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It is required to perform all tasks by assigning exactly one agent to each task in such a way that the maximum cost among the individual assignments is minimized. The term " bottleneck " is explained by a common type of application of the problem, where the cost is the duration of the task performed by an agent.
In the basic assignment problem, each agent is assigned to at most one task and each task is assigned to at most one agent. In the many-to-many assignment problem, [10] each agent i may take up to c i tasks (c i is called the agent's capacity), and each task j may be taken by up to d j agents simultaneously (d j is called the task's capacity).
This is an accepted version of this page This is the latest accepted revision, reviewed on 17 January 2025. Observation that in many real-life datasets, the leading digit is likely to be small For the unrelated adage, see Benford's law of controversy. The distribution of first digits, according to Benford's law. Each bar represents a digit, and the height of the bar is the percentage of ...
In mathematics, a limiting case of a mathematical object is a special case that arises when one or more components of the object take on their most extreme possible values. [1] For example: In statistics, the limiting case of the binomial distribution is the Poisson distribution. As the number of events tends to infinity in the binomial ...
In mathematics, the moving sofa problem or sofa problem is a two-dimensional idealization of real-life furniture-moving problems and asks for the rigid two-dimensional shape of the largest area that can be maneuvered through an L-shaped planar region with legs of unit width. [1] The area thus obtained is referred to as the sofa constant.
The strength of materials is determined using various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus ...
If we denote the area of land planted with wheat and barley by x 1 and x 2 respectively, then profit can be maximized by choosing optimal values for x 1 and x 2. This problem can be expressed with the following linear programming problem in the standard form:
Re-sawing is the splitting of 1-to-12-inch (25–305 mm) hardwood or softwood lumber into two or more thinner pieces of full-length boards. For example, splitting a 10-foot-long (3.0 m) 2×4 (1 + 1 ⁄ 2 by 3 + 1 ⁄ 2 in or 38 by 89 mm) into two 1×4s (3 ⁄ 4 by 3 + 1 ⁄ 2 in or 19 by 89 mm) of the same length is considered re-sawing.