Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: the Infinite Horizon Case

We analyze an infinite horizon, single product, periodic review model in which pricing and production/inventory decisions are made simultaneously. Demands in different periods are identically distributed random variables that are independent of each other and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. Ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered. The objective is to maximize expected discounted, or expected average profit over the infinite planning horizon. We show that a stationary (s,S,p) policy is optimal for both the discounted and average profit models with general demand functions. In such a policy, the period inventory is managed based on the classical (s,S) policy and price is determined based on the inventory position at the beginning of each period.

Adaptive deadbeat control of stochastic systems

This paper considers the use of a discrete-time deadbeat control action on systems affected by noise. Variations on the standard controller form are discussed and comparisons are made with controllers in which noise rejection is a higher priority objective. Both load and random disturbances are considered in the system description, although the aim of the deadbeat design remains as a tailoring of reference input variations. Finally, the use of such a deadbeat action within a self-tuning control framework is shown to satisfy, under certain conditions, the self-tuning property, generally though only when an extended form of least-squares estimation is incorporated.

Environmental Objectives, Cost Efficiency, and Multivariate Stochastic Control

This paper is concerned with the cost efficiency in achieving the Swedish national air quality objectives under uncertainty. To realize an ecologically sustainable society, the parliament has approved a set of interim and long-term pollution reduction targets. However, there are considerable quantification uncertainties on the effectiveness of the proposed pollution reduction measures. In this paper, we develop a multivariate stochastic control framework to deal with the cost efficiency problem with multiple pollutants. Based on the cost and technological data collected by several national authorities, we explore the implications of alternative probabilistic constraints. It is found that a composite probabilistic constraint induces considerably lower abatement cost than separable probabilistic restrictions. The trend is reinforced by the presence of positive correlations between reductions in the multiple pollutants.

Optimal IV estimation of systems with stochastic regressors and var disturbances with applications to dynamic systems

This paper considers the general problem of Feasible Generalized Least Squares Instrumental Variables (FG LS IV) estimation using optimal instruments. First we summarize the sufficient conditions for the FG LS IV estimator to be asymptotic ally equivalent to an optimal G LS IV estimator. Then we specialize to stationary dynamic systems with stationary VAR errors, and use the sufficient conditions to derive new moment conditions for these models. These moment conditions produce useful IVs from the lagged endogenous variables, despite the correlation between errors and endogenous variables. This use of the information contained in the lagged endogenous variables expands the class of IV estimators under consideration and there by potentially improves both asymptotic and small-sample efficiency of the optimal IV estimator in the class. Some Monte Carlo experiments compare the new methods with those of Hatanaka [1976]. For the DG P used in the Monte Carlo experiments, asymptotic efficiency is strictly improved by the new IVs, and experimental small-sample efficiency is improved as well.

Non-asymptotic confidence bounds for the optimal value of a stochastic program

We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds for the optimal value of the problem which are essentially better than the quality of the corresponding optimal solutions. At the same time, such bounds are more reliable than “standard” confidence bounds obtained through the asymptotic approach. We also discuss bounding the optimal value of MinMax Stochastic Optimization and stochastically constrained problems. We conclude with a small simulation study illustrating the numerical behavior of the proposed bounds.

A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)