Improving the Production Process for a Medical Device Manufacturing Company using Monte Carlo Simulation

This work studies a medical product development, assembly, and packaging company that uses a paper-based method to track jobs through their assembly process.  The paperwork often has errors, which must be corrected before distribution, causing delays in manufacturing and shipment and resulting in lost time and money.  The project team analyzed the company's production process to identify areas for improvement.  Through statistical analyses of the company’s process data, the team established error categorization, location, and probability of occurrence.  In order to address sources of error, the project team diagrammed the company's manufacturing floor and created a list of issues within each step of the manufacturing process as well as potential solutions to these problems. The team created a simulation of the manufacturing process and used this tool to analyze potential process changes to decrease the number of employee hours wasted in order to fix discrepancies.  The simulation proved to be an invaluable tool that helped the company better understand their process.  It helped to identify which jobs create the most errors, how many errors occur per month, and how much money the company loses on time spent correcting the errors. Eleven potential solutions were considered, but two of them appeared to yield the best results.  Implementing a total quality management (TQM) system would conservatively reduce error counts by 71.3%.  Implementing a start quantity to the company's electronic system would conservatively reduce mean hours wasted from 22.60 to 21.73 hours per month and mean salary lost from $519.82 to$499.80 per month.  Using insights from the simulation, the project team then coordinated with management to decide whether error rates or time and salary spent to correct errors were more important to address. As of this writing, as a result of this study, the company is taking steps to implement a TQM system in order to decrease errors in their job tracking process

An Optimization Approach to Balancing Risk and Cost in Combatant Command Capability Advocacy

Unified Combatant Commands (UCCs) have broad continuing missions around the globe where they are tasked to provide functional expertise and defense of geographical areas.  Accomplishing these missions requires a robust portfolio of military capabilities (e.g., aircraft, spacecraft, command and control systems, radar systems).  UCCs routinely perform analyses to identify gaps between capabilities required to accomplish their mission and those currently at their disposal.  Each year they submit a prioritized list of required capabilities, including new systems and greater capacity with existing systems, to the Joint Staff in the costly and time-consuming Integrated Priority List (IPL) process.  This process relies on operational art and subject matter expertise, and sometimes fails to identify acquisition opportunities that achieve an optimal balance between risk and cost.  Because this IPL process affects all of the DOD’s personnel, material, systems and missions, it is arguably the most significant analytic challenge faced by the United States military.  This article presents an integer linear programming model that computes an optimal balance between operational risk and the cost of acquiring new capabilities, and allows decision makers to identify the real-world impact of their budgetary decisions.  We apply this model to the mission of providing aerospace defense of the United States and illustrate through sensitivity analysis the meaningful insights that can be gained by studying the relationship between the risk of not achieving 100 percent radar coverage and the opportunity cost of advocating for new capabilities

Optimal Search and Interdiction Planning

International law enforcement organizations around the world endeavor to combat high drug related mortality rates by seizing illicit drugs in transit over international waters. This mission requires e ective plans that route multiple aerial searchers and position surface interdictors through large expanses of geographical areas in the presence of highly uncertain estimates about drug smuggler whereabouts. This high uncertainty combined with the challenge of coordinating search and interdiction make it particularly di cult to conduct mission planning. We present optimal search and interdiction models that address these important challenges and demonstrate how planners can used these models by applying them to a realistic counterdrug operation scenario.Office of Naval Research, Mathematical Optimization and Operations Research ProgramOffice of Naval Research, Mathematical Optimization and Operations Research Progra

Generalized Orienteering Problem with Resource Dependent Rewards

Naval Research Logistics, Vol. 60, No. 4, pp. 294ﾖ312.We introduce a generalized Orienteering Problem where, as usual, a vehicle is routed from a prescribed start node, through a directed network, to a prescribed destination node, collecting rewards at each node visited, in order to maximize the total reward along the path. In our generalization, transit on arcs in the network and reward collection at nodes both consume a variable amount of the same limited resource. We exploit this resource trade-off through a specialized branch-and-bound algorithm that relies upon partial path relaxation problems which often yield tight bounds and lead to substantial pruning in the enumeration tree. We present the Smuggler Search Problem as an important real-world application of our generalized Orienteering Problem. Numerical results show that our algorithm applied to the Smuggler Search Problem outperforms standard Mixed-Integer Nonlinear Programming solvers for moderate to large problem instances. We demonstrate model enhancements that allow practitioners to represent realistic search planning scenarios by accounting for multiple heterogeneous searchers and complex smuggler motion

A generalized orienteering problem for optimal search and interdiction planning

In order to support search planning for counterdrug operations, we introduce a generalized Orienteering Problem (OP) where transit on arcs in a network and reward collection at nodes both consume a variable amount of the same limited resource. We exploit this resource trade-o_ through a specialized branch-and-bound algorithm that relies on partial path relaxation problems, which often yield tight bounds and lead to substantial pruning in the enumeration tree. We present the Smuggler Search Problem (SSP) as a real-world application of our generalized OP. Numerical results show that our algorithm applied to the SSP outperforms standard mixed-integer nonlinear programming solvers for problems with seven or more targets. We present model enhancements that allow practitioners to represent realistic search planning scenarios. We investigate how evolving uncertainty in planning data can be addressed by a multi-stage stochastic programming model.http://archive.org/details/ageneralizedorie1094537694Major, United States Air ForceApproved for public release; distribution is unlimited

Pseudospectral collocation methods for the direct transcription of optimal control problems

This thesis is concerned with the study of pseudospectral discretizations of optimal control problems governed by ordinary differential equations and with their application to the solution of the International Space Station (ISS) momentum dumping problem. Pseudospectral methods are used to transcribe a given optimal control problem into a nonlinear programming problem. Adjoint estimates are presented and analyzed that provide approximations of the original adjoint variables using Lagrange multi pliers corresponding to the discretized optimal control problem. These adjoint estimations are derived for a broad class of pseudospectral discretizations and generalize the previously known adjoint estimation procedure for the Legendre pseudospectral discretization. The error between the desired solution to the infinite dimensional optimal control problem and the solution computed using pseudospectral collocation and nonlinear programming is estimated for linear-quadratic optimal control problems. Numerical results are given for both linear-quadratic and nonlinear optimal control problems. The Legendre pseudospectral method is applied to formulations of the ISS momentum dumping problem. Computed solutions are verified through simulations using adaptive higher order integration of the system dynamics