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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.
In mathematics and economics, transportation theory or transport theory is a name given to the study of optimal transportation and allocation of resources. The problem was formalized by the French mathematician Gaspard Monge in 1781. [1] In the 1920s A.N. Tolstoi was one of the first to study the transportation problem mathematically.
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 ...
Transshipment problems form a subgroup of transportation problems, where transshipment is allowed. In transshipment, transportation may or must go through intermediate nodes, possibly changing modes of transport. The Transshipment problem has its origins in medieval times [dubious – discuss] when trading started to become a mass phenomenon ...
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:
The vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a fleet of vehicles to traverse in order to deliver to a given set of customers?"
In the special case in which all the agents' budgets and all tasks' costs are equal to 1, this problem reduces to the assignment problem. When the costs and profits of all tasks do not vary between different agents, this problem reduces to the multiple knapsack problem. If there is a single agent, then, this problem reduces to the knapsack problem.
An assignment operation is a process in imperative programming in which different values are associated with a particular variable name as time passes. [1] The program, in such model, operates by changing its state using successive assignment statements. [2] [3] Primitives of imperative programming languages rely on assignment to do iteration. [4]