The petrochemical Industry is based upon the production of chemicals from petroleum and also deals with chemicals manufactured from the by products of petroleum refinery. At the preliminary stages of chemical plant development and design, the choice of chemical process route is the key design decision. In the past, economics were the most important criterion in choosing the chemical process route. Modified studies imply that the two of the important planning objectives for a petrochemical industry, environmental risk and the industrial safety involved in the development. For the economic evaluation of the industry, and for the proposed final chemicals products in the development, simple and clear economic indicators are needed to be able to indicate an overall economic gain in the development. Safety, as the second objective, is considered in this study as the risk of chemical plant accidents. Risk, when used as an objective function, has to have a simple quantitative form to be easily evaluated for a large number of possible plants in the petrochemical network. The simple quantitative form adopted is a safety index that enables the number of people affected by accidents resulting in chemical releases to be estimated. Environmental issues have now become important considerations due to the potential harmful impacts produced by chemical releases. In this study third objective of planning petrochemical industry was developed by involving environmental considerations and environmental risk index. Indiana Relative Chemical Hazard Score (IRCHS) was used to allow chemical industries routes to be ranked by environmental hazardous. The focus of this work is to perform early planning and decision-making for a petrochemical plants network for maximum economical gain, minimum risk to people from possible chemical accidents and minimum environmental risk. The three objectives, when combined with constraints describing the desired or the possible structure of the industry, will form an optimization model. For this study, the petrochemical planning model consists of a Mixed Integer Linear Programming (MILP) model to select the best routes from the basic feedstocks available in Kuwait -as a case study- to the desired final products with multiple objective functions. The economic, safety and environmental risk objectives usually have conflicting needs. The presence of several conflicting objectives is typical when planning. In many cases, where optimization techniques are utilized, the multiple objectives are simply aggregated into one single objective function. Optimization is then conducted to get one optimal result. This study, which is concerned with economic and risk objectives, leads to the identification of important factors that affecting the building-up of environmental management system for petrochemical industry. Moreover, the procedure of modelling and model solution can be used to simplify the decision-making for complex or large systems such as the petrochemical industry. It presents the use of simple multiple objective optimization tools within a petrochemical planning tool formulated as a mixed integer linear programming model. Such a tool is particularly useful when the decision-making task must be discussed and approved by officials who often have little experience with optimization theories

Supply chain network design (SCND) identifies the production and distribution resources essential to maximizing a network’s profit. Once implemented, a SCND impacts a network’s performance for the long-term. This dissertation extends the SCND literature both in terms of model scope and solution approach. The SCND problem can be more realistically modeled to improve design decisions by including: the location, capacity, and technology attributes of a resource; the effect of the economies of scale on the cost structure; multiple products and multiple levels of supply chain hierarchy; stochastic, dynamic, and correlated demand; and the gradually unfolding uncertainty. The resulting multistage stochastic mixed-integer program (MSMIP) has no known general purpose solution methodology. Two decomposition approaches—end-of-horizon (EoH) decomposition and nodal decomposition—are applied. The developed EoH decomposition exploits the traditional treatment of the end-of-horizon effect. It rests on independently optimizing the SCND of every node of the last level of the scenario-tree. Imposing these optimal configurations before optimizing the design decisions of the remaining nodes produces a smaller and thus easier to solve MSMIP. An optimal solution results when the discount rate is 0 percent. Otherwise, this decomposition deduces a bound on the optimality-gap. This decomposition is neither SCND nor MSMIP specific; it pertains to any application sensitive to the EoH-effect and to special cases of MSMIP. To demonstrate this versatility, additional computational experiments for a two-stage mixed-integer stochastic program (SMIP) are included. This dissertation also presents the first application of nodal decomposition in both SCND and MSMIP. The developed column generation heuristic optimizes the nodal sub-problems using an iterative procedure that provides a restricted master problem’s columns. The heuristic’s computational efficiency rests on solving the sub-problems independently and on its novel handling of the master problem. Conceptually, it reformulates the master problem to avoid the duality-gap. Technologically, it provides the first application of Leontief substitution flow problems in MSMIP and thereby shows that hypergraphs lend themselves to loosely coupled MSMIPs. Computational results demonstrate superior performance of the heuristic approach and also show how this heuristic still applies when the SCND problem is modeled as a SMIP where the restricted master problem is a shortest-path problem.

