Optimization / Operations Research /Management Science


“Operations research” and “management science” are terms that are used interchangeably to describe the area of using advanced analytical techniques to make better decisions in order to manage money, materials, information, time, equipment, and people. The essence and the nature of operations research is based on the formulation of an optimization problem and the usage of optimization methods (such as steepest descent, dynamic programming, genetic algorithm, etc.) to find optimal or acceptable solutions. These potential solutions are presented to managers who choose the best action or alternative.

Operations research project is often involved in top-level strategy development, planning, and forecasting (reference to Forecasting). They help to allocate resources, measure performance, develop schedules, design production facilities and systems, manage the supply chain, set prices, form the optimal investment portfolio, coordinate transportation and distribution, analyze large databases, etc.

We can help to formulate, solve, and promote application of a number of quantitative methods to finance (reference to Finance), marketing, health care, manufacturing, transportation and other industries:
- Linear and Quadratic programming
- Integer and Mixed programming
- Smooth and Non-smooth non-linear optimization (constrained and unconstrained)
- Global optimization
- Network flows
- Linear and non-linear regression with any types of constraints
- Optimization under uncertainty (stochastic programming)
- Multicriteria optimization
- Dissimilar optimization/decision support problems with specialized structures
- Simulation (including discrete event simulation).


Combining optimization problems with data mining, statistical analysis, forecasting, and spatial analytics can significantly widen the list of problems, mentioned above, and lead to additional increment in ROI.


Typical operations research/optimization project includes the following steps: 1. project assessment, 2. detailed formulation of an optimization/operations research problem, 3. finding optimal or acceptable solutions, 4.solution incorporation into business decision making, monitoring the results, and if necessary, modification of the problem statement and corresponding solution.


Project Assessment

Project assessment starts with translation of business problem into solvable optimization counterpart and evaluation of the feasibility and successfulness of a project implementation. In particular, project assessment phase includes:
- evaluating business objectives and goal attainability
- checking the correspondence between objectives (business questions) and data/information availability and data sufficiency
- discussing variety of problem statements, decision variables, constraints, objective function(s) and selection the most appropriate ones
- discussing uncertainty in the problem parameters, project duration, requirements, and outcomes
- determining required resources and estimating computational tractability of the problem
- discussing integration of the solution of the optimization problem  with your planning / forecasting / decision support systems and post-solution activities
- developing customized report structure
- forming  multidisciplinary  / cross-functional project team (if necessary).


Detailed formulation of an optimization/operations research problem

Reviewing available data/information sources in light of project objectives and business questions, collecting necessary expert judgments and creating data set for the analysis and optimization. Defining variables role (objective function, constraints, and decision variables) and formulating the business problem in operations research terms, selecting adequate optimization method of the problem at hand. When available data is insufficient, or requirement is to develop "if-then" scenario, then an appropriate approach can be simulation.
Estimating uncertainty in the problem formulation, problem parameters, problem solution, and incorporating the optimal/suboptimal/acceptable solution in the business decision process / business strategy. Developing the quality control procedure to monitor results.

Finding optimal or acceptable solutions

Converting formulated optimization problem into solvable counterpart by applying an available commercial tool (Excel Solver, SAS OR, Dash Optimization, etc.). Evaluating the existence of a unique optimal solution and convergence problems. Generating optimal/acceptable solutions and analyzing properties of the solutions.


Optimal Solution incorporation into business decision making

Evaluating solution accuracy and solution stability. Assessing model’s recommendations. Creating software infrastructure to incorporate optimal solution into business decision making. Setting up the report structure and reporting system. Measuring performance accuracy, identifying factors that drive discrepancy between reality and expected outcomes, and modifying/updating data/model/optimal solution.