Category: EMIS

In this presentation we will present alternative formulations of stochastic market clearing problem which are based on different algebraic representations of non-anticipativity constraints of multistage stochastic programming. These formulations result in prices which have alternative interpretations under different power system settings. We will present these interpretations along with computational results for well known testbeds.

We present a model for the selection and scheduling of R&D projects with several phases.The initial model contains two main stages development and commercialization. The goal of this model is to maximize the net present value under constraints of scientists' availability and uncertain profit. This nonlinear mixed-integer model is NP-hard and not tractable for large-scale problem instances where we use adaptive robust model, Hence, we develop a strong Mixed Integer Programming model and a heuristic algorithm. Then, we show the performance of these algorithms in terms of running time and optimality gap in experiments.

The triples formulation is a compact formulation of multicommodity network flow that provides a different representation of flow than the traditional, widely used node-arc and arc-path formulations. In the literature, the triples formulation has been applied successfully to the minimum cost multicommodity flow problem with piecewise linear cost functions in complete, undirected graphs, and the maximum concurrent flow problem. In this study we show that the triples formulation of a freight logistics application known as the backhaul profit maximization problem (BPMP) can be solved significantly faster than the existing model in the literature, which is based on the node-arc model. We also demonstrate the effectiveness of applying the triples formulation to the uncapacitated, single-commodity, fixed charge network flow problem.

Club sports in metro areas are popular nowadays, however there are key concerns for organizers, which are reducing driving time due to teams commuting to facilities in different regions while keeping league divisions competitive. A three-step approach is adopted to solve this problem. Driving time data between each location is analyzed initially, and clubs are split into several groups accordingly. Teams are assigned to groups based on their location and ranking. And these two processes are merged in the end to find the best solution. From the result, this optimization model is able to arrange games in a way that not only shortens the travel time for players, but also maintains an acceptable level of competition.

In this study we examine two stages stochastic quadratic programming problems, where the second stage itself is a quadratic programming problem with linear constraints with uncertain right-hand sides. We develop the active-set strategy obtain a estimation for the second stage. This approximation is used to design a computationally gradient solution algorithm to solve stochastic quadratic programs. We will present the convergence and numerical analysis of the algorithm.

Salesforce territory design is a process that most sales organizations labor over on an annual basis. Often business-to-business sales organizations align on geographic sales territories. Usually, this involves grouping sales units (geographic units) into larger geographic groups, called sales territories. This paper will explore how to create an optimal sales territory design that balances two fundamental constraints, equitability in the addressable market and geographic compactness. Equitability ensures that each salesperson has the same opportunity to sell and achieve sales quota. Compactness ensures that the sales territory includes sales units that are close to one another and, more specifically, adjacent to one another. This optimal territory design is then applied to a business-to-business sales organization.

This paper addresses supervised learning problems with grouping information on model coefficients given a priori. We focus on non-overlapping groups such that coefficients for each disjoint group shall be simultaneously either zero or nonzero. To deal with such group sparsity structure, we introduce a novel log-composite regularizer, which can be minimized by an iterative algorithm. In particular, our algorithm iteratively solves for a traditional group LASSO problem that involves summing up the L2 norm of each group until convergent. By updating group weights, our approach enforces a group of smaller coefficients from the previous iterate to be more likely to set to zero, compared to the group LASSO. Theoretical results include a minimizing property of the proposed model as well as the convergence of the iterative algorithm to a stationary solution under mild conditions. We conduct extensive experiments on synthetic and real datasets, indicating that our method yields superior performance over the state-of-the-art methods in linear regression and binary classification.

The goal of intensity modulated radiation therapy is to distribute a prescribed dose of radiation to cancerous tumors while sparing the surrounding healthy tissue. Current approaches implement a radiation plan such that the prescribed tumor dosage is divided equally and delivered through several treatment sessions. This equally distributed (uniform) approach involves solving an optimization problem at each treatment session without consideration of the future sessions or tumor evolution. Herein, we develop a generalization of the uniform formulation that does not automatically assume equal session tumor prescriptions (nonuniform) and also takes future decisions into consideration. This nonuniform multistage framework allows for a natural connection between treatment sessions as well as consideration for sources of uncertainty due to tumor evolution. For the proposed formulation, a sequence of prostate cancer scans provide numerical results revealing drastic improvement in tumor delivery precision while using a total dosage no more than the current practice methods.