Disclaimer: This blog, including this post, is not sponsored by CombineNet. The author is not employed by, contractually engaged with, or affiliated with CombineNet. Any and all opinions expressed herein are solely those of the author. Furthermore, the opinions expressed herein should be contrasted with the opinions of other educated professionals before the reader forms his or her own opinion. Finally, the author is neither endorsing nor dissenting the use of CombineNet’s products or services – merely trying to spread awareness on the importance of optimization and the relative uniqueness of an offering like that of CombineNet. This disclaimer holds true for each post in this multi-part series and will be repeated.

**Warning**: This is a lengthy post.

In my last post, I outlined in some detail a problem that I felt not only required BoB (Best of Breed) but required CombineNet in particular for an optimal solution. What I did not convey is that not only are there other problems out there that I could have chosen, but there are a significant number of supply-chain related problems that often require BoB.

Today I am going to discuss six problems that generally require a BoB solution. This does not mean that you would necessarily require CombineNet (there are some other optimization vendors that can tackle a few of these), but that you would require a best of breed optimization solution (similar to that offered by CombineNet) to tackle these problems and be assured that the solution you achieved was optimal.

The problems I am going to discuss are:

- Distribution Network Design
- Large Combinatorial Problems
- Large Non-Homogenous Logistics Problems
- Non-Traditional Sourcing Problems
- Very Large (Traditional) Sourcing Problems
- Regret Minimization Problems

**Distribution Network Design **

Most large retailers or distributors have large distribution networks – often dozens of locations throughout a single country or region. However, this is generally not optimal. For example, in a talk at INFORMS given by a practitioner at APL Logistics, they described how they analyzed the distribution network used by JC Penney that had almost 60 DCS (and cost over 330M / yr to operate) and using in house proprietary meta-heuristic optimization algorithms, they deduced an optimal distribution network that had only 8 DCs, saved over 30M dollars, and, on average, shaved over a day off of standard delivery times! What the presentation did not dwell on (since INFORMS is an OR conference) is that these problems are usually humongous and insanely difficult to model, yet alone solve with your average off the shelf optimization problem (as bad as the multi-level make vs. buy problem discussed in my last post) and without a best of breed solution, your chances of finding the truly optimal solution are often slim.

**Large Combinatorial Problems **

Large pure combinatorial problems are much, much harder than large pure linear problems (which optimizer’s like iLog’s CPlex can often cut through like a hot knife through butter on today’s high end machines) and significantly harder than general MIP problems. The reason is that these problems contain very large numbers of binary variables, and the best generic domain-independent techniques available are generally no better than greedy branch and bound, and for even a thousand binary variables, that could be 2^{1000}, or over a trillion evaluations. An example of a large combinatorial problem is a large marketplace auction where all the participants bid on fixed size lots which are non-decomposable. In other words, CombineNet’s (original) definition of an exchange.

How much better are best of breed solvers on large combinatorial problems? Let’s consider CombineNet’s best of breed solution customized for exchanges. According to CombineNet: “*The resulting optimal tree search algorithms are often 10,000 times faster than the state-of-the-art general-purpose MIP solvers on the hard instances of real-world market clearing*.” As I have expressed to CombineNet personnel directly, I doubt that this is the average case, but I know beyond a doubt that well defined algorithms can easily shave a factor of 100 or more off of solution time, and that this can be scaled up to almost 1000 on a multi-core machine with a smart parallel implementation. In other words, don’t always expect the best case, but the average case performance of BoB on these problems will demonstrate *significant* improvements.

**Large Non-Homogeneous Logistics Problems **

This is similar to a variation of the multi-level make vs. buy problem discussed in the last post. However, in this situation you are trying to optimally bundle your deliveries across product, and sourcing categories and choose the optimal carriers and distribution network independent of your suppliers. Given the non-uniform quotes (weight, volume, LTL, FTL), lot sizes, and various charges and surcharges often imposed by freight carriers, forwarders, loaders, unloaders, warehousers, etc., this problem can become really surly really fast on a large buy. Moreover, unlike the sourcing case where it often makes up a low percentage of your spend and a high order approximation is more than sufficient, when you aggregate your logistics across multiple categories, even a fraction of a percentage point can become significant.

