The goal of this dissertation is to study optimization models that integrate location, production, inventory and transportation decisions for industrial products and apply the knowledge gained to develop supply chains for agricultural products (biomass). We estimate unit cost for the whole biomass-to-biofuels’ supply chain which is the per gallon cost for biofuels up till it reaches the markets. The unit cost estimated is the summation of location, production, inventory holding, and transportation costs. In this dissertation, we focus on building mathematical models for designing and managing the biomass-to-biofuels’ supply chains. The computational complexity of the developed models makes it advisable to use heuristic solution procedures. We develop a Lagrangean decomposition heuristic. In our heuristic, we divide the problem into two sub-problems, sub-problem 1 is a transportation problem and sub-problem 2 is a combination of a capacitated facility location and production planning problem. Subproblem 2 is further divided by commodities. The algorithm is tested for a number of different scenarios. We also develop a decision support system (DSS) for the biomass-to-biofuels’ supply chain. In our DSS, the main problem is divided into four easy-to-solve supply chain problems. These problems were determined based on our knowledge of supply chain and discussions with the experts from the biomass and biofuels’ sector. The DSS is coded using visual basic applications (VBA) for Excel and has a simple user interface which assists the user in running different types of supply chain problems and provides results in form of reports which are easy to understand.

Addressing fairness among users and risk mitigation in the context of resource allocation in transportation systems under uncertainties poses a crucial challenge yet to be satisfactorily resolved. This dissertation attempts to address this challenge, focusing on achieving a balance between system-wide efficiency and individual fairness in stochastic transportation resource allocation problems. To study complicated fair and risk-averse resource allocation problems - from public transit to urban air mobility and multi-stage infrastructure maintenance - we develop three models: DrFRAM, FairUAM, and FCMDP. Each of these models, despite being proven NP-hard even in a simplistic case, inspires us to develop efficient solution algorithms. We derive mixed-integer linear programming (MILP) formulations for these models, leveraging the unique properties of each model and linearizing non-linear terms. Additionally, we strengthen these models with valid inequalities. To efficiently solve these models, we design exact algorithms and approximation algorithms capable of obtaining near-optimal solutions. We numerically validate the effectiveness of our proposed models and demonstrate their capability to be applied to real-world case studies to adeptly address the uncertainties and risks arising from transportation systems. This dissertation provides a foundational platform for future inquiries of risk-averse resource allocation strategies under uncertainties for more efficient, equitable, and resilient decision-making. Our adaptable framework can address a variety of transportation-related challenges and can be extended beyond the transportation domain to tackle resource allocation problems in a broader setting. / Doctor of Philosophy / In transportation systems, decision-makers constantly strive to devise the optimal plan for the most beneficial outcomes when facing future uncertainties. When optimizing overall efficiency, individual fairness has often been overlooked. Besides, the uncertainties in the transportation systems raise serious questions about the adaptability of the allocation plan. In response to these issues, we introduce the concept of fair and risk-averse resource allocation under uncertainties in this dissertation. Our goal is to formulate the optimal allocation plan that is both fair and risk-averse amid uncertainties. To tackle the complexities of fair and risk-averse resource allocation problems, we propose innovative methods and practical algorithms, including creating novel formulations as well as deriving super-fast algorithms. These solution approaches are designed to accommodate the fairness, uncertainties, and risks typically in transportation systems. Beyond theoretical results, we apply our frameworks and algorithms to real-world case studies, thus demonstrating our approaches' adaptability to various transportation systems and ability to achieve various optimization goals. Ultimately, this dissertation aims to contribute to fairer, more efficient, and more robust transportation systems. We believe our research findings can help decision-makers with well-informed choices about resource allocation in transportation systems, which, in turn, lead to the development of more equitable and reliable systems, benefiting all the stakeholders.

In this thesis, we study the role of interdiction in the Vehicle Routing Problem (VRP), which naturally arises in humanitarian logistics and military applications. We assume that in a general network, each arc has a chance to be interdicted. When interdiction happens, the vehicle traveling on this arc is lost or blocked and thus unable to continue the trip. We model the occurrence of interdiction as a given probability and consider the multi-period expected delivery. Our objective is to minimize the total travel cost or to maximize the demand fulfillment, depending on the supply quantity. This problem is called the Vehicle Routing Problem with Interdiction (VRPI). We first prove that the proposed VRPI problems are NP-hard. Then we show some key analytical properties pertaining to the optimal solutions of these problems. Most importantly, we examine Dror and Trudeau's property applied to our problem setting. Finally, we present efficient heuristic algorithms to solve these problems and show the effectiveness through numerical studies. / Thesis / Master of Science (MSc)

