Master of Science / Department of Industrial & Manufacturing Systems Engineering / Todd W. Easton / Westside High School (WHS) of Omaha, Nebraska utilizes a novel scheduling system called Modular scheduling. This system offers numerous advantages over the standard school day in terms of student learning and faculty development. Modular Scheduling allows teachers to design the structure of their own classes by adjusting the frequency, duration and location of each of their daily lessons. Additionally, teachers are able combine their classes with those of other teachers and team-teach. Modular scheduling also allows for open periods in both students’ and teachers’ schedules. During this time, students are able to complete school work or seek supplemental instruction with a teacher who is also free. Teachers are able to use their open mods to plan, meet in teams and help students who have fallen behind. Currently, a semester’s class schedules are constructed over the course of a seven week period by a full-time employee using a computer program developed in FORTRAN®. The process is extremely tedious and labor intensive which has led to considerable wasted time, cost and frustration. This thesis presents a novel scheduling program called the SMART Scheduler that is able to do in seconds what previously took weeks to accomplish. Once parameters have been input, The SMART Scheduler is able to create cohesive class schedules within a modular environment in less than 6 seconds. The research presented describes the steps that were taken in developing the SMART Scheduler as well as computational results of its implementation using actual data provided by WHS. The goal of this research is to enable WHS and other schools to efficiently and effectively utilize modular scheduling to positively affect student learning.

Master of Science / Department of Industrial and Manufacturing Systems Engineering / Todd Easton / Integer programs (IPs) are mathematical models that can provide an optimal solution to a variety of different problems. They have the ability to maximize profitability and decrease wasteful spending, but IPs are NP-complete resulting in many IPs that cannot be solved in reasonable periods of time. Cutting planes or valid inequalities have been used to decrease the time required to solve IPs. These valid inequalities are commonly created using a procedure called lifting. Lifting is a technique that strengthens existing valid inequalities without cutting off feasible solutions. Lifting inequalities can result in facet defining inequalities, the theoretically strongest valid inequalities. Because of these properties, lifting procedures are used in software to reduce the time required to solve an IP. This thesis introduces a new algorithm for synchronized simultaneous approximate lifting for multiple knapsack problems. Synchronized Simultaneous Approximate Lifting (SSAL) requires O(|E1|SLP_|E1|+|E2|,m + |E1|2) effort, where |E1| and |E2| are the sizes of sets used in the algorithm and SLP is the time to solve a linear program. It approximately uplifts two sets simultaneously to creates multiple inequalities of a particular form. These new valid inequalities generated by SSAL can be facet defining. A small computational study shows that SSAL is quick to execute, requiring fractions of a second. Additionally, applying SSAL inequalities to large knapsack problem enabled commercial software to solve faster and also eliminate off the initial linear relaxation point.

This thesis addresses three problems where a focal agent's operational policies (inventory and capacity allocation) interact with marketing decisions. The first chapter studies how wholesale all-unit discounts may lead to products being shifted from authorized retailers to discounted gray market channels. Such discounts lead to discontinuous ordercosts which may induce buyers to order up to a threshold where they receive a greater discount. The buyer in this chapter is a reseller who makes purchasing decisions while taking into account inventory holding costs, how their resale price affects consumer demand and whether or not they divert inventory to the gray market. I analyze factors which determine how the reseller balances between lowering resale prices and diverting to the gray market, both of which lower costs by shortening the time inventory is held. Modelling the decisions as a Stackelberg game, the welfare of the authorized channel participants is analyzed. Of import, consumer welfare may decrease if a gray market emerges when holding costs are low. In the latter two chapters, the supplier sells a congested service. For example, this supplier may be a courier facing stochastic buyer arrivals. Buyers vary in their value for the service and how patient they are, so the supplier may improve outcomes by providing a menu of delay levels and prices. The system is modelled as a priority queue where congestion constrains the arrival rates at each delay level. In the first study, the supplier has aggregate market data. I model the problem as an optimization subject to incentive and congestion constraints. The novel contributions include a precise description of the optimal menu as a function of the supplier's capacity (the rate at which buyers can be served). Findings include existence of distinct capacity regions where the supplier utilizes service pooling and strategic delay. In the final chapter the related welfare maximization problem is considered. Sufficient conditions for optimal pricing are derived which depend only on operational information: the current revenue must be equal to the best-case revenue subject to current prices and congestion constraints. An associated performance measure is shown to bound deviation from maximum welfare and is used as a heuristic within an adaptive pricing protocol. This protocol is shown to converges to near welfare maximizing outcomes.

