The Formulation of OR Problems
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The Formulation of OR Problems - a critical craft Miles G Nicholls mathematical programming, is the delivery of simple and relevant formulations leading to usable results. Formulation is a little hit like house painting,
of correct formulation qf this paper, 1/le problem mathematical rondels for real world situations is considered. The issue is not so much 1/ial 1/le correct formulation is required, as this is usuallj quite easilp arriced at. The issue is miiome t/iat the appropiiatejürmulation is arriced at. Y/ns is an issue that is not c/ca/I with in in i/c/i detail in undergraduate or graduate coumses. and one that pro et itioneis q/len need reminders about. An example is ofen, where the cost oJ not arrio//mg at tile mnoit appropriate model is substantial. In
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Formulation is often described as' craft more than a science, however, the emphasis in academic courses is heavily concentrated on the techniques and mathematics, rather than some of the more practical aspects of OR, such as formulation.
appropriate
The example used in this paper covers the formulation of a model of an entire aluminium
foimmmidatiin are also substantial.
smelter. In the case, the arrival at the most appropriate formulation meant that instead of
Introduction
hundreds of variables being associated with a nonlinear hi-level mathematical model (thousands when
The formulation of OR problems, whether they be at the level of a struggling undergraduate or a high flying consultant, is ncver as straight forward nor as simple as it seems. ()ne of the hardest aspects of OR (in particular applied mathematical modelling) that must be learned is that 0f formulating the problem (ie devising a mathematical representation of the problem). It is important that the representation be developed not just so that an optimal (or in reality a best practice) solution can he obtained, but rather that the simplest and most logical representation be arrived at. Many formulations of' the same problem can be developed in the real world and depending
the model was multi-period), only two variables resulted with many constraints being bounds. This had a significant impact on cost, relevance and ultimate usability not to mentioned ease of solution of the problem.
The Aluminium Smelter - General Description The development of the model of the smelter has been extensively documented (see Nicholls and Hedditch (1993), Nicholls (1995), and Nicholls (2000)). The Aluminium Smelter is at Portland
on the one arrived at the exercise can he more or less costly, efhcient and useful.
Australia and is a ASl.5 billion development on 250 acres. The model was initially developed to provide management and supervisors with the ability to determine what the optimal operating values of the key variables of the plant should he, evaluate capital expansion plans and alternative technology etc.
This Japer outlines an example from OR practice that ad
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