Evacuation planning is an important disaster management tool. A large-scale evacuation of a region by automobile is a difficult task, especially as demand is often greater than supply. This is made more difficult as the imbalance of supply and demand actually reduces supply due to congestion. Currently, most of the emphasis in evacuation planning is on supply management. The purpose of this dissertation is to introduce and study sophisticated demand management tools, specifically, staging and routing of evacuees. These tools can be used to produce evacuation strategies that reduce or eliminate congestion. A strategic planning model is introduced that accounts for evacuation dynamics and the non-linearities in travel times associated with congestion, yet is tractable and can be applied to large-scale networks. Objective functions of potential interest in evacuation planning are introduced and studied in the context of this model. Insights into the use of staging and routing in evacuation management are delineated and solution techniques are developed. Two different strategic approaches are studied in the context of this model. The first strategic approach is to control the evacuation at a disaggregate level, where customized staging and routing plans are produced for each individual or family unit. The second strategic approach is to control the evacuation at a more aggregate level, where evacuation plans are developed for a larger group of evacuees, based on pre-defined geographic areas. In both approaches, shelter requirements and preferences can also be considered. Computational experience using these two strategic approaches, and their respective solution techniques, is provided using a real network pertaining to Virginia Beach, Virginia, in order to demonstrate the efficacy of the proposed methodologies. / Ph. D.

The facility layout problem (FLP) is one of the most important and challenging problems in both the operations research and industrial engineering research domains. In FLP research, the continuous-representation-based FLP can consider all possible all-rectangular department solutions. Given this flexibility, this representation has become the representation of-choice in FLP research. Much of this research is based on a methodology of mixed integer programming (MIP) models. However, these MIP-FLP models can only solve problems with a limited number of departments to optimality due to a large number of binary variables used in the models to prevent departments from overlapping. Our research centers around the sequence-pair representation, a concept that originated in the Very Large Scale Integration (VLSI) design literature. We show that an exhaustive search of the sequence-pair solution space will result in finding the optimal layout of the MIP-FLP and that every sequence-pair solution is binary-feasible in the MIP-FLP. Based on this fact, we propose a methodology that combines the sequence-pair and MIP-FLP model to efficiently solve large continuous-representation-based FLPs. Our heuristic approach searches the sequence-pair solution space and then use the sequence-pair representation to simplify and solve the MIPFLP model. Based on this methodology, we systematically study the different aspects of the FLP throughout this dissertation. As the first contribution of this dissertation, we present a genetic algorithm based heuristic, SEQUENCE, that combines the sequence-pair representation and the most recent MIPFLP model to solve the all-rectangular-department continuous-representation-based FLP. Numerical experiments based on different sized test problems from both the literature and industrial applications are provided and the solutions are compared with both the optimal solutions and the solutions from other heuristics to show the effectiveness and efficiency of our heuristic. For eleven data sets from the literature, we provide solutions better than those previously found. For the FLP with fixed departments, many sequence-pairs become infeasible with respect to the fixed department location and dimension restrictions. As our second contribution, to address this difficulty, we present a repair operator to filter the infeasible sequence-pairs with respect to the fixed departments. This repair operator is integrated into SEQUENCE to solve the FLP with fixed departments more efficiently. The effectiveness of combining SEQUENCE and the repair operator for solving the FLP with fixed departments is illustrated through a series of numerical experiments where the SEQUENCE solutions are compared with other heuristics' solutions. The third contribution of this dissertation is to formulate and solve the FLP with an existing aisle structure (FLPAL). In many industrial layout designs, the existing aisle structure must be taken into account. However, there is very little research that has been conducted in this area. We extend our research to further address the FLPAL. We first present an MIP model for the FLPAL (MIP-FLPAL) and run numerical experiments to test the performance of the MIP-FLPAL. These experiments illustrate that the MIP-FLPAL can only solve very limited sized FLPAL problems. Therefore, we present a genetic algorithm based heuristic, SEQUENCE-AL, to combine the sequence-pair representation and MIP-FLPAL to solve larger-sized FLPAL problems. Different sized data sets are solved by SEQUENCE-AL and the solutions are compared with both the optimal solutions and other heuristics' solutions to show the effectiveness of SEQUENCE-AL. The fourth contribution of this dissertation is to formulate and solve the FLP with non-rectangular-shaped departments. Most FLP research focuses on layout design with all rectangular-shaped departments, while in industry there are many FLP applications with non-rectangular-shaped departments. We extend our research to solve the FLP with nonrectangular-shaped departments. We first formulate the FLP with non-rectangular-shaped departments (FLPNR) to a MIP model (MIP-FLPNR), where each non-rectangular department is partitioned into rectangular-shaped sub-departments and the sub-departments from the same department are connected according to the department's orientation. The effect of different factors on the performance of the MIP-FLPNR is explored through a series of numerical tests, which also shows that MIP-FLPNR can only solve limited-sized FLPNR problems. To solve larger-sized FLPNR problems, we present a genetic algorithm based heuristic, SEQUENCE-NR, along with two repair operators based on the mathematical properties of the MIP-FLPNR to solve the larger-sized FLPNR. A series of numerical tests are conducted on SEQUENCE-NR to compare the SEQUENCE-NR solutions with both the optimal solutions and another heuristic's solutions to illustrate the effectiveness of SEQUENCE-NR. As the first systematic research study on a methodology that combines the sequence-pair representation and the MIP-based FLP, this dissertation addresses different types of continuous-representation based facility layout design problems: from block layout design with and without fixed departments to re-layout design with an existing aisle structure, and from layout design with all-rectangular-shaped departments to layout design with arbitrary non-rectangular-shaped departments. For each type of layout design problem, numerical experiments are conducted to illustrate the effectiveness of our specifically designed family of sequence-pair and MIP-based heuristics. As a result, better solutions than those previously found are provided for some widely used data sets from the literature and some new datasets based on both the literature and industrial applications are proposed for the first time. Furthermore, future research that continues to combine the sequence-pair representation and the MIP-FLP model to solve the FLP is also discussed, indicating the richness of this research domain. / Ph. D.

