Amy David

USG Uses Stochastic Optimization to Lower Distribution Costs

We present a case study of a large-scale stochastic optimization problem for USG, a building supply manufacturer with plants and customers throughout North America. USG seeks to minimize total delivered cost including production and freight costs of products in its Durock® product line, subject to capacity constraints and uncertainties in both demand and production costs. We first demonstrate that demand uncertainty, rather than production-cost uncertainty, is the main cause of month-to-month variations in total cost. We then use the chance constraint method to optimize the network, and propagate uncertainty through the cost models, applying a penalty cost for unfulfilled constraints. We show that we can reduce theoretical costs by approximately 4.8 percent by optimizing the network for the 50th percentile of demand, as compared to the base case that uses demand and cost data for a single month. We implemented the new network plan via sourcing rules in both USGs order fulfillment system and Oracles advanced supply-chain planning module. Several practical delivery concerns limit the benefits realized to an amount less than the theoretical cost reductions, but savings are still considered to be substantial.

Water Management Under Weather Uncertainty

Water scarcity and the cost of treating and recycling waste water both represent constraints in operating coal-fired power plants. As the capacity of thermoelectric power generation increases in the USA (the Energy Information Administration estimates that thermoelectric power generation will grow 22 % by 2030), so does the importance of managing the water used in these plants. In a clean coal-fired power plant, water is consumed in makeups (water added to a closed cycle due to evaporation or product loss), in blowdowns (water added during the cooling cycle due to liquid removal), and in the generation process itself. The amount of water consumed varies with two ambient weather factors: the dry-bulb temperature (temperature as measured by a thermometer shielded from moisture) and the humidity of the outside air, both of which are subject to significant uncertainty, and vary with the season and geographical region.

Uncertainty Analysis and Sampling Techniques

To accommodate the diverse nature of uncertainty, different distributions can be used. Some of the representative distributions are shown in Fig. 2.2. The type of distribution chosen for an uncertain variable reflects the amount of information that is available. For example, the uniform and loguniform distributions represent an equal likelihood of a value lying anywhere within a specified range, on either a linear or logarithmic scale, respectively. Furthermore, a normal (Gaussian) distribution reflects a symmetric but varying probability of a parameter value being above or below the mean value.

The L-Shaped BONUS Algorithm

This chapter is based on a paper by Shastri and Diwekar . A variant of BONUS is presented here to solve multistage stochastic programming problems with recourse . In stochastic programming problems with recourse , there is action (x), followed by observation, and then recourse r. In these problems, the objective function has the action term, and the recourse function is dependent on the uncertainties and recourse decisions. The recourse function can be a discontinuous nonlinear function in x and r space.

Sensor Placement Under Uncertainty for Power Plants

This chapter demonstrates the use of the BONUS method, in combination with kernel density estimation, to calculate Fisher information. This concept is then applied to the problem of sensor placement in an integrated gasification combined cycle power plant, and how BONUS significantly reduces computational resources while contributing to an appropriate solution is shown. This chapter is derived from the work by Lee and Diwekar .

The Environmental Trading Problem

The increasing stringency of environmental regulations and the global rise of concerns about the environmental impact of industrial production have led to an increased focus on waste management decisions as a component of industrial sustainability. Pollutant credit trading , an approach that provides economic incentives for reducing pollution, is one novel idea introduced in an attempt to reduce the financial burden of waste management . Both the US Environmental Protection Agency (USEPA) and the US Department of Agriculture (USDA) seek to promote this type of market-based solution . However, industry-level decision making under a pollutant trading scheme faces many difficulties, especially in the presence of uncertainty. In this chapter, the L-shaped BONUS algorithm is applied to the pollutant trading problem to optimize such decisions. This chapter is based on the paper by Shastri and Diwekar .

Probability Density Functions and Kernel Density Estimation

Stochastic modeling loop in the stochastic optimization framework involves dealing with evaluation of a probabilistic objective function and constraints from the output data. Probability density functions (PDFs) are a fundamental tool used to characterize uncertain data. Equation 3.1 shows the definition of a PDF f of variable X.

The BONUS Algorithm

In this chapter we describe the basics of the Better Optimization of Nonlinear Uncertain System (BONUS) algorithm. For better readability, we also present the generalized stochastic optimization framework (Fig. 1.4 from Chap. 1) for stochastic nonlinear programming (NLP) problem in this chapter.

Water Security Networks

Because of the importance of water to all life on Earth, water security has become a critical matter in national and international sustainability. Contamination through either malicious (e.g., terrorist attacks) or accidental means (e.g., industrial accidents) could quickly become a catastrophic event. Therefore, water utilities and their related government agencies perceive a growing need to detect and minimize water contamination in distributed water networks . Much attention has been given to optimization of water network design, such as network capacity, pipe diameter and length, component failures, etc., as a means of minimizing risk (see review for sensor placement in water networks ). However, work on qualitative aspects of water network design, such as chemical propagation, concentration of disinfectants, contamination minimization, etc., is far less prominent, though such factors should be considered at the design stage to best make water networks secure from contamination .

Real-Time Optimization forWater Management

As discussed in the previous chapter, water consumption represents a critical resource in thermoelectric power generation, and can be challenging to manage due to its dependence on ambient weather conditions. Because weather conditions are both constantly changing and uncertain, a stochastic framework for real-time optimization of power generation is advantageous over a deterministic framework in maximizing power output. In this chapter, it is shown that significant cost savings can be achieved if optimization is done on an hourly basis, and the plant set points are changed accordingly.