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Integer programming (IP), also known as discrete optimization, is a way of modelling a very wide range of problems involving indivisibilities (e.g. yes/no investment decisions) and non-convexities (e.g. economies of scale and fixed cost allocation). Such problems arise in many areas; these are mentioned in the paper. However, IP demands ingenuity in both building models and in their solution. Much is still not properly understood. This paper investigates the question: ‘Is IP like Linear Programming (LP)? ’ The mathematical and economic properties of IP will be contrasted with LP. It will be suggested that the mathematics and economics of IP are still not properly understood. Many of the results which apply to LP do not apply to IP. It will be asserted that this lack of understanding reveals inadequacies in both the mathematics and economics. [ABSTRACT FROM PUBLISHER]

The predominant approach to determining replenishment batch sizes for capital constrained multi-item inventories is to assume that at some point in time the replenishment of all items will coincide, and that batch sizes are small enough that the constraint is not violated when this event occurs. However, when an inventory consists of a large number of independently replenished components, the probability that all replenishments coincide is very small. The standard approach thus results in unnecessarily conservative batch sizes that under-utilise the available resource, resulting in lower profit than would be the case if a small risk of violating the constraint was tolerated. In this paper, a new approach to determining constrained batch sizes is presented where, for a certain average investment, the probability of exceeding a binding, or fixed, constraint on capital is determined. This probability is used to define an adjustment factor to be applied to expressions for company profit so that an optimal trade-off between maximising profit and reducing risk of failure is obtained simply by optimising this adjusted profit. By optimising profit adjusted for the risk of exceeding the constraint, the new model yields batch sizes that are larger, and result in greater profitability than those recommended under traditional models. [ABSTRACT FROM AUTHOR]

A number of problems in economics, finance and insurance rely on determining the sign of the covariance of two transformations of a random variable. The classical Chebyshev's inequality offers a powerful tool for solving the problem, but it assumes that the transformations are monotonic, which is not always the case in applications. For this reason, in the present paper, we establish new results for determining the covariance sign and provide further insights into the area. Unlike many previous works, our method of analysis, which is probabilistic in its nature, does not rely on the classical Höffding's representation of the covariance or on any of its numerous extensions and generalizations. We motivate our research with several problems arising in economics, finance and insurance. [ABSTRACT FROM PUBLISHER]

An effective gearbox failure diagnosis helps prevent catastrophic gearbox failure and can contribute to significant economic benefits. This paper proposes a gear failure diagnosis method based on vector autoregressive modelling of high-frequency vibration data, dimensionality reduction applying dynamic principal component analysis (PCA) and condition monitoring using a multivariate control chart. After extracting useful information from the vibration data obtained from distinct directions via dynamic PCA, a failure diagnosis scheme is implemented and tested using real gearbox vibration data. It is shown that the failure diagnosis scheme can indicate the gear teeth failure pattern when the gear is damaged, which has not been demonstrated in the previous studies. For a comparison, PCA is applied to the same data set. The results show that the advantages of dynamic PCA over PCA for failure diagnosis using vibration data consist not only in indicating more accurately the occurrence of incipient fault and the actual gear condition, but also in a much lower false alarm rate. [ABSTRACT FROM AUTHOR]

Previous studies on hospitals' efficiency often refer to quite restrictive functional forms for the technology (Aigner et al., 1977, J. Econom., 6, 21-37). In this paper, referring to a study about some hospitals in Lombardy, we formulate convenient correctives to a statistical model based on the translogarithmic function-the most widely used flexible functional form (Christensen at at, 1973, Rev. Econ. Stat., 55, 28-45). More specifically, in order to take into consideration the hierarchical structure of the data (as in Gori et al., 2002, Stat. Appl., 14, 247-275), we propose a multilevel model, ignoring for the moment the one-side error specification, typical of stochastic frontier analysis (Aigner et al., 1977, J. Econom., 6, 21-37). Given this simplification, however, we are easily able to take into account some typical econometric problems as, e.g. heteroscedasticity. The estimated production function can be used to identify the technical inefficiency of hospitals (as already seen in previous works), but also to draw some economic considerations about scale elasticity, scale efficiency and optimal resource allocation of the productive units. We will show, in fact, that for the translogarithmic specification it is possible to obtain the elasticity of the output (regarding an input) at hospital level as a weighted sum of elasticities at ward level. Analogous results can be achieved for scale elasticity, which measures how output changes in response to simultaneous inputs variation. In addition, referring to scale efficiency and to optimal resource allocation, we will consider the results of Ray (1998, J. Prod. Anal., 11, 183-194) to our context. The interpretation of the results is surely an interesting administrative instrument for decision makers in order to analyse the productive conditions of each hospital and its single wards and also to decide the preferable interventions. [ABSTRACT FROM AUTHOR]

The Cobb-Douglas production function with Abel's (1983, Am. Econ. Rev., 173, 228-233) model is extended herein, and real options analysis (ROA) for entry-exit decision-making established utilizing Dixit's (1989b) decision model under exchange rate uncertainty. This work considers the effects of real exchange rates on strategies that determine the locations of production by firms that are entering markets in two countries. The ROA is also adopted to evaluate the switching location between two countries. A continuous-time model optimization problem is solved in closed-form. This provides a useful beginning to an important analysis of the effects on industry of exchange rate fluctuations when the optimal entry (exit) trigger for transferring locations is important for a basic global logistics model. Furthermore, a myopic solution of the optimal entry (exit) trigger, sensitivity analysis and some characteristics of the optimal production strategy are sought. This paper contributes to the problem of choice of foreign production strategy. [ABSTRACT FROM AUTHOR]

The solution to the optimal portfolio selection and consumption rule subject to Capital-at-Risk and Value-at-Risk constraints is derived via the use of stochastic dynamic programming. [ABSTRACT FROM AUTHOR]