We present works on theory and applications for Mixed Integer Quadratically Constrained Quadratic Programs (MIQCQP). We introduce new mixed integer programming (MIP)-based relaxation and approximation schemes for general Quadratically Constrained Quadratic Programs (QCQP's), and also study practical applications of QCQP's and Mixed-integer QCQP's (MIQCQP). We first address a challenging tank blending and scheduling problem regarding operations for a chemical plant. We model the problem as a discrete-time nonconvex MIQCP, then approximate this model as a MILP using a discretization-based approach. We combine a rolling horizon approach with the discretization of individual chemical property specifications to deal with long scheduling horizons, time-varying quality specifications, and multiple suppliers with discrete arrival times. Next, we study optimization methods applied to minimizing forces for poses and movements of chained Stewart platforms (SPs). These SPs are parallel mechanisms that are stiffer, and more precise, on average, than their serial counterparts at the cost of a smaller range of motion. The robot will be used in concert with several other types robots to perform complex assembly missions in space. We develop algorithms and optimization models that can efficiently decide on favorable poses and movements that reduce force loads on the robot, hence reducing wear on this machine, and allowing for a larger workspace and a greater overall payload capacity. In the third work, we present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions and formulate this approximation using mixed-integer programming (MIP). Combining this with a diagonal perturbation technique to convert a nonseparable quadratic function into a separable one, we present a mixed-integer convex quadratic relaxation for nonconvex quadratic optimization problems. We study the strength (or sharpness) of our formulation and the tightness of its approximation. We computationally demonstrate that our model outperforms existing MIP relaxations, and on hard instances can compete with state-of-the-art solvers. Finally, we study piecewise linear relaxations for solving quadratically constrained quadratic programs (QCQP's). We introduce new relaxation methods based on univariate reformulations of nonconvex variable products, leveraging the relaxation from the third work to model each univariate quadratic term. We also extend the NMDT approach (Castro, 2015) to leverage discretization for both variables in a bilinear term, squaring the resulting precision for the same number of binary variables. We then present various results related to the relative strength of the various formulations. / Doctor of Philosophy / First, we study a challenging long-horizon supply acquisition problem for a chemical plant. For this problem, constraints with products of variables are required to track raw material composition from supply carriers to storage tanks to the production feed. We apply a mixed-integer nonlinear program (MIP) approximation of the problem combined with a rolling planning scheme to obtain good solutions for industry problems within a reasonable time frame. Next, we study optimization methods applied to a robot designed as a stack of Stewart platforms (SPs), which will be used in concert with several other types robots to perform complex space missions. When chaining these SPs together, we obtain a robot that is generally stiffer more precise than a classic robot arm, enabling their potential use for a variety of purposes. Our methods can efficiently decide on favorable poses and movements for the robot that reduce force loads on the robot, hence reducing wear on this machine, and allowing for a larger usable range of motion and a greater overall payload capacity. Our final two works focus on MIP-based techniques for nonconvex QCQP's. In the first work, we break down the objective into an easy-to-handle term minus some squared terms. We then introduce an elegant new MIP-based approximation to handle these squared terms. We prove that this approximation has strong theoretical guarantees, then demonstrate that it is effective compared to other approximations. In the second, we directly model each variable product term using a MIP relaxation. We introduce two new formulations to do this that build on previous formulations, increasing the accuracy with the same number of integer variables. We then prove a variety of useful properties about the presented formulations, then compare them computationally on two families of problems.

