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This is a balanced assignment problem. Its solution is whichever combination of taxis and customers results in the least total cost. Now, suppose that there are four taxis available, but still only three customers. This is an unbalanced assignment problem. One way to solve it is to invent a fourth dummy task, perhaps called "sitting still doing ...
Flow Shop Scheduling Problem; Generalized assignment problem; Integer programming. The variant where variables are required to be 0 or 1, called zero-one linear programming, and several other variants are also NP-complete [2] [3]: MP1 Some problems related to Job-shop scheduling
A solution is an assignment from items to bins. A feasible solution is a solution in which for each bin the total weight of assigned items is at most . The solution's profit is the sum of profits for each item-bin assignment. The goal is to find a maximum profit feasible solution.
The Boolean satisfiability problem (SAT) asks to determine if a propositional formula (example depicted) can be made true by an appropriate assignment ("solution") of truth values to its variables. While it is easy to verify whether a given assignment renders the formula true , [ 1 ] no essentially faster method to find a satisfying assignment ...
This problem can be seen as a generalization of the linear assignment problem. [2] In words, the problem can be described as follows: An instance of the problem has a number of agents (i.e., cardinality parameter) and a number of job characteristics (i.e., dimensionality parameter) such as task, machine, time interval, etc. For example, an ...
The formal definition of the quadratic assignment problem is as follows: Given two sets, P ("facilities") and L ("locations"), of equal size, together with a weight function w : P × P → R and a distance function d : L × L → R. Find the bijection f : P → L ("assignment") such that the cost function:
Fair random assignment (also called probabilistic one-sided matching) is a kind of a fair division problem. In an assignment problem (also called house-allocation problem or one-sided matching), there are m objects and they have to be allocated among n agents, such that each agent receives at most one object. Examples include the assignment of ...
R vs. RE problem, where R is analog of class P, and RE is analog class NP. These classes are not equal, because undecidable but verifiable problems do exist, for example, Hilbert's tenth problem which is RE-complete. [57] A similar problem exists in the theory of algebraic complexity: VP vs. VNP problem. This problem has not been solved yet ...