In this thesis we study how to solve some nonconvex optimization problems by using methods that capitalize on the success of Linear Programming (LP) based solvers for Mixed Integer Linear Programming (MILP). A common aspect of our solution approaches is the use, development and analysis of small but strong extended LP/MILP formulations and approximations. In the first part of this work we develop an LP based branch-and-bound algorithm for mixed integer conic quadratic programs. The algorithm is based on a lifted polyhedral relaxation of conic quadratic constraints by Ben-Tal and Nemirovski. We test the algorithm on a series of portfolio optimization problems and show that it provides a significant computational advantage. In the second part we study the modeling of a class of disjunctive constraints with a logarithmic number of variables. For specially structured disjunctive constraints we give sufficient conditions for constructing MILP formulations with a number of binary variables and extra constraints that is logarithmic in the number of terms of the disjunction. Using these conditions we introduce formulations with these characteristics for SOS1, SOS2 constraints and piecewise linear functions. We present computational results showing that they can significantly outperform other MILP formulations. In the third part we study the modeling of non-convex piecewise linear functions as MILPs. We review several new and existing MILP formulations for continuous piecewise linear functions with special attention paid to multivariate non-separable functions. We compare these formulations with respect to their theoretical properties and their relative computational performance. In addition, we study the extension of these formulations to lower semicontinuous piecewise linear functions. Finally, in the fourth part we study the strength of MILP formulations for LPs with Probabilistic Constraints. We first study the strength of existing MILP formulations that only considers one row of the probabilistic constraint at a time. We then introduce an extended formulation that considers more than one row of the constraint at a time and use it to computationally compare the relative strength between formulations that consider one and two rows at a time.

Master of Agribusiness / Department of Agricultural Economics / Jason S. Bergtold / Technical support for products after the sale is commonplace in today’s businesses. Original Equipment Manufacturers (OEMs) provide technical support to their dealer channel for resolution of complex product issues. Technical support staffing levels can vary by product type, product complexity, and production volumes, and case volumes. This research seeks a better understanding of appropriate staffing levels between three product lines for one OEM. The objective of this paper is to develop a model for monthly and weekly average case volumes for the three product lines, based off of historical case volume data. This data is used to predict a product line’s (platform’s) workload based off the month of the year. The output of each platform’s monthly case volume is then used in an optimization model to determine optimal staffing levels for each platform, based off the time of the year. The models developed for each platform use a linear relationship which regresses workload on a set of binary variable for the months of the year. Each of the models developed provided statistically significant coefficients for months which contain the platform’s highest workload. The outputs from these models are used in a mixed integer nonlinear programming optimization model to determine staff level of full time equivalent (FTE) employees at each platform. Each of the three scenarios utilized in this research provide similar trends and staffing levels for each of the three product lines. Results of this research are of interest for the management of technical support staffing.

This thesis compares different mixed integer programming (MIP) formulations for sequencing of tasks in the context of avionics scheduling. Sequencing is a key concern in many discrete optimisation problems, and there are numerous ways of accomplishing sequencing with different MIP formulations. A scheduling tool for avionic systems has previously been developed in a collaboration between Saab and Linköping University. This tool includes a MIP formulation of the scheduling problem where one of the model components has the purpose to sequence tasks. In this thesis, this sequencing component is replaced with other MIP formulations in order to study whether the computational performance of the scheduling tool can be improved. Different scheduling instances and objective functions have been used when performing the tests aiming to evaluate the performances, with the computational times of the entire avionic scheduling model determining the success of the different MIP formulations for sequencing. The results show that the choice of MIP formulation makes a considerable impact on the computational performance and that a significant improvement can be achieved by choosing the most suitable one.

