Sarah M. Ryan

A Multiperiod Generalized Network Flow Model of the U.S. Integrated Energy System: Part I—Model Description

This paper is the first of a two-part paper presenting a multiperiod generalized network flow model of the integrated energy system in the United States. Part I describes the modeling approach used to evaluate the economic efficiencies of the system-wide energy flows, from the coal and natural gas suppliers to the electric load centers. Under the proposed problem formulation, fuel supply and electricity demand nodes are connected via a transportation network, and the model is solved for the most efficient allocation of quantities and corresponding prices. The methodology includes physical, economic, and environmental aspects that characterize the different networks. Part II of this paper provides numerical results that demonstrate the application of the model

On The Validity of The Geometric Brownian Motion Assumption

Abstract The geometric Brownian motion (GBM) process is frequently invoked as a model for such diverse quantities as stock prices, natural resource prices and the growth in demand for products or services. We discuss a process for checking whether a given time series follows the GBM process. Methods to remove seasonal variation from such a time series are also analyzed. Of four industries studied, the historical time series for usage of established services meet the criteria for a GBM; however, the data for growth of emergent services do not.

Hybrid robust and stochastic optimization for closed-loop supply chain network design using accelerated Benders decomposition

Environmental, social and economic concerns motivate the operation of closed-loop supply chain networks (CLSCN) in many industries. We propose a novel profit maximization model for CLSCN design as a mixed-integer linear program in which there is flexibility in covering the proportions of demand satisfied and returns collected based on the firms policies. Our major contribution is to develop a novel hybrid robust-stochastic programming (HRSP) approach to simultaneously model two different types of uncertainties by including stochastic scenarios for transportation costs and polyhedral uncertainty sets for demands and returns. Transportation cost scenarios are generated using a Latin Hypercube Sampling method and scenario reduction is applied to consolidate them. An accelerated stochastic Benders decomposition algorithm is proposed for solving this model. To speed up the convergence of this algorithm, valid inequalities are introduced to improve the lower bound quality, and also a Pareto-optimal cut generation scheme is used to strengthen the Benders optimality cuts. Numerical studies are performed to verify our mathematical formulation and also demonstrate the benefits of the HRSP approach. The performance improvements achieved by the valid inequalities and Pareto-optimal cuts are demonstrated in randomly generated instances.

Scenario construction and reduction applied to stochastic power generation expansion planning

A challenging aspect of applying stochastic programming in a dynamic setting is to construct a set of discrete scenarios that well represents multivariate stochastic processes for uncertain parameters. Often this is done by generating a scenario tree using a statistical procedure and then reducing its size while maintaining its statistical properties. In this paper, we test a new scenario reduction heuristic in the context of long-term power generation expansion planning. We generate two different sets of scenarios for future electricity demands and fuel prices by statistical extrapolation of long-term historical trends. The cardinality of the first set is controlled by employing increasing length time periods in a tree structure while that of the second set is limited by its lattice structure with periods of equal length. Nevertheless, some method of scenario thinning is necessary to achieve manageable solution times. To mitigate the computational complexity of the widely-used forward selection heuristic for scenario reduction, we customize a new heuristic scenario reduction method named forward selection in wait-and-see clusters (FSWC) for this application. In this method, we first cluster the scenarios based on their wait-and-see solutions and then apply fast forward selection within clusters. Numerical results for a twenty year generation expansion planning case study indicate substantial computational savings to achieve similar solutions as those obtained by forward selection alone.

A Markov Decision Model to Evaluate Outsourcing in Reverse Logistics

One of the most important decisions regarding reverse logistics (RL) is whether to outsource such functions or not, due to the fact that RL does not represent a production or distribution firms core activity. To explore the hypothesis that outsourcing RL functions is more suitable when returns are more variable, we formulate and analyse a Markov decision model of the outsourcing decision. The reward function includes capacity and operating costs of either performing RL functions internally or outsourcing them and the transitions among states reflect both the sequence of decisions taken and a simple characterization of the random pattern of returns over time. We identify sufficient conditions on the cost parameters and the return fraction that guarantee the existence of an optimal threshold policy for outsourcing. Under mild assumptions, this threshold is more likely to be crossed, the higher the uncertainty in returns. A numerical example illustrates the existence of an optimal threshold policy even when the sufficient conditions are not satisfied and shows how the threshold for outsourcing decreases while the probability of crossing any fixed threshold increases with the return fraction.

