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The concern about missing necessary constraints seems reasonable, but then how does the current budgeting process avoid the same concern? Perhaps it does so by

The concern about missing necessary constraints seems reasonable, but then how does the current budgeting process avoid the same concern? Perhaps it does so by changing in small steps, so that each period's budget is similar enough to the previous period's budget (which was known to have worked reasonably well) that the differences can be analyzed and the consequences understood. So something you might try, is to locate the current budget in your linear system and then find a nearby point that improves the objective function. It should then be simple to explain the proposed improvement ("move $A from B to C and $D from E to F and the objective function goes up by $G") and not too complex to examine it for missing constraints ("hang on, you can't reduce B by $A because the supplier has a minimum order"). The idea is that instead of using linear optimization to replace the current budgeting process (which is risky), to use it to generate proposals for submission to the current budgeting process, and to capture the constraints that are revealed when proposals are rejected. (But note also that it's quite likely that a real objective function will be nonlinear due to economies of scale, in which case linear optimization methods won't suffice.)

blahi 10y ago
Things like minimum orders are obvious enough that I will manage to figure them out. My colleague's concern (and I see his point) is about what happens when the solver says "stop selling coffee machines", but when we stop, consumables drop off a cliff and consumables is where we make the profit.
- ColinWright 10y ago
  So there's a missing constraint that M >= S/1000 or similar, where M=machines and S=supplies. And yes, that is an issue that needs to be considered. Over 10s or 100s of thousands of items that becomes difficult, but it's still the case that the system you describe now is not really under control. But perhaps your senior colleague is right, and that's just the way it has to be. However, one person's time spent investigating this properly might be money well spent.
  - blahi 10y ago
    Yeah, but that's the problem. There is no way to know all the relationships. This was an obvious one, there are a lot more subtle ones. In any case, the comments have been very helpful. A gradual implementation is the only sane way to go. Politics are not too big of an issue, if I can make a concise case and what's a better way to do it than a small project.
    - ColinWright 10y ago
      Documenting these relationships would potentially be a really, really valuable thing to do "going forward". It helps to make explicit things that are currently implicit, and possibly unknown. It then opens up the possibilities of making optimisations like using Linear Programming, but at the very least it reduces risk and helps to share knowledge. Good luck!

blahi 10y ago

Things like minimum orders are obvious enough that I will manage to figure them out. My colleague's concern (and I see his point) is about what happens when the solver says "stop selling coffee machines", but when we stop, consumables drop off a cliff and consumables is where we make the profit.

ColinWright 10y ago
So there's a missing constraint that M >= S/1000 or similar, where M=machines and S=supplies. And yes, that is an issue that needs to be considered. Over 10s or 100s of thousands of items that becomes difficult, but it's still the case that the system you describe now is not really under control. But perhaps your senior colleague is right, and that's just the way it has to be. However, one person's time spent investigating this properly might be money well spent.
- blahi 10y ago
  Yeah, but that's the problem. There is no way to know all the relationships. This was an obvious one, there are a lot more subtle ones. In any case, the comments have been very helpful. A gradual implementation is the only sane way to go. Politics are not too big of an issue, if I can make a concise case and what's a better way to do it than a small project.
  - ColinWright 10y ago
    Documenting these relationships would potentially be a really, really valuable thing to do "going forward". It helps to make explicit things that are currently implicit, and possibly unknown. It then opens up the possibilities of making optimisations like using Linear Programming, but at the very least it reduces risk and helps to share knowledge. Good luck!