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A new technique for assessing the sensitivity and stability of efficiency classifications in Data Envelopment Analysis (DEA) is presented. Here developed for the ratio (CCR) model, this technique extends easily to other DEA variants. An organization's input-outut vector serves as the center for a cell within which the organization's classification remains unchanged under perturbations of the data. For the ll, l~. and generalized l~. norms, the radius of the maximal cell can be computed using linear programming formulations. This radius can be interpreted as a measure of the classifications stability, especially with respect to errors in the data.

We analyze a periodic-review inventory model where the decision maker can buy from either of two suppliers. With the first supplier, the buyer incurs a high variable cost but negligible fixed cost; with the second supplier, the buyer incurs a lower variable cost but a substantial fixed cost. Consequently, ordering costs are piecewise linear and concave. We show that a reduced form of generalized s S policy is optimal for both finite and (discounted) infinite-horizon problems, provided that the demand density is log-concave. This condition on the distribution is much less restrictive than in previous models. In particular, it applies to the normal, truncated normal, gamma, and beta distributions, which were previously excluded. We concentrate on the situation in which sales are lost, but explain how the policy, cost assumptions, and proofs can be altered for the case where excess demand is backordered. In the lost sales case, the optimal policy will have one of three possible forms: a base stock policy for purchasing exclusively at the high variable cost (HVC) supplier; an s LVC S LVC policy for buying exclusively from the low variable cost (LVC) supplier; or a hybrid s S HVC S LVC policy for buying from both suppliers.

We consider the impact of variable production costs on competitive behavior in a duopoly where manufacturers compete on quality and price in a two-stage game. In the pricing stage, we make no assumptions regarding these costs--other than that they are positive and increasing in quality--and no assumptions about whether or not the market is covered. In the quality stage, we investigate a broad family of variable cost functions and show how the shape of these functions impacts equilibrium product positions, profits, and market coverage. We find that seemingly slight changes to the cost function's curvature can produce dramatically different equilibrium outcomes, including the degree of quality differentiation, which competitor is more profitable (the one offering higher or lower quality), and the nature of the market itself (covered or uncovered). Our model helps to predict and explain the diversity of outcomes we see in practice--something the previous literature has been unable to do.game theory, operations strategy, quality competition

We investigate the use of a canonical version of a discrete choice model due to Daganzo (1979) [Daganzo C (1979) Multinomial Probit: The Theory and Its Application to Demand Forecasting (Academic Press, New York).] in optimal pricing and assortment planning. In contrast to multinomial and nested logit (the prevailing choice models used for optimizing prices and assortments), this model assumes a negatively skewed distribution of consumer utilities, an assumption we motivate by conceptual arguments as well as published work. The choice probabilities in this model can be derived in closed form as an exponomial (a linear function of exponential terms). The pricing and assortment planning insights we obtain from the exponomial choice (EC) model differ from the literature in two important ways. First, the EC model allows variable markups in optimal prices that increase with expected utilities. Second, when prices are exogenous, the optimal assortment may exhibit leapfrogging in prices, i.e., a product can be skipped in favor of a lower-priced one depending on the utility positions of neighboring products. These two plausible pricing and assortment patterns are ruled out by multinomial logit (and by nested logit within each nest). We provide structural results on optimal pricing for monopoly and oligopoly cases, and on the optimal assortments for both exogenous and endogenous prices. We also demonstrate how the EC model can be easily estimated—by establishing that the log-likelihood function is concave in model parameters and detailing an estimation example using real data.

Current debates in the insurance and public policy literatures over health care financing and cost control measures continue to focus on managed care and HMOs. The lower utilization rates found in HMOs (compared to traditional fee-for-service indemnity plans) have generally been attributed to the organization's incentive to eliminate all unnecessary medical services. As a consequence HMOs are often considered to be a more efficient arrangement for delivering health care. However, it is important to make a distinction between utilization and efficiency (the ratio of outcomes to resources). Few studies have investigated the effect that HMO arrangements would have on the actual efficiency of health care delivery. Because greater control over provider autonomy appears to be a recurrent theme in the literature on reform, it is important to investigate the effects these restrictions have already had within the HMO market. In this article, the efficiencies of two major classes of HMO arrangements are compared using "game-theoretic" data envelopment analysis (DEA) models. While other studies confirm that absolute costs to insurance firms and sponsoring companies are lowered using HMOs, our empirical findings suggest that, within this framework, efficiency generally becomes worse when provider autonomy is restricted. This should give new fuel to the insurance companies providing fee-for-service (FFS) indemnification plans in their marketplace contentions. Copyright The Journal of Risk and Insurance.

This paper develops an order-up-to S inventory model that is designed to handle multiple items, resource constraints, lags in delivery, and lost sales without sacrificing computational simplicity. Mild conditions are shown to ensure that the expected average holding cost and the expected average shortage cost are separable convex functions of the order-up-to levels. We develop nonparametric estimates of these costs and use them in conjunction with linear programming to produce what is termed the "LP policy." The LP policy has two major advantages over traditional methods: first, it can be computed in complex environments such as the one described above; and second, it does not require an explicit functional form of demand, something that is difficult to specify accurately in practice. In two numerical experiments designed so that optimal policies could be computed, the LP policy fared well, differing from the optimal profit by an average of 2.20% and 1.84%, respectively. These results compare quite favorably with the errors incurred in traditional methods when a correctly specified distribution uses estimated parameters. Our findings support the effectiveness of this mathematical programming technique for approximating complex, real-world inventory control problems.Inventory, Heuristic Approximation, Nonparametric Estimation, Separable Convex Programming, Linear Programming

This paper demonstrates that a class of two-person games with ratio payoff functions can be solved using equivalent primal-dual linear programming formulations. The game's solution contains specialized information which may be used to conduct the efficiency evaluation currently done by the CCR ratio model of Data Envelopment Analysis (DEA). Consequently a rigorous connection between DEA's CCR model and the theory of games is established. Interpretations of these new solutions are discussed in the context of current ongoing applications.game theory, data envelopment analysis, linear programming, efficiency