Price discriminationPrice discrimination is a microeconomic pricing strategy where identical or largely similar goods or services are sold at different prices by the same provider in different market segments. Price discrimination is distinguished from product differentiation by the more substantial difference in production cost for the differently priced products involved in the latter strategy. Price differentiation essentially relies on the variation in the customers' willingness to pay and in the elasticity of their demand.
Linear programmingLinear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.
Feasible regionIn mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. This is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down.
Branch and boundBranch and bound (BB, B&B, or BnB) is a method for solving optimization problems by breaking them down into smaller sub-problems and using a bounding function to eliminate sub-problems that cannot contain the optimal solution. It is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search: the set of candidate solutions is thought of as forming a rooted tree with the full set at the root.
AlgorithmIn mathematics and computer science, an algorithm (ˈælɡərɪðəm) is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning), achieving automation eventually.
Cutting-plane methodIn mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, as well as to solve general, not necessarily differentiable convex optimization problems. The use of cutting planes to solve MILP was introduced by Ralph E. Gomory.
Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
Price fixingPrice fixing is an anticompetitive agreement between participants on the same side in a market to buy or sell a product, service, or commodity only at a fixed price, or maintain the market conditions such that the price is maintained at a given level by controlling supply and demand. The intent of price fixing may be to push the price of a product as high as possible, generally leading to profits for all sellers but may also have the goal to fix, peg, discount, or stabilize prices.
Pricing strategiesA business can use a variety of pricing strategies when selling a product or service. To determine the most effective pricing strategy for a company, senior executives need to first identify the company's pricing position, pricing segment, pricing capability and their competitive pricing reaction strategy. Pricing strategies and tactics vary from company to company, and also differ across countries, cultures, industries and over time, with the maturing of industries and markets and changes in wider economic conditions.
Multi-objective optimizationMulti-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of multiple-criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multi-objective is a type of vector optimization that has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives.
Convex optimizationConvex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
Predatory pricingPredatory pricing is a commercial pricing strategy which involves the use of large scale undercutting to eliminate competition. This is where an industry dominant firm with sizable market power will deliberately reduce the prices of a product or service to loss-making levels to attract all consumers and create a monopoly. For a period of time, the prices are set unrealistically low to ensure competitors are unable to effectively compete with the dominant firm without making substantial loss.
Cutting stock problemIn operations research, the cutting-stock problem is the problem of cutting standard-sized pieces of stock material, such as paper rolls or sheet metal, into pieces of specified sizes while minimizing material wasted. It is an optimization problem in mathematics that arises from applications in industry. In terms of computational complexity, the problem is an NP-hard problem reducible to the knapsack problem. The problem can be formulated as an integer linear programming problem.
Price gougingPrice gouging is the practice of increasing the prices of goods, services, or commodities to a level much higher than is considered reasonable or fair. Usually, this event occurs after a demand or supply shock. This commonly applies to price increases of basic necessities after natural disasters. The term can also be used to refer to profits obtained by practices inconsistent with a competitive free market, or to windfall profits. In some jurisdictions of the United States during civil emergencies, price gouging is a specific crime.
Karmarkar's algorithmKarmarkar's algorithm is an algorithm introduced by Narendra Karmarkar in 1984 for solving linear programming problems. It was the first reasonably efficient algorithm that solves these problems in polynomial time. The ellipsoid method is also polynomial time but proved to be inefficient in practice. Denoting as the number of variables and as the number of bits of input to the algorithm, Karmarkar's algorithm requires operations on -digit numbers, as compared to such operations for the ellipsoid algorithm.
PriceA price is the (usually not negative) quantity of payment or compensation expected, required, or given by one party to another in return for goods or services. In some situations, the price of production has a different name. If the product is a "good" in the commercial exchange, the payment for this product will likely be called its "price". However, if the product is "service", there will be other possible names for this product's name.
Search algorithmIn computer science, a search algorithm is an algorithm designed to solve a search problem. Search algorithms work to retrieve information stored within particular data structure, or calculated in the search space of a problem domain, with either discrete or continuous values. Although search engines use search algorithms, they belong to the study of information retrieval, not algorithmics. The appropriate search algorithm to use often depends on the data structure being searched, and may also include prior knowledge about the data.
Tacit collusionTacit collusion is a collusion between competitors, which do not explicitly exchange information and achieving an agreement about coordination of conduct. There are two types of tacit collusion – concerted action and conscious parallelism. In a concerted action also known as concerted activity, competitors exchange some information without reaching any explicit agreement, while conscious parallelism implies no communication. In both types of tacit collusion, competitors agree to play a certain strategy without explicitly saying so.
Randomized roundingWithin computer science and operations research, many combinatorial optimization problems are computationally intractable to solve exactly (to optimality). Many such problems do admit fast (polynomial time) approximation algorithms—that is, algorithms that are guaranteed to return an approximately optimal solution given any input. Randomized rounding is a widely used approach for designing and analyzing such approximation algorithms.
Shadow priceA shadow price is the monetary value assigned to an abstract or intangible commodity which is not traded in the marketplace. This often takes the form of an externality. Shadow prices are also known as the recalculation of known market prices in order to account for the presence of distortionary market instruments (e.g. quotas, tariffs, taxes or subsidies). Shadow prices are the real economic prices given to goods and services after they have been appropriately adjusted by removing distortionary market instruments and incorporating the societal impact of the respective good or service.
