Collaborative Logistics in Vehicle Routing

Less-Than-Truckload (LTL) carriers generally serve geographical regions that are more localized than the inter-city routes served by truckload carriers. That localization can lead to urban freight transportation routes that overlap. If trucks are traveling with less than full loads there may exist opportunities for carriers to collaborate over such routes. That is, Carrier A will also deliver one or more shipments of Carrier B. This will improve vehicle asset utilization and reduce asset-repositioning costs, and may also lead to reduced congestion and pollution in cities. We refer to the above coordination as “collaborative routing”. In our framework for collaboration, we also propose that carriers exchange goods at logistics platforms located at the entry point to a city. This is referred to as “entry-point collaboration”. One difficulty in collaboration is the lack of facilities to allow transfer of goods between carriers. We highlight that the reduction in pollution and congestion under our proposed framework will give the city government an incentive to support these initiatives by providing facilities. Further, our analysis has shown that contrary to the poor benefits reported by previous work on vehicle routing with transshipment, strategic location of transshipment facilities in urban areas may solve this problem and lead to large cost savings from transfer of loads between carriers. We also present a novel integrated three-phase solution method. Our first phase uses either a modified tabu search, or a guided local search, to solve the vehicle routing problems with time windows that result from entry-point collaboration. The preceding methods use a constraint programming engine for feasibility checks. The second phase uses a quad-tree search to locate facilities. Quad-tree search methods are popular in computer graphics, and for grid generation in fluid simulation. These methods are known to be efficient in partitioning a two-dimensional space for storage and computation. We use this efficiency to search a two-dimensional region and locate possible transshipment facilities. In phase three, we employ an integrated greedy local search method to build collaborative routes, using three new transshipment-specific moves for neighborhood definition. We utilize an optimization module within local search to combine multiple moves at each iteration, thereby taking efficient advantage of information from neighborhood exploration. Extensive computational tests are done on random data sets which represent a city such as Toronto. Sensitivity analysis is performed on important parameters to characterize the situations when collaboration will be beneficial. Overall results show that our proposal for collaboration leads to 12% and 15% decrease in route distance and time, respectively. Average asset utilization is seen to increase by about 5% as well

Physical vs Virtual Corporate Power Purchase Agreements: Meeting Renewable Targets Amid Demand and Price Uncertainty

Power purchase agreements (PPAs) have become an important corporate procurement vehicle for renewable power, especially among companies that have committed to targets requiring a certain fraction of their power demand be met by renewables. PPAs are long-term contracts that provide renewable energy certificates (RECs) to the corporate buyer and take two main forms: Physical vs Virtual. Physical PPAs deliver power in addition to RECs, while virtual PPAs are financial contracts that hedge (at least partially) power price uncertainty. We compare procurement portfolios that sign physical PPAs with ones that sign virtual PPAs, focusing on fixed-volume contracts and emphasizing uncertainties in power demand and the prices of power and RECs. In particular, we first analyze a two-stage stochastic model to understand the behavior of procurement quantities and costs when using physical and virtual PPAs as well as variants that limit risk. We subsequently formulate a Markov decision process (MDP) that optimizes the multi-stage procurement of power to reach and sustain a renewable procurement target. By leveraging state-of-the-art reoptimization techniques, we solve this MDP on realistic instances to near optimality, and highlight the relative benefits of using PPA types to meet a renewable target

First-Order Methods for Convex Constrained Optimization under Error Bound Conditions with Unknown Growth Parameters

We propose first-order methods based on a level-set technique for convex constrained optimization that satisfies an error bound condition with unknown growth parameters. The proposed approach solves the original problem by solving a sequence of unconstrained subproblems defined with different level parameters. Different from the existing level-set methods where the subproblems are solved sequentially, our method applies a first-order method to solve each subproblem independently and simultaneously, which can be implemented with either a single or multiple processors. Once the objective value of one subproblem is reduced by a constant factor, a sequential restart is performed to update the level parameters and restart the first-order methods. When the problem is non-smooth, our method finds an $\epsilon$-optimal and $\epsilon$-feasible solution by computing at most $O(\frac{G^{2/d}}{\epsilon^{2-2/d}}\ln^3(\frac{1}{\epsilon}))$ subgradients where $G>0$ and $d\geq 1$ are the growth rate and the exponent, respectively, in the error bound condition. When the problem is smooth, the complexity is improved to $O(\frac{G^{1/d}}{\epsilon^{1-1/d}}\ln^3(\frac{1}{\epsilon}))$. Our methods do not require knowing $G$, $d$ and any problem dependent parameters

Approximate Dynamic Programming for Commodity and Energy Merchant Operations

<p>We study the merchant operations of commodity and energy conversion assets. Examples of such assets include natural gas pipelines systems, commodity swing options, and power plants. Merchant operations involves managing these assets as real options on commodity and energy prices with the objective of maximizing the market value of these assets. The economic relevance of natural gas conversion assets has increased considerably since the occurrence of the oil and gas shale boom; for example, the Energy Information Agency expects natural gas to be the source of 30% of the world's electricity production by 2040 and the McKinsey Global Institute projects United States spending on energy infrastructure to be about 100 Billion dollars by 2020. Managing commodity and energy conversion assets can be formulated as intractable Markov decision problems (MDPs), especially when using high dimensional price models commonly employed in practice. We develop approximate dynamic programming (ADP) methods for computing near optimal policies and lower and upper bounds on the market value of these assets. We focus on overcoming issues with the standard math programming and financial engineering ADP methods, that is, approximate linear programing (ALP) and least squares Monte Carlo (LSM), respectively. In particular, we develop: (i) a novel ALP relaxation framework to improve the ALP approach and use it to derive two new classes of ALP relaxations; (ii) an LSM variant in the context of popular practice-based price models to alleviate the substantial computational overhead when estimating upper bounds on the market value using existing LSM variants; and (iii) a mixed integer programming based ADP method that is exact with respect to a policy performance measure, while methods in the literature are heuristic in nature. Computational experiments on realistic instances of natural gas storage and crude oil swing options show that both our ALP relaxations and LSM methods are efficient and deliver near optimal policies and tight lower and upper bounds. Our LSM variant is also between one and three orders of magnitude faster than existing LSM variants for estimating upper bounds. Our mixed integer programming ADP model is computationally expensive to solve but its exact nature motivates further research into its solution. We provide theoretical support for our methods: By deriving bounds on approximation error we establish the optimality of our best ALP relaxation class in limiting regimes of practical relevance and provide a theoretical perspective on the relative performance of our LSM variant and existing LSM variants. We also unify different ADP methods in the literature using our ALP relaxation framework, including the financial engineering based LSM method. In addition, we employ ADP to study the novel application of jointly managing storage and transport assets in a natural gas pipeline system; the literature studies these assets in isolation. We leverage our structural analysis of the optimal storage policy to extend an LSM variant for this problem. This extension computes near optimal policies and tight bounds on instances formulated in collaboration with a major natural gas trading company. We use our extension and these instances to answer questions relevant to merchants managing such assets. Overall, our findings highlight the role of math programming for developing ADP methods. Although we focus on managing commodity and energy conversion assets, the techniques in this thesis have potential broader relevance for solving MDPs in other application contexts, such as inventory control with demand forecast updating, multiple sourcing, and optimal medical treatment design.</p