Some assumptions for the objective functions and constraint functions are given under the conditions of convex and generalized convex, which are based on theF-convex,ρ-convex, and(F,ρ)-convex. The sufficiency of Kuhn-Tucker optimality conditions and appropriate duality results are proved involving(F,ρ)-convex,(F,α,ρ,d)-convex, and generalized(F,α,ρ,d)-convex functions.

We consider two parallel queues, each with independent Poisson arrival rates, that are tended by a single server. The exponential server devotes all of its capacity to the longer of the queues. If both queues are of equal length, the server devotesνof its capacity to the first queue and the remaining1−νto the second. We obtain exact integral representations for the joint probability distribution of the number of customers in this two-node network. Then we evaluate this distribution in various asymptotic limits, such as large numbers of customers in either/both of the queues, light traffic where arrivals are infrequent, and heavy traffic where the system is nearly unstable.

This paper presents a novel application of operations research to support decision making in blood distribution management. The rapid and dynamic increasing demand, criticality of the product, storage, handling, and distribution requirements, and the different geographical locations of hospitals and medical centers have made blood distribution a complex and important problem. In this study, a real blood distribution problem containing 24 hospitals was tackled by the authors, and an exact approach was presented. The objective of the problem is to distribute blood and its products among hospitals and medical centers such that the total waiting time of those requiring the product is minimized. Following the exact solution, a hybrid heuristic algorithm is proposed. Computational experiments showed the optimal solutions could be obtained for medium size instances, while for larger instances the proposed hybrid heuristic is very competitive.

This paper is concerned with the problem of finding the optimal production schedule for an inventory model with time-varying demand and deteriorating items over a finite planning horizon. This problem is formulated as a mixed-integer nonlinear program with one integer variable. The optimal schedule is shown to exist uniquely under some technical conditions. It is also shown that the objective function of the nonlinear obtained from fixing the integrality constraint is convex as a function of the integer variable. This in turn leads to a simple procedure for finding the optimal production plan.

We study empirically and analytically growth and fluctuation of firm size distribution. An empirical analysis is carried out on a US data set on firm size, with emphasis on one-time distribution as well as growth-rate probability distribution. Both Pareto's law and Gibrat's law are often used to study firm size distribution. Their theoretical relationship is discussed, and it is shown how they are complementable with a bimodal distribution of firm size. We introduce economic mechanisms that suggest a bimodal distribution of firm size in the long run. The mechanisms we study have been known in the economic literature since long. Yet, they have not been studied in the context of a dynamic decision problem of the firm. Allowing for these mechanism thus will give rise to heterogeneity of firms with respect to certain characteristics. We then present different types of tests on US data on firm size which indicate a bimodal distribution of firm size.

This paper reviews the most relevant literature on efficient models and methods for packing circular objects/items into Euclidean plane regions where the objects/items and regions are either two- or three-dimensional. These packing problems are NP hard optimization problems with a wide variety of applications. They have been tackled using various approaches-based algorithms ranging from computer-aided optimality proofs, to branch-and-bound procedures, to constructive approaches, to multi-start nonconvex minimization, to billiard simulation, to multiphase heuristics, and metaheuristics.

Discriminant Analysis (DA) is widely applied in many fields. Some recent researches raise the fact that standard DA assumptions, such as a normal distribution of data and equality of the variance-covariance matrices, are not always satisfied. A Mathematical Programming approach (MP) has been frequently used in DA and can be considered a valuable alternative to the classical models of DA. The MP approach provides more flexibility for the process of analysis. The aim of this paper is to address a comparative study in which we analyze the performance of three statistical and some MP methods using linear and nonlinear discriminant functions in two-group classification problems. New classification procedures will be adapted to context of nonlinear discriminant functions. Different applications are used to compare these methods including the Support Vector Machines- (SVMs-) based approach. The findings of this study will be useful in assisting decision-makers to choose the most appropriate model for their decision-making situation.

A trust-region-based BFGS method is proposed for solving symmetric nonlinear equations. In this given algorithm, if the trial step is unsuccessful, the linesearch technique will be used instead of repeatedly solving the subproblem of the normal trust-region method. We establish the global and superlinear convergence of the method under suitable conditions. Numerical results show that the given method is competitive to the normal trust region method.