Innovation diffusion models have been studied extensively to forecast and explain the adoption process for new products or services. These models are often formulated using one of two approaches: The first, and most common is a macro-level approach that aggregates much of the market behaviour. An advantage of this method is that forecasts and other analyses may be performed with the necessity of estimating few parameters. The second is a micro-level approach that aims to utilize microeconomic information pertaining to the potential market and the innovation. The advantage of this methodology is that analyses allow for a direct understanding of how potential customers view the innovation. Nevertheless, when individuals are making adoption decisions, the reality of the situation is that the process consists of at least two stages: First, a potential adopter must become aware of the innovation; and second the aware individual must decide to adopt. Researchers, have studied multi-stage diffusion processes in the past, however a majority of these works employ a macro-level approach to model market flows. As a result, a direct understanding of how individuals value the innovation is lacking, making it impossible to utilize this information to model realistic word-of-mouth behaviour and other network dynamics. Thus, we propose a two-stage integrated model that utilizes the benefits of both the macro- and micro-level approaches. In the first stage, potential customers become aware of the innovation, which requires no decision making by the individual. As a result, we employ a macro-level diffusion process to describe the first stage. However, in the second stage potential customers decide whether to adopt the innovation or not, and we utilize a micro-level methodology to model this. We further extend the application to include forward looking behaviour, heterogeneous adopters and segmented Bayesian learning, and utilize the adopter's satisfaction levels to describe biasing and word-of-mouth behaviour. We apply the proposed model to Canadian colour-TV data, and cross-validation results suggest that the new model has excellent predictive capabilities. We also apply the two-stage model to early U.S. hybrid-electric vehicle data and results provide insightful managerial observations.

A previous approach to robust intensity-modulated radiation therapy (IMRT) treatment planning for moving tumours in the lung involves solving a single planning problem before treatment and using the resulting solution in all of the subsequent treatment sessions. In this thesis, we develop two adaptive robust IMRT optimization approaches for lung cancer, which involve using information gathered in prior treatment sessions to guide the reoptimization of the treatment for the next session. The first method is based on updating an estimate of the uncertain effect, while the second is based on additionally updating the dose requirements to account for prior errors in dose. We present computational results using real patient data for both methods and an asymptotic analysis for the first method. Through these results, we show that both methods lead to improvements in the final dose distribution over the traditional robust approach, but differ greatly in their daily dose performance.

A previous approach to robust intensity-modulated radiation therapy (IMRT) treatment planning for moving tumours in the lung involves solving a single planning problem before treatment and using the resulting solution in all of the subsequent treatment sessions. In this thesis, we develop two adaptive robust IMRT optimization approaches for lung cancer, which involve using information gathered in prior treatment sessions to guide the reoptimization of the treatment for the next session. The first method is based on updating an estimate of the uncertain effect, while the second is based on additionally updating the dose requirements to account for prior errors in dose. We present computational results using real patient data for both methods and an asymptotic analysis for the first method. Through these results, we show that both methods lead to improvements in the final dose distribution over the traditional robust approach, but differ greatly in their daily dose performance.

Pricing and capacity allocation are two important decisions that a service provider needs to make to maximize service quality and profit. This thesis attempts to address the pricing and capacity planning problems in operations management from the following three aspects. We first study a capacity planning and short-term demand management problem faced by firms with industrial customers that are insensitive to price incentives when placing orders. Industrial customers usually have downstream commitments that make it too costly to instantaneously adjust their schedule in response to price changes. Rather, they can only react to prices set at some earlier time. We propose a hierarchical planning model where price decisions and capacity allocation decisions must be made at different points of times. Customers first sign a service contract specifying how capacity at different times will be priced. Then, when placing an order, they choose the service time that best meets their needs. We study how to price the capacity so that the customers behave in a way that is consistent with a targeted demand profile at the order period. We further study how to optimally allocate capacity. Our numerical computations show that the model improves the operational revenue substantially. Second, we explore how a profit maximizing firm is to locate a single facility on a general network, to set its capacity and to decide the price to charge for service. Stochastic demand is generated from nodes of the network. Customers demand is sensitive to both the price and the time they expect to spend on traveling and waiting. Considering the combined effect of location and price on the firm's profit while taking into account the demand elasticity, our model provides managerial insights about how the interactions of these decision variables impact the firm's profit. Third, we extend this single facility problem to a multiple facility problem. Customers have multiple choices for service. The firm maximizes its profit subject to customers' choice criteria. We propose a system optimization model where customers cooperate with the firm to choose the facility for service and a user equilibrium model where customers choose the facilities that provide the best utility to them. We investigate the properties of the optimal solutions. Heuristic algorithms are developed for the user equilibrium model. Our results show that capacity planning and location decisions are closely related to each other. When customers are highly sensitive to waiting time, separating capacity planning and location decisions could result in a highly suboptimal solution.

