To qualify for mathematical optimization, a problem should have:
• An objective function, which needs to be minimized or maximized (such as profit, cost, or waiting time for trains).
• Constraints that limit the full exploitation of the objective function (such as the available capacity).
• Variables – of actual decisions to be taken – within the objective function and constraints (such as the amount of money you want to invest in a certain fund, or the question of whether or not to schedule a particular job on a particular machine).
Traveling Salesman Problem: nothing compared to yours?
Here's a rule of thumb that goes for most optimization problems: the number of possible solutions increases exponentially when you add instances. This is illustrated by the well-known Traveling Salesman Problem, which states a salesman should visit N cities – each only once – after which he must return to his hometown, minimizing the distance traveled. Now, if N = 4, there are 12 possible routes. But if N = 10, our salesman suddenly has 181,440 potential pathways. And once we reach N = 60, the number of roads home is 1080, which almost equals the number of atoms in the universe. Even if you've got the fastest supercomputer, it would take over 1057 years to calculate all possible answers and pick the best one.
On top of that, the Traveling Salesman Problem in no way reflects the size and complexity of the issues many companies face on a day-to-day basis. So, what should you do?
How to crack your supply chain puzzle
Good news: you don't need a supercomputer to crack your type of puzzle. Don't underestimate your manual planners: depending on the complexity of your optimization problem, they can reach a solution that is 70% – 90% as good as its optimal counterpart. If you want to increase this percentage, only optimization software can help you, as it's capable of evaluating thousands of solutions within seconds to select the best one among them.
Considering the above, isn't optimization software always the best way to go? Well, not necessarily. Before you decide whether implementing such software really is the right solution for your company, you need to consider some key aspects:
The quality of software can differ significantly. Basically, you need to look at two aspects: 1) how easy is it to adapt the software in such a way that it fits perfectly with your constraints and variables, and 2) how close does the software get to an optimal solution within a reasonable amount of time? A low fit, for example, would require you to have sufficient resources for adapting the plan. And if the software provides a better solution but takes a long time to calculate it, a manual solution might be more practical after all.
Your problem should be complex enough and needs to be solved with different instances regularly. Again, don't rule out your planners: optimization software doesn’t capture the ‘soft’ knowledge that planners possess (e.g. this order should be handled first, as it was placed by one of our most important clients).
Keep in mind that software calculates the best planning in terms of your objective, and the answer might be neither simple nor straightforward. Therefore, software planning may differ each day and create confusion on the work floor. This can cause productivity to drop lower than when you’d have a manual planning. So if your problem isn't that complex, optimize the simplicity of your way of working – not your planning!