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Vendor Managed Inventory (VMI), Consignment Inventory (CI) and a combination of both (C&VMI) are supply-chain sourcing agreements between a vendor and customer. VMI allows the vendor to initiate orders on behalf of the customer. In CI, the customer pays for the goods supplied by the vendor only upon use. The vendor under C&VMI decides customer-replenishments, and owns the goods replenished until they are deployed by the customer. Our thesis studies these agreements in three essays. <br /><br /> The first essay considers a vendor <em>V</em> that manufactures a particular product at a unique location. That item is sold to a single retailer, the customer <em>C</em>. Three cases are treated in detail: Independent decision making (no agreement between the parties); VMI, whereby the supplier <em>V</em> initiates orders on behalf of <em>C</em>; and Central decision making (both Vendor and Customer are controlled by the same corporate entity). <br /><br /> Values of some cost parameters may vary between the three cases, and each case may cause a different actor to be responsible for particular expenses. Under a constant demand rate, optimal solutions are obtained analytically for the customer's order quantity, the vendor's production quantity, hence the parties' individual and total costs in the three cases. Inequalities are obtained to delineate those situations in which VMI is beneficial. <br /><br /> The problem setting in the second essay is the same with that of Essay 1, but the sourcing agreements investigated are now CI and C&VMI. In CI, as in the usual independent-sourcing approach, the customer has authority over the timing and quantity of replenishments. CI seems to favour the customer because, in addition, he pays for the goods only upon use. Under a C&VMI agreement, the vendor still owns the goods at the customer's premises, but at least can determine how much to store there. <br /><br /> The second essay thus contrasts the cases CI and C&VMI, and compares each of them to a no-agreement case. General conditions under which those cases create benefits for the vendor, the customer and the whole chain are determined. <br /><br /> Essay 3 investigates VMI and C&VMI separately for a vendor and multiple customers who face time-varying, but deterministic demand for a single product. In any of those agreements, the vendor seeks the best set of customers to achieve economies of scale. MIP models are developed to find that set of customers, and to determine the vendor's optimal production, transportation, and customer-replenishment quantities. The model for VMI is solved using a heuristic that produces two sub-models, and uses hierarchical solution approach for production, customer-replenishment and transportation decisions. C&VMI model is solved using Lagrangian relaxation. Various numerical examples are used to test the solution approaches used. <br /><br /> In the mean time, the customers can guarantee to be no worse off under VMI or C&VMI than the no-agreement case by setting the right levels of maximum inventory. A model to determine those levels and a solution algorithm are also proposed in Essay 3. <br /><br /> The first two essays can help a vendor or customer in a supply chain to determine the least costly sourcing option, which depends on the relative values of various cost parameters. A vendor with multiple customers can make use of the results in the third essay, which reveal the best possible economies of scale under VMI or C&VMI. Those customers can guarantee to be no worse of than traditional sourcing when they set the proposed levels of maximum inventory.

A VLSI chip can today contain hundreds of millions transistors and is expected to contain more than 1 billion transistors in the next decade. In order to handle this rapid growth in integration technology, the design procedure is therefore divided into a sequence of design steps. Circuit layout is the design step in which a physical realization of a circuit is obtained from its functional description. Global routing is one of the key subproblems of the circuit layout which involves finding an approximate path for the wires connecting the elements of the circuit without violating resource constraints. The global routing problem is NP-hard, therefore, heuristics capable of producing high quality routes with little computational effort are required as we move into the Deep Sub-Micron (DSM) regime. In this thesis, different approaches for global routing problem are first reviewed. The advantages and disadvantages of these approaches are also summarized. According to this literature review, several mathematical programming based global routing models are fully investigated. Quality of solution obtained by these models are then compared with traditional Maze routing technique. The experimental results show that the proposed model can optimize several global routing objectives simultaneously and effectively. Also, it is easy to incorporate new objectives into the proposed global routing model. To speedup the computation time of the proposed ILP based global router, several hierarchical methods are combined with the flat ILP based global routing approach. The experimental results indicate that the bottom-up global routing method can reduce the computation time effectively with a slight increase of maximum routing density. In addition to wire area, routability, and vias, performance and low power are also important goals in global routing, especially in deep submicron designs. Previous efforts that focused on power optimization for global routing are hindered by excessively long run times or the routing of a subset of the nets. Accordingly, a power efficient multi-pin global routing technique (PIRT) is proposed in this thesis. This integer linear programming based techniques strives to find a power efficient global routing solution. The results indicate that an average power savings as high as 32\% for the 130-nm technology can be achieved with no impact on the maximum chip frequency.