Background: In treatment planning for intensity-modulated proton therapy (IMPT), we aim to deliver the prescribed dose to the target yet minimize the dose to adjacent healthy tissue. Mixed-integer programming (MIP) has been applied in radiation therapy to generate treatment plans. However, MIP has not been used effectively for IMPT treatment planning with dose-volume constraints. In this study, we incorporated dose-volume constraints in an MIP model to generate treatment plans for IMPT. Methods: We created a new MIP model for IMPT with dose volume constraints. Two groups of IMPT treatment plans were generated for each of three patients by using MIP models for a total of six plans: one plan was derived with the Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method while the other plan was derived with our MIP model with dose-volume constraints. We then compared these two plans by dose-volume histogram (DVH) indices to evaluate the performance of the new MIP model with dose-volume constraints. In addition, we developed a model to more efficiently find the best balance between tumor coverage and normal tissue protection. Results: The MIP model with dose-volume constraints generates IMPT treatment plans with comparable target dose coverage, target dose homogeneity, and the maximum dose to organs at risk (OARs) compared to treatment plans from the conventional quadratic programming method without any tedious trial-and-error process. Some notable reduction in the mean doses of OARs is observed. Conclusions: The treatment plans from our MIP model with dose-volume constraints can meetall dose-volume constraints for OARs and targets without any tedious trial-and-error process. This model has the potential to automatically generate IMPT plans with consistent plan quality among different treatment planners and across institutions and better protection for important parallel OARs in an effective way.

This thesis proposes and verifies a number of optimization models for re-designing a master surgery schedule with minimized peak inpatient load at the ward. All models include limitations on Operating Rooms and surgeons availability. Surgeons` preference is included with regards to a consistent weekly schedule over a cycle. The uncertain in patients` length of stay was incorporated using discrete probability distributions unique to each surgeon. Furthermore, robust optimization was utilized to protect against the uncertainty in the number of inpatients a surgeon may send to the ward per block. Different scenarios were developed that explore the impact of varying the availability of operating rooms on each day of the week. The models were solved using Cplex and were verified by an Arena simulation model.

The management of large-scale transportation infrastructure is becoming a very complex task for the urban areas of this century which are covering bigger geographic spaces and facing the inclusion of connected and self-controlled vehicles. This new system paradigm can leverage many forms of sensing and interaction, including a high-scale mobile sensing approach. To obtain a high penetration sensing system on urban areas more practical and scalable platforms are needed, combined with estimation algorithms suitable to the computational capabilities of these platforms. The purpose of this work was to develop a transportation framework that is able to handle different kinds of sensing data (e.g., connected vehicles, loop detectors) and optimize the traffic state on a defined traffic network. The framework estimates the traffic on road networks modeled by a family of Lighthill-Whitham-Richards equations. Based on an equivalent formulation of the problem using a Hamilton-Jacobi equation and using a semi-analytic formula, I will show that the model constraints resulting from the Hamilton-Jacobi equation are linear, albeit with unknown integer variables. This general framework solve exactly a variety of problems arising in transportation networks: traffic estimation, traffic control (including robust control), cybersecurity and sensor fault detection, or privacy analysis of users in probe-based traffic monitoring systems. This framework is very flexible, fast, and yields exact results. The recent advances in sensors (GPS, inertial measurement units) and microprocessors enable the development low-cost dedicated devices for traffic sensing in cities, 5 which are highly scalable, providing a feasible solution to cover large urban areas. However, one of the main problems to address is the privacy of the users of the transportation system, the framework presented here is a viable option to guarantee the privacy of the users by design.

The purpose of this thesis is to provide a new scheduling model of a large constellation of imaging satellites that does not use a heuristic solving method. The objective is to create a mixed-integer linear model that would be competitive in speed and in its closeness to reality against a current model using simulated annealing, while trying to improve both models. Each satellite has the choice between a number of possible events, each event having a utility and a cost, and the chosen schedule must take into account numerous time-related constraints. The main difficulties appeared in modeling realistically a battery level and in handling infeasible configurations due to inaccurate parameters. The obtained linear model has enabled a better understanding of the performance of the simulated annealing solver, and could also be adapted to different real-world scheduling problems.

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