We present a graph sampling and coarsening scheme (gSC) for computing lower and upper bounds for large-scale supply chain models. An edge sampling scheme is used to build a low-complexity problem that is used to finding an approximate (but feasible) solution for the original model and to compute a lower bound (for a maximization problem). This scheme is similar in spirit to the so-called sample average approximation scheme, which is widely used for the solution of stochastic programs. A graph coarsening (aggregation) scheme is used to compute an upper bound and to estimate the optimality gap of the approximate solution. The coarsening scheme uses node sampling to select a small set of support nodes that are used to guide node/edge aggregation and we show that the coarsened model provides a relaxation of the original model and a valid upper bound. We provide evidence that gSC can yield significant improvements in solution time and memory usage over state-of-the-art solvers. Specifically, we study a supply chain design model (a mixed-integer linear program) that contains over 38 million variables and show that gSC finds a solution with an optimality gap of < 0.5% in less than 22 minutes.

We developed a distributed algorithm that is based on the adaptive alternating direction multiplier method (ADMM) for solving large-scale supply chain (SC) models. This algorithm exploits the block structure of SC model and decomposes the model into simpler subproblems with closed-form solutions. This algorithm uses a normalized residual balancing (NRB) approach to improve the robustness of ADMM performance with respect to the penalty parameter. This algorithm enables the solution and analysis of large-scale SC problems and alleviates the need for solvers. We accelerate ADMM by leveraging the parallel computing architecture of a graphics processing unit (GPU). We study a real-world SC model that contains over 30 million variables and show that this scheme yields significant improvement in solution time (3-6x) over state-of-the-art linear programming solvers.

We investigate the economic viability of using flexible electrolysis units to produce hydrogen. This approach can help reduce hydrogen production costs by strategically participating in electricity markets while, at the same time, providing demand flexibility services to the power grid. Our study integrates high-fidelity process simulations, optimization tools, and density functional theory calculations to explore the viability of this approach and to compare its performance against traditional processes that use hydrogen produced via methane reforming. Our results show that the proposed electrification framework is cost-competitive under certain electricity markets. Specifically, our approach can automatically estimate the levelized cost of hydrogen (LCOH) as a function of time-varying electricity prices (from day-ahead and real-time prices) and of key techno-economic parameters of the process.

We present a computational framework for investigating the economics of phosphorus  recovery infrastructures in the dairy sector based on cyanobacteria cultivation. Our framework integrates supply chain and techno-economic analysis to assess the potential of large- and small-scale open pond raceways and bag photobioreactors. We explore the integration of these cultivation systems with anaerobic digestion, dry algae biomass production, and biofuel/biogas production units. To guide our assessment, we propose three economic indicators that we call the “social milk incentives” (SMI), “social animal incentives” (SAI), and “social phosphorus incentives” (SPI). The SMI is defined as the revenue necessary to achieve a zero net present value (NPV) for the infrastructure, relative to the total amount of milk produced in the studied region. The SAI is the revenue required relative to the number of cows in the region and the SPI is the revenue required relative to the total P recovered by the infrastructure. These indicators facilitate comparisons between alternative infrastructure layouts, highlight incentives needed, and can help communicate hidden costs of dairy farming to the public. We use our framework to analyze infrastructures that recover P in the upper Yahara watershed region in the State of Wisconsin, which currently faces severe nutrient pollution. 

The optimal design and synthesis of the poultry litter valorization process is addressed in this paper. A superstructure, which consists of seven processing sections, is proposed for treating poultry litter. Nine thermal conversion technologies, five oil upgrading units, three hydrogen production options and two power generation alternatives are considered. Based on the proposed superstructure, a mixed integer nonlinear fractional programming (MINLFP) model is developed to maximize the return on investment (ROI) of waste valorization process. The solution strategies, including piecewise linear approximation and parametric reformulation, are employed to convert the original MINLFP problem into a computationally tractable mixed integer linear program

In this project, we present a mathematical model for optimizing an interplant heat exchanger network (HEN) for multiple time periods. The HEN connects individual plants through a centralized utility system using steam as the heat transfer medium. While previous research has primarily focused on minimizing the cost of such systems, this study introduces the additional objective of minimizing environmental impact. The proposed model utilizes the maximum representative approach to formulate a flexible network capable of operating under the worst conditions. The effectiveness of the model is demonstrated through a case study.

In this project, we present an optimization model for a cooling water system that simultaneously optimizes both the cooler network and the pump network. These subsystems are traditionally optimized separately, but the intrinsic connections between pump cost, cooler cost, and cooling water flow rate require them to be considered together. The proposed model employs a series-parallel superstructure for the cooler network to reduce the flow rate and minimize pumping cost, and a main-auxiliary pumps structure in the pumping system to reduce energy consumption. The model is formulated as a mixed-integer nonlinear programming problem with the goal of minimizing the total annual cost of the system. The effectiveness of the proposed model is demonstrated through a case study.