Assignment Problem With Constraints Meaning

The assignment problem is defined as follows:

There are a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary depending on the agent-task assignment. It is required to perform all tasks by assigning exactly one task to each agent in such a way that the total cost of the assignment is minimized.

The number of tasks is larger than the number of agents.

My problem statement though imposes an additional constraint on the above.

Each task belongs to exactly one 'category'. Each 'category' has an associated maximum number of tasks that can be assigned. Enforce this constraint on the earlier definition.

For a layman's example, consider this -

A restaurant serves n customers (agents), and has on it's menu m possible dishes (tasks), with m > n. Each customer gives his preference for each of the m dishes, which is the cost for this particular assignment problem. Find a solution which minimizes cost i.e. which gives each customer a dish that is as high on their preference as possible.

Additionally, each dish belong to a certain cuisine (category). The restaurant can only make a certain number of dishes per cuisine. Enforce this constraint on the problem above.

I understand that this is a very specific problem, but any help would be appreciated.

I am currently solving the first part of the problem using the Hungarian Algorithm for assignment.


Operations Research

Description: OR professionals in every field of study will find information of interest in this balanced, full-spectrum industry review. Essential reading for practitioners, researchers, educators and students of OR.
  • Computing and decision technology
  • Environment, energy and natural resources
  • Financial services
  • Logistics and supply chain operations
  • Manufacturing operations
  • Optimization
  • Public and military services
  • Simulation
  • Stochastic models
  • Telecommunications
  • Transportation

Coverage: 1956-2012 (Vol. 4, No. 1 - Vol. 60, No. 6)

Moving Wall: 5 years (What is the moving wall?)

The "moving wall" represents the time period between the last issue available in JSTOR and the most recently published issue of a journal. Moving walls are generally represented in years. In rare instances, a publisher has elected to have a "zero" moving wall, so their current issues are available in JSTOR shortly after publication.
Note: In calculating the moving wall, the current year is not counted.
For example, if the current year is 2008 and a journal has a 5 year moving wall, articles from the year 2002 are available.

Terms Related to the Moving Wall
Fixed walls: Journals with no new volumes being added to the archive.
Absorbed: Journals that are combined with another title.
Complete: Journals that are no longer published or that have been combined with another title.

ISSN: 0030364X

EISSN: 15265463

Subjects: Business & Economics, Business

Collections: Arts & Sciences IV Collection, Business & Economics Collection, Business I Collection, JSTOR Essential Collection

One thought on “Assignment Problem With Constraints Meaning

Leave a Reply

Your email address will not be published. Required fields are marked *