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POOptimizing lumber purchasing
 

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    <p><strong>I would like to know how to classify the following optimization problem.</strong></p> <p>A lumber yard sells 2x4's in various stock lengths. For example, an 8ft could be $3 and a 10ft could be $4, while a 14ft might be $5.50. Importantly, the lengths are not linearly related to price and not all discrete lengths can be purchased as stock. It can be assumed that the available stock units are inexhaustible in these discrete lengths.</p> <pre><code>length cost 7.7ft $2.75 8ft $3.00 10ft $4.00 14ft $5.50 </code></pre> <p>I need to create a set of 2x4's with given lengths by cutting them from the above stock (say I need lengths of 2ft, 2.5ft, 6ft once all is said and done). Also, each "cut" incurs a material cost of 1/8" (i.e. 0.0104ft). The solution of the problem is an assignment of each desired length to a piece of stock with the total cost of all stock minimized. In this example, the optimal solution minimizing cost is to buy a 14ft board at $5.50. (A runner-up solution is to buy two 8ft boards and allocate as {6ft} and {2ft, 0.0104ft, 2.5ft} for a cost of $6.)</p> <p><strong>It does not seem to be a Knapsack-class problem. It does not seem to be a cutting stock problem (because I would like to minimize cost rather than minimize waste). What sort of problem is this, and how can I go about efficiently solving it?</strong></p> <p>(As an after-note, this is a non-fictional problem I have solved in the obvious, inefficient way using multiset partitions and iteration in Haskell. The runtime is prohibitive to practical use with more than 23 desired lengths and 6 available stock sizes.)</p>
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