Workforce planning in service systems is essential for customer satisfaction and profitability. Typical decisions include hiring levels, shift design, break scheduling, movement of workers around facilities, and matching worker skills to the requirements of tasks. The complexity of these decisions grows when realistic factors such as spatiotemporal demand dynamics, system performance assessment, or skill learning are incorporated into planning. As a result, optimal (or near-optimal) workforce plans should utilize resources efficiently and achieve satisfactory levels of service. This dissertation provides models and solution algorithms for three problems in service system optimization, which include realistic workforce management planning, nonlinear dynamics, and scheduling of tasks. The second chapter studies an airport security screening process and prescribes a daily operational plan, including service rate (i.e., number of servers), scheduling, and resource allocation decisions. The non-stationary arrivals are predicted and known in advance. A discrete-time queuing model that relies on a simple approximation and flow conservation equations embedded in a mixed-integer programming formulation, where consecutive time periods are connected. A multi-step solution method is proposed to optimize various metrics, such as maximum allowed queue lengths and wait times. The third chapter extends the model from the second chapter. In this case, resources can move between different server locations, and their transit time is unproductive. Movement dynamics are captured via a multi-commodity flow model on a time-expanded network. A new discrete-time queue approximation scheme addresses the inaccuracies in existing methods stemming from server overload and underload fluctuations. Problem-specific valid inequalities are derived to improve the solution time, and a temporal decomposition algorithm is proposed to find initial feasible solutions. The last chapter focuses on a medium to long-term scheduling problem with embedded workforce management decisions. The classic formulation for multi-mode multi-skill resource-constrained project scheduling problem is extended to incorporate worker task learning and training dynamics simultaneously. A discretization scheme to model the nonlinear learning process resulting from job assignments is developed. Training of workers is enabled to acquire new skills. A mixed-integer programming formulation is introduced, and a sequential solution scheme is proposed. The trade-offs between project duration and workforce skill composition objectives are investigated.

Environmental problems are more abundant because of the rapid increase in urbanization, climate change, and population growth leading to the depletion of natural resources and endangerment of some species. The availability of infrastructure as well as socio-economic factors facilitate the illicit trade of wildlife through supply chain networks, adding further threats to species. Ecosystem conservation and protection of wildlife from illegal trade and poaching is fundamental to guarantee the survival of endangered species. Conservation efforts require a landscape approach that incorporates spatial features for the effective functionality of the selected reserve. This dissertation studies combinatorial optimization problems with application to two classes of societal problems: landscape conservation and disruption of illicit supply chains. The first and second chapter propose a mixed-integer formulation to model the reserve design problem with budget and ecological constraints. The first uses the radius of the smallest circle enclosing the selected areas as a metric of compactness. An extension of the model is proposed to solve the multi reserve design problem and the reserve expansion problem. The solution approach includes warm start heuristic, separation problem and cuts to improve model performance. The enhanced model outperforms the linearized and the equivalent nonlinear model. The second chapter uses the Reock’s metric as a metric of compactness. The solution approach includes warm start heuristic, knapsack based separation problem to inject solutions, and cuts to improve model performance. The enhanced model outperforms the default model. The third chapter proposes an integer programming model to solve the wildlife corridor design problem with minimum width requirement and a budget constraint. A separation algorithm is proposed to identify boundary patches and violations in the corridor width. A branch-and-cut approach is proposed to induce the corridor width and is tested on real-life landscape. The fourth chapter proposes an integer programming formulation to model the disruption of illicit supply chain problem. The proposed model enforces that at least x paths must be disrupted for an Origin-Destination pair to be disrupted and at least y arcs must be disrupted for a path to be disrupted. The proposed model is tested on real-life road networks.

Networks are a versatile modeling tool for the cyber and physical infrastructure that characterize society. They can be used to describe system spatiotemporal dynamics, including distribution of commodities, movement of agents, and data transmission. This flexibility has resulted in the widespread use of network optimization techniques for decision-making in telecommunications, transportation, commerce, among other systems. However, realistic network problems are typically large-scale and require the use of integer variables to incorporate design or logical system constraints. This makes such problems hard to solve and precludes their wide applicability in the solution of applied problems. This dissertation studies four large-scale optimization problems with underlying network structure in different domain applications, including wireless sensor networks, wastewater monitoring, and scheduling. The problems of interest are formulated using mixed-integer optimization formulations. The proposed solution approaches in this dissertation include branch-and-cut and heuristic algorithms, which are enhanced with network-based valid inequalities and network reduction techniques. The first chapter studies a relay node placement problem in wireless sensor networks, with and without the presence of transmission obstacles in the deployment region. The proposed integer linear programming approach leverages the underlying network structure to produce valid inequalities and network reduction heuristics, which are incorporated in the branch-and-bound exploration. The solution approach outperforms the equivalent nonlinear model and solves instances with up to 1000 sensors within reasonable time. The second chapter studies the continuous version of the maximum capacity (widest) path interdiction problem and introduces the first known polynomial time algorithm to solve the problem using a combination of binary search and the discrete version of the Newton’s method. The third chapter explores the service agent transport interdiction problem in autonomous vehicle systems, where an agent schedules service tasks in the presence of an adversary. This chapter proposes a single stage branch-and-cut algorithm to solve the problem, along with several enhancement techniques to improve scalability. The last chapter studies the optimal placement of sensors in a wastewater network to minimize the maximum coverage (load) of placed sensors. This chapter proposes a branch-and-cut algorithm enhanced with network reduction techniques and strengthening constraints.

