Inventory financing under Risk-Adjusted-Return-On-Capital criterion

Risk-Adjusted-Return-On-Capital (RAROC) is a loan-pricing criterion under which a bank sets the loan term such that a certain rate of return is achieved on the regulatory capital required by the Basel regulation. Some banks calculate the amount of regulatory capital for each loan under the standardized approach (“standardized banks,” the regulatory capital is proportional to the loan amount), and others under the internal rating-based (IRB) approach (“IRB banks,” the regulatory capital is related to the Value-at-Risk of the loan). This article examines the impact of the RAROC criterion on the bank's loan-pricing decision and the retailer's inventory decision. We find that among the loan terms that satisfy the bank's RAROC criterion, the one that benefits the retailer the most requires the bank to specify an inventory advance rate in addition to the interest rate. Under this loan term, the retailer's inventory level is more sensitive to his asset level when facing an IRB bank compared to a standardized bank. An IRB (standardized) loan leads to higher profit and inventory level for retailers with high (low) asset. For retailers with medium asset, an IRB loan results in a higher retailer profit but a lower consumer welfare. Calibrated numerical study reveals that the benefit of choosing standardized banks (relative to IRB banks) can be as high as 30% for industries with severe capital constraints, volatile demands, and low profit margins, highlighting the importance for retailers to carefully choose the type of banks to borrow from. When the interest rate is capped by regulation, retailers borrowing from a standardized bank are more likely to be influenced by the interest rate cap than those borrowing from an IRB bank. Under strong empire-building incentives (the bank will offer loan terms to maximize the size of the loan), retailers with medium initial asset level shift their preference from IRB banks to standardized banks.     

Statistical analysis of very high-dimensional data sets of hierarchically structured binary variables with missing data: An application to marine corps readiness evaluations

The present analysis deals with very high-dimensional data sets, each one containing close to 900 binary variables. Each data set corresponds to an evaluation of one complex system. These data sets are characterized by large portions of missing data where, moreover, the unobserved variables are not the same in different evaluations. Thus, the problems which confront the statistical analysis are those of multivariate binary data analysis, where the number of variables is much larger than the sample size and in which missing data varies with the sample elements. The variables, however, are hierarchically structured and the problem of clustering variables to groups does not exist in the present study. In order to motivate the statistical problem under consideration, the Marine Corps Combat Readiness Evaluation System (MCCRES) is described for infantry battalions and then used for exposition. The present article provides a statistical model for data from MCCRES and develops estimation and prediction procedures which utilize the dependence structure. The E-M algorithm is applied to obtain maximum-likelihood estimates of the parameters of interest. Numerical examples illustrate the proposed methods.     

A multiserver queue with markovian arrivals and group services with thresholds

We consider a multiserver queueing system in which arrivals are governed by a Markovian arrival process. The system is attended by K identical exponential servers. Under a dynamic probabilistic service rule which depends on two threshold parameters, this model is studied as a Markov process. The steady-state probability vector is shown to be of (modified) matrix-geometric type. Efficient algorithmic procedures for the computation of the steady-state probability vector and some key performance measures of the system are developed. Some numerical examples are discussed. © 1993 John Wiley & Sons, Inc.     

A finite capacity GI/PH/1 queue with group services

We consider a finite-capacity single-server queue in which arrivals occur one at a time, according to a renewal process. The successive service times are mutually independent and have a common phase-type distribution. The customers are served in groups of size at least L, a preassigned threshold value. Explicit analytic expressions for the steady-state queue-length densities at arrivals and at arbitrary time points, and the throughput of the system are obtained. The Laplace-Stieltjes transform of the stationary waiting-time distribution of an admitted customer at points of arrivals is computed. It is shown to be of phase type when the arrival process is also of phase type. Efficient algorithmic procedures for the steady-state analysis of the model are presented. These procedures are used in arriving at an optimal value for L that minimizes the mean waiting time of an admitted customer. A conjecture on the nature of the mean waiting time is proposed.     

An improved branch and bound procedure for n × m flow shop problems

This paper considers the classical nXm flow shop sequencing problem. An improved branch and bound procedure is proposed. Computational experience shows that the proposed procedure is more efficient compared to the existing optimizing procedures.