**Non-Traditional Sourcing Problems **

Most Platform Optimization Engines are optimized for traditional sourcing problems – this means that they are generally not optimized for non-traditional sourcing problems. (Why should they be? Most of the problems you face are traditional everyday sourcing problems.) But every now and again you might have a non-traditional sourcing problem. One example – cell phone plan optimization. Cell phone plans are expertly crafted to be as confusing as possible to make sure the carrier maximizes profit at your expense. If you’re a small company, it probably isn’t worth the hassle trying to figure it out and standardize on a common carrier plan – the costs of manpower and resulting therapy costs will probably outweigh the savings, but if you are a large company, you can save hundreds of thousands of dollars, if not millions, with the right company wide plan (which will probably consist of different sub-plans for different groups and individuals, but all on the same corporate contract). That’s why Soligence has a solution just centered around cell phone plan optimization.

Another example, as conveyed to me by Paul Martyn himself (CombineNet’s Chief Marketing Officer and premiere evangelist on the CombineNotes blog) is energy utilization optimization. If you are a large corporation that produces energy for your production operations and consumes it from the grid, whether you realize it or not, you have a sophisticated form of an energy trading problem. If you can produce enough extra energy to add to the grid, should you, and when? If you have the potential to store energy, then adding energy to the grid at peak hours and only siphoning off extra energy at non-peak hours could slash digits off of your energy bill. Furthermore, shifting your operations so that your maximum energy utilization only occurs at non-peak hours could also save you bags of money. Considering this isn’t a traditional energy trading model, traditional production model, or traditional operations research planning model, its easy to see why you might have to call on BoB.

*Very* Large (Traditional) Sourcing Problems

POE, especially a well designed and implemented POE that uses real optimization technology as its underpinnings, excels at traditional sourcing problems. It’s what POE was built for. That being said, POE is built on off-the-shelf optimizers, and off-the-shelf optimizers are designed for general purpose needs. That means that they will hit their breaking points before a custom designed best of breed solution, even though they improve every year. For example, leading solvers can easily crunch MIP problems with hundreds of thousands of variables and pure LP problems with millions of variables, but once your MIP problems contain millions of variables and your LP problems tens of millions of variables, you’ll start to notice a performance degradation, which could be rapid and considerable when you get close to the underlying solver’s breaking point. When your encounter the odd problem that is this large, a best of breed solution that also integrates domain intelligence can save you a lot of time and rapidly increase your chance of finding the optimal business solution in the finite timeframe that you have to make a decision.

**Regret Minimization Problems **

Most of the time you know the problem you need to solve, the associated constraints, and the associated costs. But every now and again you don’t. For example, you need to rationalize your supply base but do not know the optimal number of suppliers. In most products, you have to choose a number or run multiple scenarios with different numbers and then take the best one. Although this approach can be effective, it doesn’t help you understand why a certain solution is best or guide you to the best solution. A best of breed solution that manages the search algorithm can not only guide you to a potentially optimal solution but inform you of nearby solutions that are invalidated by your soft or uncertain constraints. This is very difficult for a platform optimization engine – since it generally cannot guide the search. The best it can do is run different scenario formulations, show you nearby answers, and identify constraint conflict sets. It’s a good approach, but for a strategic problem, the more you know, and the faster you know it, the better you are.

By now, you’re probably asking *does BoB have the upper hand*? Well, even though BoB can solve a slew of problems that POE cannot and it’s always theoretically possible to *tone down* a solution, whereas it’s not always theoretically possible to *built up* a solution, the reality is that, as I’ve said before, when it comes to optimization, one size does not fit all and using a sledgehammer on a finishing nail is not always effective. Furthermore, these are not your everyday problems. It often takes years to realize the savings from distribution network redesign, reverse auctions and sealed bid negotiations are generally not combinatorial exchanges, you do not redesign your transportation network after every sourcing event, most of your sourcing problems are traditional, most of your sourcing problems are of a manageable size with proper strategic sourcing, and if you don’t know what your constraints should be on a regular basis, you have deeper problems you need to solve first. That’s why an upcoming post will focus on POE, the everyday hero, in more detail. When combined with this post, you should have a better understanding of where each technology can be helpful to you.

Disclaimer II: Although this blog, including this post, is not sponsored by CombineNet and the author is not employed by, contractually engaged with, or affiliated with CombineNet, the author is going to report, in full disclosure, that CombineNet did allow the author to use one of their free registrations at INFORMS (of which they were a sponsor), as well as buying the author lunch.