A stochastic programming approach to resource-constrained assignment problems

We address the resource-constrained generalizations of the assignment problem with uncertain resource capacities, where the resource capacities have an unknown distribution that can be sampled. We propose three stochastic programming-based formulations that can be used to solve this problem, and provide exact and approximate solution techniques for the resulting models. We also present numerical results for a large set of numerical problems. The results indicate that the solutions obtained using the stochastic programming approaches perform significantly better than those obtained using expected values of capacities in a deterministic solution strategy. In addition, stochastic-programming-based approximations are computationally as efficient as deterministic techniques

Route Optimization Tool (RoOT) for distribution of vaccines and health products

Delivery of health products from provinces or districts to health facilities, including temperature-sensitive vaccines, is one of the most effective interventions to ensure availability of supplies and save lives in low- and middle-income countries. Currently, routes are hand drawn by logisticians that are adjusted based on vehicle availability and quantity of products. Easy-to-use supply chain tools are needed that planners can use in real-time to create or adjust routes for available vehicles and road conditions. Efficient and optimized distribution is even more critical with the COVID-19 vaccine distribution. We develop a Route Optimization Tool (RoOT) using a variant of a Vehicle Routing and Scheduling Algorithm (VeRSA) that is coded in Python, but reads and writes Excel files to make data input and using outputs easier. The tool takes into account cold chain distribution, is easy-to-use, and provides routes quickly within two minutes. RoOT can be used for routine operations or in emergency situations, such as delivery of new COVID-19 vaccine. The tool has a user-centric design with easy dropdown menus and the ability to optimize on time, risk, or combination of both. Training of logisticians in Mozambique indicate that RoOT is easy to use and provides a tool to improve planning and efficient distribution of health products, especially vaccines. We illustrate using RoOT in an emergency situation, such as a cyclone. RoOT is an open-source tool for optimal routing of health products. It provides optimized routes faster than most commercial software, and is tailored to meet the needs of government stakeholders. Currently, RoOT does not allow multi-day routes, and is designed for trips that can be completed within twenty-four hours. Areas for future development include multi-day routing and integration with mapping software to facilitate distance calculations and visualization of routes

A light-touch routing optimization tool (RoOT) for vaccine and medical supply distribution in Mozambique.

Planning vaccine distribution in rural and urban poor communities is challenging, due in part to inadequate vehicles, limited cold storage, road availability, and weather conditions. The University of Washington and VillageReach jointly developed and tested a user-friendly, Excel spreadsheet based optimization tool for routing and scheduling to efficiently distribute vaccines and other medical commodities to health centers across Mozambique. This paper describes the tool and the process used to define the problem and obtain feedback from users during the development. The distribution and routing tool, named route optimization tool (RoOT), uses an indexing algorithm to optimize the routes under constrained resources. Numerical results are presented using five datasets, three realistic and two artificial datasets. RoOT can be used in routine or emergency situations, and may be easily adapted to include other products, regions, or logistic problems

Pure adaptive search in monte carlo optimization

Pure adaptive search constructs a sequence of points uniformly distributed within a corresponding sequence of nested regions of the feasible space. At any stage, the next point in the sequence is chosen uniformly distributed over the region of feasible space containing all points that are equal or superior in value to the previous points in the sequence. We show that for convex programs the number of iterations required to achieve a given accuracy of solution increases at most linearly in the dimension of the problem. This compares to exponential growth in iterations required for pure random search.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47920/1/10107_2005_Article_BF01582296.pd

Random search algorithms

Random search algorithms are useful for many ill-structured global optimization problems with continuous and/or discrete variables. Typically random search algorithms sacrifice a guarantee of optimality for finding a good solution quickly with convergence results in probability. Random search algorithms include simulated annealing, tabu search, genetic algorithms, evolutionary programming, particle swarm optimization, ant colony optimization, cross-entropy, stochastic approximation, multistart and clustering algorithms, to name a few. They may be categorized as global (exploration) versus local (exploitation) search, or instance-based versus model-based. However, one feature these methods share is the use of probability in determining their iterative procedures. This article provides an overview of these random search algorithms, with a probabilistic view that ties them together. A random search algorithm refers to an algorithm that uses some kind of randomness or probability (typically in the form of a pseudo-random number generator) in the definition of the method, and in the literature, may be called a Monte Carlo method or a stochastic algorithm. The term metaheuristic is also commonly associated with random search algorithms. Simulated annealing, tabu search, genetic algorithms, evolutionary programming, particle swarm optimization, ant colony optimization, cross-entropy, stochastic approximation, multi-start, clustering algorithms, and other random search methods are being widely applied to continuous and discrete global optimization problems, see, for example

Incorporating uncertainty into a supplier selection problem

Supplier selection is an important strategic supply chain design decision. Incorporating uncertainty of demand and supplier capacity into the optimization model results in a robust selection of suppliers. A two-stage stochastic programming (SP) model and a chance-constrained programming (CCP) model are developed to determine a minimal set of suppliers and optimal order quantities with consideration of business volume discounts. Both models include several objectives and strive to balance a small number of suppliers with the risk of not being able to meet demand. The SP model is scenario-based and uses penalty coefficients whereas the CCP model assumes a probability distribution and constrains the probability of not meeting demand. Both formulations improve on a deterministic mixed integer linear program and give the decision maker a more complete picture of tradeoffs between cost, system reliability and other factors. We present Pareto-optimal solutions for a sample problem to demonstrate the benefits of the SP and CCP models. In order to describe the tradeoffs between costs and risks in an analytical form, we use multi-parametric programming techniques to more completely analyze the alternative Pareto-optimal supplier selection solutions in the CCP model. This analysis gives insights into the robustness of the solutions with respect to number of suppliers, costs and probability of not meeting demand.Robust supplier selection Plan for uncertainty Stochastic programming Chance-constraint programming Multi-parametric programming Tradeoffs between risk and cost