This thesis addresses three problems where a focal agent's operational policies (inventory and capacity allocation) interact with marketing decisions. The first chapter studies how wholesale all-unit discounts may lead to products being shifted from authorized retailers to discounted gray market channels. Such discounts lead to discontinuous ordercosts which may induce buyers to order up to a threshold where they receive a greater discount. The buyer in this chapter is a reseller who makes purchasing decisions while taking into account inventory holding costs, how their resale price affects consumer demand and whether or not they divert inventory to the gray market. I analyze factors which determine how the reseller balances between lowering resale prices and diverting to the gray market, both of which lower costs by shortening the time inventory is held. Modelling the decisions as a Stackelberg game, the welfare of the authorized channel participants is analyzed. Of import, consumer welfare may decrease if a gray market emerges when holding costs are low. In the latter two chapters, the supplier sells a congested service. For example, this supplier may be a courier facing stochastic buyer arrivals. Buyers vary in their value for the service and how patient they are, so the supplier may improve outcomes by providing a menu of delay levels and prices. The system is modelled as a priority queue where congestion constrains the arrival rates at each delay level. In the first study, the supplier has aggregate market data. I model the problem as an optimization subject to incentive and congestion constraints. The novel contributions include a precise description of the optimal menu as a function of the supplier's capacity (the rate at which buyers can be served). Findings include existence of distinct capacity regions where the supplier utilizes service pooling and strategic delay. In the final chapter the related welfare maximization problem is considered. Sufficient conditions for optimal pricing are derived which depend only on operational information: the current revenue must be equal to the best-case revenue subject to current prices and congestion constraints. An associated performance measure is shown to bound deviation from maximum welfare and is used as a heuristic within an adaptive pricing protocol. This protocol is shown to converges to near welfare maximizing outcomes.

Pricing and capacity allocation are two important decisions that a service provider needs to make to maximize service quality and profit. This thesis attempts to address the pricing and capacity planning problems in operations management from the following three aspects. We first study a capacity planning and short-term demand management problem faced by firms with industrial customers that are insensitive to price incentives when placing orders. Industrial customers usually have downstream commitments that make it too costly to instantaneously adjust their schedule in response to price changes. Rather, they can only react to prices set at some earlier time. We propose a hierarchical planning model where price decisions and capacity allocation decisions must be made at different points of times. Customers first sign a service contract specifying how capacity at different times will be priced. Then, when placing an order, they choose the service time that best meets their needs. We study how to price the capacity so that the customers behave in a way that is consistent with a targeted demand profile at the order period. We further study how to optimally allocate capacity. Our numerical computations show that the model improves the operational revenue substantially. Second, we explore how a profit maximizing firm is to locate a single facility on a general network, to set its capacity and to decide the price to charge for service. Stochastic demand is generated from nodes of the network. Customers demand is sensitive to both the price and the time they expect to spend on traveling and waiting. Considering the combined effect of location and price on the firm's profit while taking into account the demand elasticity, our model provides managerial insights about how the interactions of these decision variables impact the firm's profit. Third, we extend this single facility problem to a multiple facility problem. Customers have multiple choices for service. The firm maximizes its profit subject to customers' choice criteria. We propose a system optimization model where customers cooperate with the firm to choose the facility for service and a user equilibrium model where customers choose the facilities that provide the best utility to them. We investigate the properties of the optimal solutions. Heuristic algorithms are developed for the user equilibrium model. Our results show that capacity planning and location decisions are closely related to each other. When customers are highly sensitive to waiting time, separating capacity planning and location decisions could result in a highly suboptimal solution.

This thesis describes a new theoretical framework for characterizing legal systems and legal thought. Broadly speaking, legal systems can be characterized as undertaking three functional activities: the intake, processing and distribution of information. The thesis defines and explains what those three activities consist of, their interrelation and describes some of the emergent phenomena which arise as a result of their co-existence. Additionally, examples are provided which show elements of legal systems having behavior neatly predicted by information-first methods of analysis. The aim is to develop information-related tools to understand the function of legal systems and subsystems in society by reference to those three activities, and a robust set of fields and concepts are presented for future development.