This paper presents an asymptotic analysis of hierarchical manufacturing systems with stochastic demand and machines subject to breakdown and repair as the rate of change in machine states approaches infinity. This situation gives rise to a limiting problem in which the stochastic machine...

This paper introduces recent developments in the analysis of inventory systems with partial observations. The states of these systems are typically conditional distributions, which evolve in infinite dimensional spaces over time. Our analysis involves introducing unnormalized probabilities to...

In this technical note we give a short proof based on standard results in convex analysis of some important characterization results listed in Theorem 3 and 4 of [1]. Actually our result is slightly general since we do not specify the convex set X. For clarity we use the same notation for the...

The present paper proposes a new approach to solve generalized fractional programming problems through user interaction. Capitalizing on two alternatives, we review the Dinkelbach-type methods and set forth the main difficulty in applying these methods. In order to cope with this difficulty, we...

Many practical optimization problems are characterized by some flexibility in the problem constraints, where this flexibility can be exploited for additional trade-off between improving the objective function and satisfying the constraints. Especially in decision making, this type of flexibility...

In this paper, we develop a rigorous new framework for the concepts of forecast and decision horizons. These concepts are conditional in nature and, in turn, enable us to unify the existing concepts of “strong” and “weak” horizons. Moreover, we are able to precisely state the question of...

Capacity expansion is the process of providing new facilities over time to meet rising demand. A general mathematical model of this process is presented, incorporating uncertain future demand (including the possibility of 'surprises'), non-zero lead times and random cost overruns. In this model...

We provide results for an efficient analytical valuation of partial moments of the multivariate Gaussian distribution over convex polyhedrons to aid the solution, sensitivity analysis and structural analysis of a large number of two-stage resource acquisition and allocation problems. These...

This paper proposes a new methodology to solve partially observed inventory problems. Generally, these problems have infinitedimensional states that are conditional distribution of the inventory level. Our methodology involves linearizing the state transitions via unnormalized probabilities. It...

This paper presents an asymptotic analysis of control models governed by stochastic ordinary differential equations. A sufficient condition of near-optimal controls is given based on Ekeland's principle. It is shown that, under some concavity assumptions, the e-maximum condition in terms of the...