What are Assignment Models?
Assignment models are used to estimate the traffic flows on a network.
Traffic Assignment Models estimate the flow on a street or highway network using an input matrix of flows that indicate the volume of traffic between origin and destination (O-D) pairs. They also take input on the network topology, link characteristics, and link performance functions. The flows for each O-D pair are loaded onto the network based on the travel time or impedance of the alternative paths that could carry this traffic. The traffic assignment model predicts the network flows that are associated with future planning scenarios, and generates estimates of the link travel times and related attributes that are the basis for benefits estimation and air quality impacts. The traffic assignment model is also used to generate the estimates of network performance that are used in the mode choice and trip distribution or destination choice stages of many models.
Transit Assignment Models are used to estimate the number of passengers that use transit segments and routes in a transit network as a function of transit level of service and fare. These models take as input an O-D matrix of passenger demand and a transit network, and produce transit segment, stop level, route level, and aggregate ridership statistics.
The Assignment Model
The assignment model is used to solve the traditional one to one assignment problem of assigning employees to jobs, employees to machines, machines to jobs, etc. The model is a special case of the transportation method. In order to generate an assignment problem it is necessary to provide the number of jobs and machines and indicate whether the problem is a minimization or maximization problem. The number of jobs and machines do not have to be equal but usually they are.
Objective function. The objective can be to minimize or to maximize. This is set at the creation screen but can be changed in the data screen.
The table below shows data for a 7 by 7 assignment problem. Our goal is to assign each salesperson to a territory at minimum total cost. There must be exactly one salesperson per territory and exactly one territory per salesperson.
The data structure is nearly identical to the structure for the transportation model. The basic difference is that the assignment model does not display supplies and demands since they are all equal to one.
The results are very straightforward.
Assignments. The 'Assigns's in the main body of the table are the assignments which are to be made. For example, Mort is to be assigned to Pennsylvania, Chorine is to be assigned to Florida, Bruce is to be sent to Canada, Beth is to work the streets of New York, Lauren is across the river in New Jersey, Eddie works Europe and Brian will work in Mexico.
Total cost. The total cost appears in the upper left cell. In this example the total cost is given by $191.
The assignments can also be given in list form as shown below.
The marginal costs can be displayed also. For example, if we want to assign Chorine to Pennsylvania then the total will increase by $6 to $197.
NOTE: To preclude an assignment from being made (in a minimization problem) you should enter a very large cost. If you enter an 'x' then the program will place a high cost in that cell.