This thesis presents a multi-stage linear stochastic mixed integer programming (SMIP) model for planning power generation in a pool-type day-ahead electricity market. The model integrates a reserve demand curve and shares most of the features of a stochastic unit commitment (UC) problem, which is known to be NP-hard. We capture the stochastic nature of the problem through scenarios, resulting in a large-scale mixed integer programming (MIP) problem that is computationally challenging to solve. Given that an independent system operator (ISO) has to solve such a problem within a time requirement of an hour or so, in order to release operating schedules for the next day real-time market, the problem has to be solved efficiently. For that purpose, we use some approximations to maintain the linearity of the model, parsimoniously select a subset of scenarios, and invoke realistic assumptions to keep the size of the problem reasonable. Even with these measures, realistic-size SMIP models with binary variables in each stage are still hard to solve with exact methods. We, therefore, propose a scenario-rolling heuristic to solve the SMIP problem. In each iteration, the heuristic solves a subset of the scenarios, and uses part of the obtained solution to solve another group in the subsequent iterations until all scenarios are solved. Two numerical examples are provided to test the performance of the scenario-rolling heuristic, and to highlight the difference between the operative schedules of a deterministic model and the SMIP model. Motivated by previous studies on pricing MIP problems and their applications to pricing electric power, we investigate pricing issues and compensation schemes using MIP formulations in the second part of the thesis. We show that some ideas from the literature can be applied to pricing energy/reserves for a relatively realistic model with binary variables, but some are found to be impractical in the real world. We propose two compensation schemes based on the SMIP that can be easily implemented in practice. We show that the compensation schemes with make-whole payments ensure that generators can have non-negative profits. We also prove that under some assumptions, one of the compensation schemes has the interesting theoretical property of minimizing the variance of the profit of generators to zero. Theoretical and numerical results of these compensation schemes are presented and discussed.

The focus of this thesis is to explore a new mechanism to give added incentive to invest in new capacities in deregulated electricity markets. There is a lot of concern in energy markets, regarding lack of sufficient private sector investment in new capacities to generate electricity. Although some markets are using mechanisms to reward these investments directly, e.g., by governmental subsidies for renewable sources such as wind or solar, there is not much theory to guide the process of setting the reward levels. The proposed mechanism involves a long term planning model, maximizing the social welfare measured as consumers’ plus producers’ surplus, by choosing new generation capacities which, along with still existing capacities, can meet demand. Much previous research in electricity capacity planning has also solved optimization models, usually with continuous variables only, in linear or non-linear programs. However, these approaches can be misleading when capacity additions must either be zero or a large size, e.g., the building of a nuclear reactor or a large wind farm. Therefore, this research includes binary variables for the building of large new facilities in the optimization problem, i.e. the model becomes a mixed integer linear or nonlinear program. It is well known that, when binary variables are included in such a model, the resulting commodity prices may give insufficient incentive for private investment in the optimal new capacities. The new mechanism is intended to overcome this difficulty with a capacity price in addition to the commodity price: an auxiliary mathematical program calculates the minimum capacity price that is necessary to ensure that all firms investing in new capacities are satisfied with their profit levels. In order to test the applicability of this approach, the result of the suggested model is compared with the Ontario Integrated Power System Plan (IPSP), which recommends new generation capacities, based on historical data and costs of different sources of electricity generation for the next 20 years given a fixed forecast of demand.

A workforce plan states the number of workers required at any point in time. Efficient workforce plans can help companies achieve their organizational goals while keeping costs low. In ever increasing globalized work market, companies need a competitive edge over their competitors. A competitive edge can be achieved by lowering costs. Labour costs can be one of the significant costs faced by the companies. Efficient workforce plans can provide companies with a competitive edge by finding low cost options to meet customer demand. This thesis studies the problem of determining the required number of workers when there are two categories of workers. Workers belonging to the first category are trained to work on one type of task (called Specialized Workers); whereas, workers in the second category are trained to work in all the tasks (called Flexible Workers). This thesis makes the following three main contributions. First, it addresses this problem when the demand is deterministic and stochastic. Two different models for deterministic demand cases have been proposed. To study the effects of uncertain demand, techniques of Robust Optimization and Robust Mathemat- ical Programming were used. The thesis also investigates methods to solve large instances of this problem; some of the instances we considered have more than 600,000 variables and constraints. As most of the variables are integer, and objective function is nonlinear, a commercial solver was not able to solve the problem in one day. Initially, we tried to solve the problem by using Lagrangian relaxation and Outer approximation techniques but these approaches were not successful. Although effective in solving small problems, these tools were not able to generate a bound within run time limit for the large data set. A number of heuristics were proposed using projection techniques. Finally this thesis develops a genetic algorithm to solve large instances of this prob- lem. For the tested population, the genetic algorithm delivered results within 2-3% of optimal solution.

A t-design is a combinatorial structure consisting of a collection of blocks over a set of points satisfying certain properties. The existence of t-designs given a set of parameters can be reduced to finding nonnegative integer solutions to a given integer matrix equation. The matrix in this equation can be quite large, but by prescribing the automorphism group of the design, the matrix in the equation can be made more manageable so as to allow the equation to be solved via integer programming tools; this fact was developed by Kramer and Mesner. Algorithms to generate the matrix equation generally follow a simple template. In this thesis, a generic framework for generating the Kramer-Mesner matrix equation and solving it via integer programming is presented.