Due to environmental and geopolitical reasons, many countries are embracing electric vehicles (EVs) as an alternative to gasoline powered automobiles. Other alternative-fuel vehicles (AFVs) powered by compressed gas, hydrogen or biodiesel have also been tested for replacing gasoline powered vehicles. However, since the associated refueling infrastructure of AFVs is sparse and is gradually being built, the distance between recharging points (RPs) becomes a crucial prohibitive attribute in attracting drivers to use such vehicles. Optimally locating RPs will both increase demand and help in developing the refueling infrastructure.

The major emphasis in this dissertation is the development of theories and associated algorithms for a new set of location problems defined on continuous network space related to siting multiple RPs for range limited vehicles.

This dissertation covers three optimization problems: locating multiple RPs on a line network, locating multiple RPs on a comb tree network, and locating multiple RPs on a general tree network. For each of the three problems, finding the minimum number of RPs needed to refuel all Origin-Destination (O-D) flows is considered as the first objective. For this minimum number, the location objective is to locate this number of RPs to minimize weighted sum of the travelling distance for all O-D flows. Different exact algorithms are proposed to solve each of the three algorithms.

In the first part of this dissertation, the simplest case of locating RPs on a line network is addressed. Scenarios include single one-way O-D pair, multiple one-way O-D pairs, round trips, etc. A mixed integer program with linear constraints and quartic objective function is formulated. A finite dominating set (FDS) is identified, and based on the existence of FDS, the problem is formulated as a shortest path problem. In the second part, the problem is extended to comb tree networks. Finally, the problem is extended to general tree networks. The extension to a probabilistic version of the location problem is also addressed.

Conservation planning is fundamental to guarantee the survival of endangered species and to preserve the ecological values of some ecosystems. Planning land acquisitions increasingly requires a landscape approach to mitigate the negative impacts of spatial threats such as urbanization, agricultural development, and climate change. In this context, landscape connectivity and compactness are vital characteristics for the effective functionality of conservation reserves. Connectivity allows species to travel across landscapes, facilitating the flow of genes across populations from different protected areas. Compactness measures the spatial dispersion of protected sites, which can be used to mitigate risk factors associated with species leaving and re-entering the reserve. This research proposes an optimization model to identify areas to protect while enforcing connectivity and compactness. In the suggested projected area, this research builds upon existing methods and develops an alternative metric of compactness that penalizes the selection of patches of land with few protected neighbors. The new metric is referred as leaf because it intends to minimize the number of selected areas with 1 neighboring protected area. The model includes budget and minimum selected area constraints to reflect realistic financial and ecological requirements. Using a lexicographic approach, the model can improve the compactness of conservation reserves obtained by other methods. The use of the model is illustrated by solving instances of up to 1100 patches.

Carbon Capture and Storage (CCS) is a climate stabilization strategy that prevents CO2 emissions from entering the atmosphere. Despite its benefits, impactful CCS projects require large investments in infrastructure, which could deter governments from implementing this strategy. In this sense, the development of innovative tools to support large-scale cost-efficient CCS deployment decisions is critical for climate change mitigation. This thesis proposes an improved mathematical formulation for the scalable infrastructure model for CCS (SimCCS), whose main objective is to design a minimum-cost pipe network to capture, transport, and store a target amount of CO2. Model decisions include source, reservoir, and pipe selection, as well as CO2 amounts to capture, store, and transport. By studying the SimCCS optimal solution and the subjacent network topology, new valid inequalities (VI) are proposed to strengthen the existing mathematical formulation. These constraints seek to improve the quality of the linear relaxation solutions in the branch and bound algorithm used to solve SimCCS. Each VI is explained with its intuitive description, mathematical structure and examples of resulting improvements. Further, all VIs are validated by assessing the impact of their elimination from the new formulation. The validated new formulation solves the 72-nodes Alberta problem up to 7 times faster than the original model. The upgraded model reduces the computation time required to solve SimCCS in 72% of randomly generated test instances, solving SimCCS up to 200 times faster. These formulations can be tested and then applied to enhance variants of the SimCCS and general fixed-charge network flow problems. Finally, an experience from testing a Benders decomposition approach for SimCCS is discussed and future scope of probable efficient solution-methods is outlined.