The terms Operations Research and Management Science tend to be used synonymously. Operations research (or operational research, as it’s called in Europe) refers to scientific methods (statistical and mathematical modeling, experiments, simulation, and optimization) applied to the solution of complex business problems. Operations research is about deriving optimal solutions to maximize sales or profits and/or to minimize costs, losses, or risks.

The basic tools of operations research are probability theory, Monte Carlo methods, stochastic processes, queuing models, transportation models, network models, game theory, linear and nonlinear programming, dynamic programming, Markov decision processes, input-output analysis, choice modeling, econometric modeling, and other mathematical techniques and algorithms. The ultimate goal is to create a mathematical model that simulates real-world processes and systems so that optimal solutions can be found. Computer science technologies and software development capabilities are often critical components in successful operations research projects.

• Distribution system optimization. What is the optimal number of warehouses, trucks and routes to minimize out-of-stocks, or minimize distribution costs or maximize delivery speeds? Where should the warehouses be located? What are the most efficient delivery routes? What size should the trucks be? How should the products be packaged and palletized for most efficient shipping?
• Retail site selection optimization. Which markets offer the greatest potential for new retail outlets? What store density maximizes sales revenue or profits? What’s the interaction between advertising investments and number of retail units? What sections of a metropolitan area offer the greatest potential for new retail units? What specific retail locations will yield the greatest return on investment? What deployment of retail units minimizes supply chain and distribution costs?
• Store design optimization. What type of store design will maximize consumer visits, time spent in store, or sales? What elements of store design are most important to consumers, and what arrangements of these elements are optimal? How should store design vary to maximize appeal to a particular demographic target or for a given location? What product mix corresponds to and supports the optimal store design? 
• Store merchandise optimization. What is the optimal mix of merchandise in a given store to maximize sales or profits? How should this optimal mix vary across different types of geographic areas and demographic groups? How should this product mix vary throughout the business cycle? What are the optimal marketing elements to support the optimal merchandise mix?
• Retail category optimization. There are many categories of products within a retail store. Retailers often strive to maximize sales within each category. What is the optimal mix of brands, sizes, and facings to increase category sales? Will optimization of one category negatively affect other categories? How can product categories be optimized without hurting overall store sales?
• Supply chain optimization. What’s the optimal way to manage the flow of raw materials, components, and supplies from various vendors to the manufacturer, under conditions of varying and uncertain demand?
• Manufacturing/Production optimization. What organization, machines, processes, and work flows will maximize quality, minimize costs, and maximize output? Optimizing manufacturing processes must be closely integrated with optimization of the related supply chain and distribution system.
• Network optimization. How should airports be designed to handle luggage and passenger flow? How should traffic lights be organized and timed to maximize traffic flow? What is the optimal design of an electrical grid or a communications network?
• Transportation optimization. What route structure minimizes the number of trucks, railcars, or school buses needed to achieve a certain service threshold or minimizes waiting times? Which common carriers provide the most efficient distribution services for a particular business? How should these transportation solutions vary as conditions change (weather, time of day, traffic density, etc.)?
• Scheduling optimization. What type of schedule or scheduling system will yield the greatest revenue, minimize costs, reduce delivery times, or meet other objectives? How should scheduling change as conditions and the business environment change?
• Strategy optimization. What markets, technologies, systems and processes, products and services, and positioning and messages will achieve the greatest long-term success for a given brand, business unit, or corporation? That is, what is the optimal business model for a given company in a given industry?
• Trading and markets optimization. Some problems can be addressed via artificial markets (e.g., “cap and trade”) wherein interested parties bid against each other and trade with each other. What is the optimal way to build such a market, and how can the results be evaluated and understood?