For central banks, managing the minting is one of the most important task since a shortage yields negative economic and social impacts, and the budget committed for minting is one of the largest within the central banks. Hence, the central bank requires to find the mixture of coins to be produced that satisfies the demand, inventory and production constraints while minimizing the cost. We propose a mixed-integer programming model that minimize the cost of minting by reducing the number of extra-shifts required while fulfilling the constraints. We also perform a simulation with data of a central bank which shows that the model reduces in 24\% the cost of extra-shifts used during 21 quarters, compared with the spreadsheet based approach used currently at the operation.
In Finland colorectal cancer (CRC) incidence rates have steadily increased over the last decades and as of 2017, CRC is the sixth most common cause of death. CRC is a crucial concern for the public health of Finland. We optimize the faecal immunochemical test (FIT) cut-off level for specified target populations with regard to minimization of cancer prevalence with Decision Programming, which is a novel approach to solving discrete multi-stage decision problems under uncertainty. The results present optimal cut-off levels for Finnish target groups with different colonoscopy capacity constraints…
The traditional demand-responsive paratransit system plays an important role in connecting people to health care, particularly those who are carless, low-income, senior, underinsured/uninsured, or who have a disability. However, the existing paratransit system usually has low service quality due to long waiting times, low operation frequencies, and high costs. In order to improve the service quality, we propose to design a new demand-responsive paratransit system that offers public, Uber-like options for non-emergency medical transportation. Mixed integer programming models are thus developed …
Designing efficient algorithms to compute Nash equilibria poses considerable challenges in Algorithmic Game Theory and Optimization. In this work, we employ integer programming techniques to compute Nash equilibria in Integer Programming Games, a class of simultaneous and non-cooperative games where each player solves a parametrized integer program. We introduce ZERO Regrets, a general and efficient cutting plane algorithm to compute, enumerate, and select Nash equilibria. Our framework leverages the concept of equilibrium inequality, an inequality valid for any Nash equilibrium, and the assoc…
Indirect trajectory optimization methods such as Differential Dynamic Programming (DDP) have found considerable success when only planning under dynamic feasibility constraints. Meanwhile, nonlinear programming (NLP) has been the state-of-the-art approach when faced with additional constraints (e.g., control bounds, obstacle avoidance). However, a na$ï$ve implementation of NLP algorithms, e.g., shooting-based sequential quadratic programming (SQP), may suffer from slow convergence -- caused from natural instabilities of the underlying system manifesting as poor numerical stability within the o…
We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges). Under this setting, reliability is defined as the probability of finding a path between sources and sink nodes under random component failures and we show that this measure can be computed by solving a stochastic mixed-integer program. The stochastic programming setting allows us to account for system constraints and general probability distributions to charac…
The Electric Multiple Unit (EMU) circulation plan is the foundation of EMU assignment and maintenance planning,and its primary task is to determine the connections of trains in terms of train timetable and maintenance constraints. We study the problem of optimizing EMU circulation plan, and a 0-1 integer programming model is presented on the basis of train connection network design. The model aims at minimizing the total connection time of trains and maximizing the travel mileage of each EMU circulation, and it meets the maintenance constraints from two aspects of mileage and time cycle. To so…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is located at the intersection of the constraints defining the extreme vertex. By identifying the constraints that limit the growth of the objective function value, we formulate linear equations system leading to the optimization problem's solution.The most complex operation of the algorithm is the inversion of a matrix sized by the number of dimensions of the pro…
This study focuses on Multi-Channel Transcranial Electrical Stimulation, a non-invasive brain method for stimulating neuronal activity under the influence of low-intensity currents. We introduce mathematical formulation for finding a current pattern which optimizes a L1-norm fit between a given focal target distribution and volume current density inside the brain. L1-norm is well-known to favor well-localized or sparse distributions compared to L2-norm (least-squares) fitted estimates. We present a linear programming approach which performs L1-norm fitting and penalization of the current patte…
Lean manufacturing is a production method focused on reducing production times, eliminating waste, and synchronizing production with fluctuating demand. A standard lean manufacturing methodology is the product wheel, a repeating sequence of production of various items. If this product wheel sequence is short, it is easier to interrupt or alter production to adjust for failures or fluctuations in demand, so the manufacturing process is leaner. However, a sequence that is too short results in frequent changeover from the production of one item to the next, yielding higher costs. This study formu…
The most common approaches for solving stochastic resource allocation problems in the research literature is to either use value functions ("dynamic programming") or scenario trees ("stochastic programming") to approximate the impact of a decision now on the future. By contrast, common industry practice is to use a deterministic approximation of the future which is easier to understand and solve, but which is criticized for ignoring uncertainty. We show that a parameterized version of a deterministic lookahead can be an effective way of handling uncertainty, while enjoying the computational si…
The problem of optimizing over the cone of nonnegative polynomials is a fundamental problem in computational mathematics, with applications to polynomial optimization, control, machine learning, game theory, and combinatorics, among others. A number of breakthrough papers in the early 2000s showed that this problem, long thought to be out of reach, could be tackled by using sum of squares programming. This technique however has proved to be expensive for large-scale problems, as it involves solving large semidefinite programs (SDPs). In the first part of this thesis, we present two methods for…
The well-known Influence Maximization (IM) problem has been actively studied by researchers over the past decade, with emphasis on marketing and social networks. Existing research have obtained solutions to the IM problem by obtaining the influence spread and utilizing the property of submodularity. This paper is based on a novel approach to the IM problem geared towards optimizing clicks and consequently revenue within anOnline Social Network (OSN). Our approach diverts from existing approaches by adopting a novel, decision-making perspective through implementing Stochastic Dynamic Programmin…
We consider the problem of mapping a logical quantum circuit onto a given hardware with limited two-qubit connectivity. We model this problem as an integer linear program, using a network flow formulation with binary variables that includes the initial allocation of qubits and their routing. We consider several cost functions: an approximation of the fidelity of the circuit, its total depth, and a measure of cross-talk, all of which can be incorporated in the model. Numerical experiments on synthetic data and different hardware topologies indicate that the error rate and depth can be optimized…
