We propose a mathematical model which considers the series-type product structure with n−1 predecessors. Our objective is to obtain the optimal production functions, in the planning horizon [0,T ], based on the assumptions (1) that the cost of production unit is a linear function of production quantity in a time unit, (2) that sales of finished goods occur at the end of planning horizon, and (3...

The norm is one of the fundamental concepts of linear algebra and functional analysis. The notion of the norm is often employed in engineering, e.g. in control engineering, where main application is calculating the norm of the transfer function. Unfortunately existing methods are applicable for systems that can be described using Laplace transform, i.e. linear time-invariant (LTI) systems. An o...

We analyze losses resulting from uncertain transition probabilities in Markov decision processes with bounded nonnegative rewards. We assume that policies are pre-computed using exact dynamic programming with the estimated transition probabilities, but the system evolves according to different, true transition probabilities. Our approach analyzes the growth of errors incurred by stepping backwa...

In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas, such as the Cox-Ross-Rubinstein formula, are naturally derived from game-th...

In home health care, continuity of care, wherein a patient is always visited by the same nurse, can be just as important as cost, as it is closely correlated to quality of care. While a patient typically receives care for two to three months, such that assigning a nurse to a patient impacts operations for lengthy periods of time, previous research focusing on continuity of care uses planning ho...

In this expository paper we illustrate the generality of game theoretic probability protocols of Shafer and Vovk (2001) in finite-horizon discrete games. By restricting ourselves to finite-horizon discrete games, we can explicitly describe how discrete distributions with finite support and the discrete pricing formulas, such as the Cox-Ross-Rubinstein formula, are naturally derived from game-th...

The property that an optimal solution to the problem of minimizing a continuous concave function over a compact convex set in IRn is attained at an extreme point is generalized by the Bauer Minimum Principle to the infinite dimensional context. The problem of approximating and characterizing infinite dimensional extreme points thus becomes an important problem. Consider now an infinite dimensio...

We present an optimization model to find joint inspection and maintenance policies for infrastructure facilities under performance model uncertainty. The objective in the formulation is to minimize the total expected social cost of managing facilities over a finite planning horizon. As in recent optimization models, performance model uncertainty is accounted for by representing facility deterio...

An inventory model for deteriorating items over a fuzzy random planning horizon incorporating inflation and time value of money is studied. It is assumed that planning horizon follows exponential distribution with imprecise parameter. The model is formulated using cost minimization principle. As the fuzzy cost cannot be minimized directly, the possibilistic mean value of the fuzzy cost is found...

This paper is concerned with the control of constrained linear discrete-time systems subject to bounded state disturbances and arbitrary convex state and input constraints. The paper employs a class of finite horizon feedback control policies parameterized as affine functions of the system state, calculation of which has recently been shown to be tractable via a convex reparameterization. When ...