Abstract: In time dependent models, the objective is to find the optimal times (continuous) at which activities occur and resources are utilized. These models arise whenever a schedule of activities needs to be constructed. A common approach consists of discretizing the planning time and then restricting the decisions to those time points. However, this approach leads to very large formulations that are intractable in practice. In this work, we study the Continuous Time Inventory Routing Problem with Out-and-Back Routes (CIRP-OB). In this problem, a company manages the inventory of its customers, resupplying a single product from a single facility during a finite time horizon. The product is consumed at a constant rate (product per unit of time) by each customer. The customers have local storage capacity. The goal is to find the minimum cost delivery plan with out-and-back routes only that ensures that none of the customers run out of product during the planning period. We study the Dynamic Discovery Discretization algorithm (DDD) to solve the CIRP-OB by using partially constructed time-expanded networks. This method iteratively discovers time points needed in the network to find optimal continuous time solutions. We test this method by using randomly generated instances in which we find provable optimal solutions.

Abstract: We propose a novel two-phase bounding and decomposition approach to compute optimal and near-optimal solutions to large-scale mixed-integer investment planning problems that have to consider a large number of operating subproblems, each of which is a convex optimization. Our motivating application is the planning of power transmission and generation in which policy constraints are designed to incentivize high amounts of intermittent generation in electric power systems. The bounding phase exploits Jensen's inequality to define a lower bound, which we extend to stochastic programs that use expected-value constraints to enforce policy objectives. The decomposition phase, in which the bounds are tightened, improves upon the standard Benders' algorithm by accelerating the convergence of the bounds. The lower bound is tightened by using a Jensen's inequality-based approach to introduce an auxiliary lower bound into the Benders master problem. Upper bounds for both phases are computed using a sub-sampling approach executed on a parallel computer system. Numerical results show that only the bounding phase is necessary if loose optimality gaps are acceptable. However, the decomposition phase is required to attain optimality gaps. Use of both phases performs better, in terms of convergence speed, than attempting to solve the problem using just the bounding phase or regular Benders decomposition separately. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.

Abstract: Forest ecosystems are recognized for their large capacity to store carbon (C) in their aboveground and belowground biomass and soil pools. While the distribution of C among ecosystem pools has been extensively studied, less is known about nitrogen (N) and phosphorus (P) pools and how these stocks relate to each other. There is also a need to understand how biotic and abiotic ecosystem properties drive the magnitude and distribution of CN-P stocks. We studied a temperate rainforest in southern South America to answer the following questions: 1) how are C-N-P total stocks distributed among the different ecosystem pools?, 2) how do C:N, C:P and N:P ratios vary among ecosystem pools?, and 3) which are the main biotic and abiotic drivers of C-N-P stocks? We established 33 circular plots to estimate C, N, and P stocks in different pools (i.e. trees, epiphytes, understory, necromass, leaf litter, and soil) and a set of biotic (e.g., tree density and richness) and abiotic variables (e.g., air temperature, humidity and soil depth). We used structural equation modeling to identify the relative importance of environmental drivers on C-N-P stocks. We found that total ecosystem stocks (mean +/- SE) were 1062 +/- 58 Mg C ha-1, 28.8 +/- 1.5 Mg N ha-1, and 347 +/- 12.5 kg P ha-1. The soil was the largest ecosystem pool, containing 68%, 92%, and 73% of the total C, N, and P stocks, respectively. Compared to representative temperate forests, the soil of this forest contains the largest concentrations and stocks of C and N. The low P stock and wide soil C:P and N:P ratios suggest that P may be limiting forest productivity. The ecosystem C-N-P stocks were mainly driven by abiotic properties measured in the study area, however for N stocks, variables such as plant diversity and canopy openness were also relevant. Our results provide evidence about the importance not only of understanding the differences in C, N, and P stocks but also of the factors that drive such differences. This is key to inform conservation policies related to preserving old-growth forests in southern South America, which indeed are facing a rapid land-use change process.