Stanley J. Garstka

On decision rules in stochastic programming

The paper surveys the basic results and nonresults for decision rules in stochastic programming. It exhibits some of the difficulties encountered when trying to restrict the class of acceptable rules to those possessing specific functional forms. A liberal dosage of examples is provided which illustrate various cases. The treatment is unified by making use of the equivalence of various formulations which have appeared in the literature. An appendix is devoted to the P-model for stochastic programs with chance constraints.

The "Balanced Scorecard": development and implementation in an academic clinical department.

If quality medical education is to survive in the increasingly competitive marketplace, medical schools need to adopt new tools that measure the value of all initiatives, both financial and non-financial, so that they can make informed decisions about their missions and future direction. The authors describe a tool of this kind called the Balanced Scorecard (originally created for traditional businesses), outline the version of it that they developed for the Department of Anesthesiology at Yale University School of Medicine, and discuss the first year of implementation (which began in 1997). The Balanced Scorecard is a set of measures designed to examine an organizations performance from the following four perspectives and to answer the key question suggested by each perspective: (1) The learning and growth perspective: Can we continue to improve and create value? (2) The internal business perspective: What must we excel at? (3) The customer perspective: How do our customers see us? (4) The financial perspective: How do we look to our shareholders? The first year of implementation of this approach at the Department of Anesthesiology involved creating measures of the four perspectives, determining whether data could be found for each measure and whether the data were in usable forms, and educating and involving the faculty in the process. The authors discuss the pros and cons of the Balanced Scorecard approach that they observed during the first year, and conclude with a list of seven lessons learned (e.g., start with measures that already exist). Overall, they are convinced that the Balanced Scorecard can be of great value to a department, even if the full implementation takes several years to complete.

Computation in Discrete Stochastic Programs with Recourse

This paper presents a solution procedure for discrete stochastic programs with recourse linear programs under uncertainty. It views the m stochastic elements of the requirements vector as an m-dimensional space in which each combination of the discrete values is a lattice point. For a given second-stage basis, certain of the lattice points are feasible. A procedure is presented to delete infeasible points from the space. Thus, the aggregate probability associated with points feasible for this basis can be enumerated, and used to weight the vector of dual variables defined by the basis. Finally, the paper presents a systematic procedure for changing optimal bases so that a feasible and optimal basis is found for every lattice point.

The Optimal Review Period in a Dynamic Inventory Model

Consider a single-item, periodic review, infinite-horizon, undiscounted, inventory model with stochastic demands, proportional holding and shortage costs, and full backlogging. Orders can arrive in every period, and the cost of receiving them is negligible (as in a JIT setting). Every T periods, one observes the current stock level and orders deliveries for the next T periods, thus incurring a fixed setup cost. The goal is to find a review period T and an ordering policy that minimize the long run expected average cost per period. Flynn and Garstka (Flynn, J., S. Garstka. 1990. A dynamic inventory model with periodic auditing. Opns. Res. 38 1089–1103.) characterize an optimal ordering policy when T is fixed and study a myopic policy whose cost is often close to the optimal cost. This paper covers the problem of selecting T. We prove an optimal review period T* exists, characterize its properties, and present methods for its computation. We also study an approximation to T* based on the myopic policy of ou...

A Dynamic Inventory Model with Periodic Auditing

Consider a single-item, periodic review, stationary inventory model with stochastic demands, proportional ordering costs, and convex holding and shortage costs, where shortages are backordered and Veinotts well known terminal condition holds. Orders can be scheduled for any period, but the actual inventory level is determined every T periods through an audit. This leads to a dynamic programming model where stage n contains periods n-1T + 1 through nT. For both discounted and averaging criteria, a simple rule optimally describes the orders for the T periods of a stage as a function of the state beginning inventory level and the cumulative T-period order. The latter is optimally determined by a base stock policy with two base stock levels: one for the final stage, another for the rest. The horizon may be finite or infinite. Methods are presented for computing optimal policies, together with bounds on the costs of suboptimal myopic policies. Models with proportional costs and continuous demands are studied in detail. Computational experiments indicate that myopic policies perform quite well for such models. The selection of a best review period T is covered briefly. Applications of our model include just in time settings where audit decisions play a negligible role.

Models For Computing Upper Error Limits In Dollar-Unit Sampling

Auditors frequently rely on statistical sampling procedures to verify the correctness of an account balance. One such procedure, dollar-unit sampling (DUS), has been specifically developed for use in the auditing environment where very low error rates in account balances are often encountered. A development of DUS, along with discussions of its particular advantages and shortcomings, can be found in Anderson and Teitlebaum [1973], Kaplan [1975], Meikle [1972], and Neter, Goodfellow, and Loebbecke [1973]. The purpose of this paper is to investigate how one aspect of the DUS procedure can be improved. In particular, I propose alternative methods of computing upper error limits on the book value of the account being audited once the DUS sample has been selected. Using the compound Poisson process to model the error rate and the distribution of error sizes in the population of dollars being audited, I show (through simulations) how rather crude models of this type can be effectively integrated with Bayesian procedures to compute much tighter upper error limits than those obtained by the usual DUS method. The specific models developed in this paper are intended to be examples of the types of models about which auditors should begin thinking. The analysis also illustrates the usefulness of prior information about the population being audited in making upper error limit statements about the population.

Distribution functions in stochastic programs with recourse: A parametric analysis

This paper studies the behavior of the optimum value of a two-stage stochastic program with recourse (random right-hand sides) as the mean and covariance matrices defining the random variables in the program are perturbed. Several results for convex programs are developed and are used to study the effect such perturbations have on the regularity properties of the stochastic programs. Cost associated with incorrectly specifying the mean and covariance matrices are discussed and estimated. A stochastic programming model in which the random variable is dependent on the first-stage decision is presented.

An economic interpretation of stochastic programs

The purpose of this note is to interpret a class of stochastic programming problems in economic terms. The primal stochastic program is shown to represent a certain production program of an entrepreneur. The dual program, which is also a stochastic program, represents the problem of a contractor who desires to purchase the entrepreneurs resources and sell product back to him.

On duality in stochastic programming with recourse

This short paper compares dual programs of stochastic programs with recourse. It explains why the discrepancy exists between two such dual programs recently appearing in the literature. An example is presented which illustrates the difference.

Discussion of an Empirical Study of Error Characteristics in Audit Populations

Empirical studies of error characteristics in accounting populations should enable auditors systematically and intelligently to select estimators to be used in an audit. My comments on this particular study are grouped into two categories. First, I discuss the reasonableness of the error characteristics chosen to be reported. Then I comment on what the objectives of such an analysis are or should be.