The global energy requirement is increasing at a rapid pace and fossil fuels have been one of the major players in meeting this growing energy demand. However, the resources for fossil fuels are finite. Therefore, it is essential to develop renewable energy sources like biofuels to help address growing energy needs. A key aspect in the production of biofuel is the biomass logistics chain that constitutes a complex collection of activities, which must be judiciously executed for a cost-effective operation. In this thesis, we introduce a two-phase optimization-simulation approach to determine tactical biomass logistics-related decisions cost effectively in view of the uncertainties encountered in real-life. These decisions include number of trucks to haul biomass from storage locations to a bio-refinery, the number of unloading equipment sets required at storage locations, and the number of satellite storage locations required to serve as collection points for the biomass secured from the fields. Later, an operational-level decision support tool is introduced to aid the "feedstock manager" at the bio-refinery by recommending which satellite storage facilities to unload, how much biomass to ship, how to allocate existing resources (trucks and unloading equipment sets) during each time period, and how to route unloading equipment sets between storage facilities. Another problem studied is the "Bale Collection Problem" associated with the farmgate operation. It is essentially a capacitated vehicle routing problem with unit demand (CVRP-UD), and its solution defines a cost-effective sequence for collecting bales from the field after harvest. / Master of Science

Closed-loop supply chains (CLSC) though present for decades, have seen significant research in optimization only in the last five years. Traditional sustainable CLSCs have generally implemented a Carbon Cap Trading (CCT), Carbon Cap (CC), or Carbon Taxes methodology to set carbon emissions limits but fail to minimize these emissions explicitly. Moreover, the traditional CCT model discourages investment in greener technologies by favoring established logistics over eco-friendly alternatives. This research tackles the sustainable CLSC problem by proposing a mixed-integer linear programming (MILP) carbon-conscious textit{p}-hub location model having the objective of minimizing emissions subject to profit constraints. The model is then extended to incorporate multi-periodicity, transportation modes, and end-of-life periods with a bi-objective cost and emissions function. Additionally, the model accounts for long-term planning and optimization, considering changes in demand and returns over time by incorporating a time dimension. The model's robustness and solving capabilities were tested for the case of electric vehicle (EV) battery supply chains. Demand for EVs is projected to increase by 18% annually, and robust supply chain designs are crucial to meet this demand, making this sector an important test case for the model to solve. Two baseline cases with minimum cost and minimum emissions objectives were tested, revealing a significant gap in emissions and underlining the need for an emissions objective. A sensitivity analysis was conducted on key parameters focusing on minimizing emissions; the analysis revealed that demand, return rates, and recycling costs greatly impact CLSC dynamics. The results showcase the model's capability of tackling real-world case scenarios, thus facilitating comprehensive decision-making goals in carbon-conscious CSLC design. / Master of Science / Closed-loop supply chain (CLSC) is a supply chain that recycles used products back to the manufacturer. CLSCs have been around for decades, but significant progress in optimizing them has only emerged over the last five years. Sustainable CLSC models often include limits on carbon emissions but usually don't directly minimize them. Traditional CLSC models tend to prioritize established logistics over greener technologies, discouraging investment in eco-friendly options. This study addresses this problem by introducing a mathematical model designed to minimize emissions while considering profit constraints. The model is expanded to factor in different time periods, transportation methods, and end-of-use phases with two goals in mind: cost and emissions. Additionally, it incorporates long-term planning, accounting for shifts in customer demand and product returns. The model's effectiveness was tested with electric vehicle (EV) battery supply chains, which serve as an important example given the predicted annual 18% growth in EV demand and the crucial need for efficient supply chain design. Two baseline scenarios were examined: one aiming to minimize costs and the other to minimize emissions. The results showed a notable disparity in emissions between the two, underscoring the importance of an emissions-focused objective. Key parameters, such as demand, return rates, and recycling costs, demonstrated a significant impact on CLSC operations. The findings highlight the model's ability to handle real-world challenges, enabling informed decision-making for designing carbon-conscious CLSCs.

