Hi all, I'm looking for some good examples of interesting/novel math programming objective functions you've seen applied in the literature. In particular, outside of some of the traditional ones like maximizing profits / minimizing costs. For example, the routing of hazardous waste across the country could be formulated as maximizing the distance from population centers (subject to other operational constraints like it arriving in a reasonable time). Thanks!

asked 22 Jan '13, 13:26

AndyT's gravatar image

AndyT
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Some of the examples that came to my mind right now are as follows:

  1. Similar to your own example, p-Dispersion problem tries to locate p facilities on a network as dispersed as possible.
  2. Many scheduling problems have total tardiness or number of tary jobs as their performance criterion. These two crtiteria reflect on customer service level. In addition, there are total completion time or total flow time objectives that have more meanings than just costs.
  3. Many supply chain deisgn and planning problems have a customer service level objetive function (usually within a multi-objective setting). For example in supply chain network design, it's usually a good idea to consider a service level objective function (e.g., total or maximum tardiness in delivering products) along a cost minimizing objective function.
  4. In sustainable supply chain problems, you have to consider some of kind objective function that could represent environmental issues (e.g., minimize CO emmission or scrape parts).

I think if you follow multi-objective optimization problems within various areas such as SCM, you could come up with more examples.

link

answered 22 Jan '13, 14:09

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Ehsan ♦
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Thanks Ehsan, these are some good examples

(22 Jan '13, 14:20) AndyT

In forming a single team, you can maximize either some measure of team efficacy or some measure of internal cohesion (how well the team members get along).

In forming multiple teams, you may want to minimize the differences in (perceived) efficacy between teams. This comes up when assigning players in a golf scramble, assigning players to teams in a recreational league (where the league forms the teams) and assigning students (particularly MBAs) to project or study teams.

I saw one application (not sure it was published) where the objective was to generate binary vectors (I forget to what end) while maximizing the minimum Hamming distance between them.

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answered 22 Jan '13, 16:36

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Paul Rubin ♦♦
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The solution to a sudoku game is presented in the GNU Linear Programming Kit (GLPK). There are lots more unusual models in this kit's demonstration models catalog.

link

answered 22 Jan '13, 20:46

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Geoffrey
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