In this thesis we address three related topic in the field of Operations Research. Firstly we discuss the problems and limitation of most common solvers for linear programming, precision. We then present a solver that generate rational optimal solutions to linear programming problems by solving a succession of (increasingly more precise) floating point approximations of the original rational problem until the rational optimality conditions are achieved. This method is shown to be (on average) only 20% slower than the common pure floating point approach, while returning true optimal solutions to the problems. Secondly we present an extension of the Local Cut procedure introduced by Applegate et al, 2001, for the Symmetric Traveling Salesman Problem (STSP), to the general setting of MIP problems. This extension also proves finiteness of the separation, facet and tilting procedures in the general MIP setting, and also provides conditions under which the separation procedure is guaranteed to generate cuts that separate the current fractional solution from the convex hull of the mixed-integer polyhedron. We then move on to explore some configurations for local cuts, realizing extensive testing on the instances from MIPLIB. Those results show that this technique may be useful in general MIP problems, while the experience of Applegate et al, shows that the ideas can be successfully applied to structures problems as well. Thirdly we present an extensive computational experiment on the TSP and Domino Parity inequalities as introduced by Letchford, 2000. This work also include a safe-shrinking theorem for domino parity inequalities, heuristics to apply the planar separation algorithm introduced by Letchford to instances where the planarity requirement does not hold, and several practical speed-ups. Our computational experience showed that this class of inequalities effectively improve the lower bounds from the best relaxations obtained with Concorde, which is one of the state of the art solvers for the STSP. As part of these experience, we solved to optimality the (up to now) largest two STSP instances, both of them belong to the TSPLIB set of instances and they have 18,520 and 33,810 cities respectively.

This thesis sets out to analyze how restricting rest (sleep) locations for long-haul truckers may impact operational productivity, given hours-of-service regulations. Productivity in this thesis is measured by the minimum number of unique drivers required to feasibly execute a set of load requests over a known planning horizon. When drivers may stop for rest at any location, they may maximize utilization under regulated driving hours. When drivers may only rest at certain discrete locations, their productivity may be diminished since they may no longer be able to fully utilize available service hours. These productivity losses may require trucking firms to operate larger driver fleets. This thesis addresses two specific challenges presented by this scenario; first, understanding how a given discrete set of rest locations may affect driver fleet size requirements; and second, how to determine optimal discrete locations for a fixed number of rest facilities and the potential negative impact on fleet size of non-optimally located facilities. The minimum fleet size problem for a single origin-destination leg with fixed possible rest locations is formulated as a minimum cost network flow with additional bundling constraints. A mixed integer program is developed for solving the single-leg rest facility location problem. Tractable adaptations of the basic models to handle problems with multiple lanes are also presented. This thesis demonstrates that for typical long-haul lane lengths the effects of restricting rest to a relatively few fixed rest locations has minimal impact on fleet size. For an 18-hour lane with two rest facilities, no increase in fleet size was observed for any test load set instances with exponentially distributed interdeparture times. For test sets with uniformly distributed interdeparture times, additional required fleet sizes ranged from 0 to 11 percent. The developed framework and results should be useful in the analysis of truck transportation of security-sensitive commodities, such as food products and hazardous materials, where there may exist strong external pressure to ensure that drivers rest only in secure locations to reduce risks of tampering.

This dissertation considers graph theoretic generalizations of the maximum clique problem. Models that were originally proposed in social network analysis literature, are investigated from a mathematical programming perspective for the first time. A social network is usually represented by a graph, and cliques were the first models of "tightly knit groups" in social networks, referred to as cohesive subgroups. Cliques are idealized models and their overly restrictive nature motivated the development of clique relaxations that relax different aspects of a clique. Identifying large cohesive subgroups in social networks has traditionally been used in criminal network analysis to study organized crimes such as terrorism, narcotics and money laundering. More recent applications are in clustering and data mining wireless networks, biological networks as well as graph models of databases and the internet. This research has the potential to impact homeland security, bioinformatics, internet research and telecommunication industry among others. The focus of this dissertation is a degree-based relaxation called k-plex. A distance-based relaxation called k-clique and a diameter-based relaxation called k-club are also investigated in this dissertation. We present the first systematic study of the complexity aspects of these problems and application of mathematical programming techniques in solving them. Graph theoretic properties of the models are identified and used in the development of theory and algorithms. Optimization problems associated with the three models are formulated as binary integer programs and the properties of the associated polytopes are investigated. Facets and valid inequalities are identified based on combinatorial arguments. A branch-and-cut framework is designed and implemented to solve the optimization problems exactly. Specialized preprocessing techniques are developed that, in conjunction with the branch-and-cut algorithm, optimally solve the problems on real-life power law graphs, which is a general class of graphs that include social and biological networks. Computational experiments are performed to study the effectiveness of the proposed solution procedures on benchmark instances and real-life instances. The relationship of these models to the classical maximum clique problem is studied, leading to several interesting observations including a new compact integer programming formulation. We also prove new continuous non-linear formulations for the classical maximum independent set problem which maximize continuous functions over the unit hypercube, and characterize its local and global maxima. Finally, clustering and network design extensions of the clique relaxation models are explored.