Optimization & operations research

An optimization model does not settle for a solution that looks good. It looks for one that can be proven best.

Which plant serves an order, which product a line runs, which supplier a fuel comes from. Looked at one by one, each is a reasonable decision. Taken together, they produce a combination far better than anything found by hand.

When you actually need optimization

If these three signs show up together, you have an optimization problem.

The decisions are coupled. The production plan changes the procurement decision, which changes cost, which in turn changes the production plan. That loop cannot be closed by hand.

There are too many options to try. A three-month planning exercise at MMK involved more than 4,000 open orders with an average of nine raw material candidates each. The resulting combinations ran into the hundreds of thousands.

The objectives conflict. Maximizing profit lowers demand fulfillment; raising capacity utilization creates inventory cost. Someone has to decide how much weight each objective carries, and that decision should be based on numbers.

How we work

We write the problem down first. Which decisions are being made, which constraints can never be violated, what exactly are we improving? This is usually the longest step: some of what the floor calls a rule turns out to be habit, and some real constraints are things everyone knows but nobody wrote down.

We separate hard constraints from soft ones. A kiln’s capacity cannot be exceeded, so that is a hard constraint. A safety stock level can be breached at a known cost. This distinction directly decides whether the model finds a solution at all.

We build multi-objective. A model locked to a single objective is not accepted on the floor. At Çimsa, profitability, order fulfillment and capacity utilization are weighted per scenario. At MMK the objective function is lexicographic: profit first, then the number of distinct raw materials used.

We build a scenario layer. A model is most useful when it can answer “what happens if we raise this capacity” with a number.

The methods we use

Mixed-integer programming is the backbone of most problems. We use weighting and lexicographic ordering for multi-objective work, and decomposition techniques on large problems. Our solver is IBM ILOG CPLEX. Models are written in OPL and connect directly to the database.

Handover

Our aim is for the company to run the process itself once the project ends. At Çimsa the team was trained in mathematical modelling and optimization, and the model became something they run in-house.

Hand an optimization system to a team that cannot operate it and it gets shelved within months. So we plan training into the project from the start instead of adding it at the end.