This thesis focuses on the challenges that arise from the scheduling of heat exchanger network maintenance problems which undergo fouling and run continuously over time. The original contributions of the current research consist of the development of novel optimisation methodologies for the scheduling of cleaning actions in heat exchanger network problems, the application of the novel solution methodology developed to other general maintenance scheduling problems, the development of a stochastic programming formulation using this optimisation technique and its application to these scheduling problems with parametric uncertainty. The work presented in this thesis can be divided into three areas. To efficiently solve this non-convex heat exchanger network maintenance scheduling problem, new optimisation strategies are developed. The resulting contributions are outlined below. In the first area, a novel methodology is developed for the solution of the heat exchanger network maintenance scheduling problems, which is attributed towards a key discovery in which it is observed that these problems exhibit bang-bang behaviour. This indicates that when integrality on the binary decision variables is relaxed, the solution will tend to either the lower or the upper bound specified, obviating the need for integer programming solution techniques. Therefore, these problems are in ac- tuality optimal control problems. To suitably solve these problems, a feasible path sequential mixed integer optimal control approach is proposed. This methodology is coupled with a simple heuristic approach and applied to a range of heat exchanger network case studies from crude oil refinery preheat trains. The demonstrated meth- odology is shown to be robust, reliable and efficient. In the second area of this thesis, the aforementioned novel technique is applied to the scheduling of the regeneration of membranes in reverse osmosis networks which undergo fouling and are located in desalination plants. The results show that the developed solution methodology can be generalised to other maintenance scheduling problems with decaying performance characteristics. In the third and final area of this thesis, a stochastic programming version of the feasible path mixed integer optimal control problem technique is established. This is based upon a multiple scenario approach and is applied to two heat exchanger network case studies of varying size and complexity. Results show that this methodology runs automatically with ease without any failures in convergence. More importantly due to the significant impact on economics, it is vital that uncertainty in data is taken into account in the heat exchanger network maintenance scheduling problem, as well as other general maintenance scheduling problems when there is a level of uncertainty in parameter values.

Norrmejerier står inför förändringar vad gäller både mjölkkonsumtion och flytt av produktionen från Luleå mejeri till Umeå mejeri inom en snar framtid. Det har gett behov av ett verktyg för att snabbt kunna fatta beslut om systemet kan hantera en ökad mängd volym och antal produktkategorier. För att ta fram ett sådant verktyg skapades en matematisk optimeringsmodell uppbyggd i programvaran Python som gör det möjligt att köra programmet för olika scenarion. Modellen använder optimeringslösaren Pulp för att hitta en lösning på problemet. Den matematiska modellen baseras på Multi Commodity Flow Problem med tidsvariabel i kombination med Flow-shop scheduling och har modifierats efter systemet på Umeå mejeri. Det är en pessimistisk modell baserat på de antaganden som gjorts i rapporten. Programmet baseras på ett dygns produktion och avgör, genom att minimera den totala tiden det tar för flödet genom processen, om det finns kapacitet för en ökad produktion. Systemet i projektet är uppdelat i två subnätverk på grund av tidskomplexiteten och resultaten visar att implementering av en ytterligare produktkategori kan hanteras av båda subnätverken. En ökad volym med 10% av den befintliga kan endast hanteras av den första delen av nätverket. Det betyder att det finns tekniska begränsningar i det andra subnätverket. Genom tillägg av extra noder som kan användas till en viss straffkostnad kunde flaskhalsar identifieras och det visade sig att pastör 2P1 är en uppenbar flaskhals i systemet. Om man ökar produktionen ytterligare kan även silosarna behöva utökas för att hantera flödet. / Norrmejerier is facing changes in terms of both milk consumption and a move of the production from Luleå dairy to Umeå dairy in the near future. This has given rise to the need of a tool that quickly can make descisions about whether the system can handle an increased amount of volume and number of product categories. To produce such a tool a mathematical optimization model was created in Python which makes it possible to run the program for different scenarios. The model uses the optimization solver Pulp. The mathematical model is based on Multi Commodity Flow Problem with time variable combined with Flow-shop scheduling and has been modified according to the system at Umeå dairy. Based on the assumptions made in the report it is a pessimistic model. The program is based on one day's production and determines by minimizing the total time it takes for the flow to pass through the system, to see if there is enough capacity for increased production. The system in the project is divided into two subnetworks due to the time complexity and the results show that implementation of an additional product category can be handled by both subnetworks. An increased volume of 10% of the existing volume can only be handled by the first part of the network. This means that there are technical limitations in the second subnetwork. By adding extra nodes that can be used for a certain penalty cost, bottlenecks could be identified and it turned out that Pasteur 2P1 is an obvious bottleneck in the system. If the production increases further the silos may also need to be expanded to handle the flow in the system.