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This is an unbalanced assignment problem. One way to solve it is to invent a fourth dummy task, perhaps called "sitting still doing nothing", with a cost of 0 for the taxi assigned to it. This reduces the problem to a balanced assignment problem, which can then be solved in the usual way and still give the best solution to the problem.
The Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal–dual methods.It was developed and published in 1955 by Harold Kuhn, who gave it the name "Hungarian method" because the algorithm was largely based on the earlier works of two Hungarian mathematicians, Dénes Kőnig and Jenő Egerváry.
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:
These costs may vary based on the assignment of agent to a combination of job characteristics - specific task, machine, time interval, etc. The problem is to minimize the total cost of assigning the agents so that the assignment of agents to each job characteristic is an injective function , or one-to-one function from agents to a given job ...
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.
A variety of variants deal with the number of such assignments: MAJ-SAT asks if the majority of all assignments make the formula TRUE. It is known to be complete for PP, a probabilistic class. #SAT, the problem of counting how many variable assignments satisfy a formula, is a counting problem, not a decision problem, and is #P-complete.
Donald Trump mocked Canadian Prime Minister Justin Trudeau after his top minister’s surprise resignation following a clash on how to handle the president-elect’s looming tariffs.
The weapon target assignment problem (WTA) is a class of combinatorial optimization problems present in the fields of optimization and operations research.It consists of finding an optimal assignment of a set of weapons of various types to a set of targets in order to maximize the total expected damage done to the opponent.