMIC RETURNS TO ATTENDING A RACIALLY DIVERSE COLLEGE

This article evaluates the frequently argued but heretofore little tested hypothesis that increasing minority representation in elite colleges generates tangible benefits for majority‐race students. Using data on graduates of 30 selective universities, we find only weak evidence of any relationship between collegiate racial composition and the postgraduation outcomes of white or Asian students. Moreover, the strongest evidence we uncover suggests that increasing minority representation by lowering admission standards is unlikely to produce benefits and may in fact cause harm by reducing the representation of minority students on less selective campuses. While affirmative action may still be desirable for the benefits it conveys to minority students, these results provide little support for “spillover” effects on majority‐race students. (JEL I2, J15, J24)

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Estimation of Stratified Mark‐Specific Proportional Hazards Models with Missing Marks

Abstract. An objective of randomized placebo‐controlled preventive HIV vaccine efficacy trials is to assess the relationship between the vaccine effect to prevent infection and the genetic distance of the exposing HIV to the HIV strain represented in the vaccine construct. Motivated by this objective, recently a mark‐specific proportional hazards (PH) model with a continuum of competing risks has been studied, where the genetic distance of the transmitting strain is the continuous ‘mark’ defined and observable only in failures. A high percentage of genetic marks of interest may be missing for a variety of reasons, predominantly because rapid evolution of HIV sequences after transmission before a blood sample is drawn from which HIV sequences are measured. This research investigates the stratified mark‐specific PH model with missing marks where the baseline functions may vary with strata. We develop two consistent estimation approaches, the first based on the inverse probability weighted complete‐case (IPW) technique, and the second based on augmenting the IPW estimator by incorporating auxiliary information predictive of the mark. We investigate the asymptotic properties and finite‐sample performance of the two estimators, and show that the augmented IPW estimator, which satisfies a double robustness property, is more efficient.     

WHAT IS HAPPENING TO THE IMPACT OF FINANCIAL DEEPENING ON ECONOMIC GROWTH?

Although the finance‐growth relationship is now firmly entrenched in the empirical literature, we show that it is not as strong in more recent data as it was in the original studies with data for the period from 1960 to 1989. We consider several explanations. First, we find that the incidence of financial crises is related to the dampening of the effect of financial deepening on growth. Excessive financial deepening or too rapid a growth of credit may have led to both inflation and weakened banking systems which in turn gave rise to growth‐inhibiting financial crises. Excessive financial deepening may also be a result of widespread financial liberalizations in the late 1980s and early 1990s in countries that lacked the legal or regulatory infrastructure to exploit financial development successfully. However, we find little indication that liberalizations played an important direct role in reducing the effect of finance. Similarly, there is little evidence that the growth of equity markets in recent years has substituted for debt financing and led to a reduced role of financial deepening on growth. (JEL E44, G10, O40)     

A COMPARATIVE ANALYSIS OF THE NATIVITY WEALTH GAP*

We investigate the relative wealth position of immigrant households residing in Australia, Germany, and the United States. In Germany and the United States, wealth differentials stem from differences in the educational attainment and demographic characteristics of the native and immigrant populations, rather than income differentials. In contrast, the small nativity wealth gap in Australia exists because immigrants to Australia do not translate their relative educational and demographic advantage into a wealth advantage. Overall, we find substantial disparity in the economic well‐being of immigrant and native families which is largely consistent with domestic labor markets and immigration policies. (JEL F22, D31)     

Psycho-Drama as a Medium for Intermediate Treatment

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