Toward scalable, parallel progressive hedging for stochastic unit commitment

Given increasing penetration of variable generation units, there is significant interest in the power systems research community concerning the development of solution techniques that directly address the stochasticity of these sources in the unit commitment problem. Unfortunately, despite significant attention from the research community, stochastic unit commitment solvers have not made their way into practice, due in large part to the computational difficulty of the problem. In this paper, we address this issue, and focus on the development of a decomposition scheme based on the progressive hedging algorithm of Rockafellar and Wets. Our focus is on achieving solve times that are consistent with the requirements of ISO and utilities, on modest-scale instances, using reasonable numbers of scenarios. Further, we make use of modest-scale parallel computing, representing capabilities either presently deployed, or easily deployed in the near future. We demonstrate our progress to date on a test instance representing a simplified version of the US western interconnect (WECC-240).

Determining Inventory Levels in a CONWIP Controlled Job Shop

We extend the concept of CONWIP control to a job shop setting, in which multiple products with distinct routings compete for the same set of resources. The problem is to determine the fixed overall WIP level and its allocation to product types (WIP mix) to meet a uniformly high customer service requirement for each product type. We formulate an optimization problem for an open queuing network model in which customer orders pull completed products from the system. Then, assuming heavy demand, we derive a throughput target for each product type in a closed queuing network and provide a simple heuristic to find a minimum total WJP and WIP mix that will achieve an operating throughput close to this target. In numerical examples, the WIP mix suggested by this approach achieves the customer service requirement with a relatively low total WIP

Allocating work in process in a multiple-product CONWIP system with lost sales

To operate a multiple-product manufacturing system under a CONWIP control policy, one must decide how to assign kanbans to products. With a fixed total number of kanbans in a competitive environment, the goal is to determine their allocation to product types in order to minimize lost sales equitably. In particular, we consider systems in which the products may make multiple visits to the same station with a different processing time distribution on each repeat visit. With a fixed number of kanbans dedicated to each product, the system is modeled as a multiple-chain multiple-class closed queuing network. A nonlinear program simultaneously provides an approximate performance evaluation and optimizes the allocation of kanbans to product types. In numerical examples, the allocations identified are similar to those obtained by exhaustive enumeration with simulation, but frequently differ significantly from a naïve allocation according to demand rates. A variant of the model that minimizes the total work-in-process to achieve specified throughput targets yields results similar to a previous heuristic method.

Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

We present a method for computing lower bounds in the progressive hedging algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated during execution of the standard PHA. We report computational results on stochastic unit commitment and stochastic server location problem instances, and explore the relationship between key PHA parameters and the quality of the resulting lower bounds.

Temporal vs. Stochastic Granularity in Thermal Generation Capacity Planning with Wind Power

We propose a stochastic generation expansion model, where we represent the long-term uncertainty in the availability and variability in the weekly wind pattern with multiple scenarios. Scenario reduction is conducted to select a representative set of scenarios for the long-term wind power uncertainty. We assume that the short-term wind forecast error induces an additional amount of operating reserves as a predefined fraction of the wind power forecast level. Unit commitment (UC) decisions and constraints for thermal units are incorporated into the expansion model to better capture the impact of wind variability on the operation of the system. To reduce computational complexity, we also consider a simplified economic dispatch (ED) based model with ramping constraints as an alternative to the UC formulation. We find that the differences in optimal expansion decisions between the UC and ED formulations are relatively small. We also conclude that the reduced set of scenarios can adequately represent the long-term wind power uncertainty in the expansion problem. The case studies are based on load and wind power data from the state of Illinois.