End effects in capacity expansion models with finite horizons

Capacity expansion models are typically formulated in the context of some finite horizon. Because the firm lasts longer than the horizon, a bias can enter into the optimal solution from the model horizon chosen. Recently, Grinold [8] has proposed a “dual-equilibrium method” for ameliorating possible distortions. Although the dual-equilibrium method has superior analytical properties to other methods, it is conceptually more complex. In this paper it is shown that there are situations where the “primal-equilibrium” approach of Manne [15] provides equivalent results and that the use of annualized capital costs in the objective function, although somewhat less efficient, results in a similar model.     

The procurement problem: An integer programming problem well suited to a solution using duality

A procurement problem, as formulated by Murty [10], is that of determining how many pieces of equipment units of each of m types are to be purchased and how this equipment is to be distributed among n stations so as to maximize profit, subject to a budget constraint. We have considered a generalization of Murty's procurement problem and developed an approach using duality to exploit the special structure of this problem. By using our dual approach on Murty's original problem, we have been able to solve large problems (1840 integer variables) with very modest computational effort. The main feature of our approach is the idea of using the current evaluation of the dual problem to produce a good feasible solution to the primal problem. In turn, the availability of good feasible solutions to the primal makes it possible to use a very simple subgradient algorithm to solve the dual effectively.     

Tabular aids for fitting weibull moment estimates

Moment estimators for the parameters of the Weibull distribution are considered in the context of analysis of field data. The data available are aggregated, with individual failure times not recorded. In this case, the complexity of the likelihood function argues against the use of maximum-likelihood estimation, particularly for relatively large sets of data, and moment estimators are a reasonable alternative. In this article, we derive the asymptotic covariance matrix of the moment estimators, and provide listings for BASIC computer programs which generate tables useful for calculation of the estimates as well as for estimating the asymptotic covariance matrix using aggregated data.     

A time dependent continuous review inventory model with compound poisson demand

We discuss a time dependent optimal ordering policy for a finite horizon inventory system for which the provision of service is essential and thus no stockout is allowed. It is assumed that the system can place an order at any point in time during the horizon when it cannot meet the customer's demand and that lead time is negligible. The demand is considered to be distributed as a compound Poisson process with known parameters and the functional equation approach of dynamic programming is used to formulate the objective function. An algorithm has been developed to obtain the solution for all the cases. In addition, analytical solutions of the basic equation under two limiting conditions are presented.     

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.     

An optimum multiechelon repair policy and stockage model

Currently, sophisticated multiechelon models compute stockage quantities for spares and repair parts that will minimize total inventory investment while achieving a target level of weapon system operational availability. The maintenance policies to be followed are input to the stockage models. The Optimum Allocation of Test Equipment/Manpower Evaluated Against Logistics (OATMEAL) model will determine optimum maintenance as well as stockage policies for a weapon system. Specifically, it will determine at which echelon each maintenance function should be performed, including an option for component or module throwaway. Test equipment requirements to handle work load at each echelon are simultaneously optimized. Mixed-integer programming (MIP) combined with a Lagrangian approach are used to do the constrained cost minimization, that is, to minimize all costs dependent on maintenance and stockage policies while achieving a target weapons system operational availability. Real-life test cases are included.