Reprinted from Compass News, number 5, fall 1997
Wastes from chemical production plants often contain highly toxic or at least harmful substances. Many of these wastes need special post-processing or even decomposition at very high temperatures. A major European pharmaceutical and chemicals company runs a powerful special waste furnace for this purpose. Mixed-integer linear programming (MILP) helped to run the furnace with maximum throughput and in a most economic mode.
Temperatures of 1200 degrees Celsius are needed to burn the substances, delivered in barrels, one way or reusable, containers of many different sizes, or in liquid or pasteous form. The principle of the furnace is simple. It consists mainly of a huge, slightly inclined tube, pivoting about its main axis, in which the wastes are slowly moved forward by the rotation of the tube. An oil burner reaching into the front end propels a flame through the length of the tube. The remainders can be categorized as ashes, slag and gas. The solid remainders, ashes and slag, are collected separately in containers; the gaseous substances are post-treated in a separate vertical fire chamber and are then finally filtered.
Problems arise when more than one type of waste is processed at the same time, which is normally unavoidable if a reasonable throughput is targeted. Combinations can lead to interactions between chemical components, which in turn can have negative effects on the equipment. Furthermore, law restricts the amount of each substance per cubic meter of exhaust gas. All this requires a careful selection of the process mix. However, the mix is kept constant for a certain time, usually a shift or half a shift. So, using the best possible combination during one time slice can lead to a low throughput during the next one, due to an accumulation of noncombinable wastes.
It is at this point that a powerful operations research method comes into play: MlLP. The complexity of the problem, somewhere between optimization and planning, has been known from the beginning as being non-trivial. Thus, an effective approach to the solution called for a powerful optimization tool. AMPL Plus was chosen as the modeling tool, CPLEX for the optimization kernel, and the familiar-to-everybody Excel to create the user interface.
The approach taken to address the problem took five steps. First, we needed to see what the responsible managers consider as "optimal". Of course, without knowing, they asked for a multicriterial objective. Throughput must be at the highest possible level. Mix changes from shift to shift must be as small as possible (to avoid excessive stock re-arranging). Burnoff of the important slag layer in the furnace tube must be at the lowest possible level. Filter load for the different waste components must be as even as possible. As might be expected, lots more wishes, many in competition to the others, were put forward.
Second, we did not choose a multicriterial objective weighting scheme, but picked the most important requirement as the target function: economy. This meant defining the objective as throughput. The other goal variables were taken care of by narrowing their bandwidth by constraints.
Third, time had to be quantified into reasonable segments. We took an hour as the minimum unit. During this time the mix is expected to be constant. The planning period was restricted to a maximum of 4 shifts, 8 hours each. Thus the complexity of the integer part is of the magnitude 4 x 8 x (4 out of 50).The latter factor expresses the fact that 4 different waste forms can be processed at the same time in parallel, and 50 is a reasonable average number of different wastes in stock.
Fourth, constraints were subdivided into two groups: logistic or handling restrictions, and chemical and physical restrictions. On one hand, the maximum process per time unit is limited by the number of process conveyors (there are 2) and the number of pumps for liquid and pasteous forms (again, there are 2) as well as their power. On the other hand, handling barrels and boxes can be time consuming, especially if they have to be put onto the conveyor with a loading crane. Thus, handling time again limits the maximum throughput.
At this point an intricate problem showed up. If one only picks out the wastes that are best to combine for the next time slice, this leads to strong segmentation of the stock because of small remainders of some of these wastes. This then causes difficulty in selecting the appropriate wastes from the stock mix. The solution to this, the fifth step, was achieved by optimizing over more than one shift and weighing the first one highest, the last one lowest. Thus, because there are constantly new deliveries of waste coming in, the next shift has to be optimized again shortly before it begins.
The prototype of our model has now been tested in the real world. Stock lists were typed in by hand, since there was not yet any connection to the existing process control system. The recommendations to the shift personnel as to which wastes to burn during the next time slice resulted in a significantly better overall usage of the furnace and in more evenly distributed filter load of the gaseous substances.
It was estimated that throughput of the waste treatment was increased by approximately 20% and the slag burnoff in the main chamber was much lower with the optimized mix. While the optimization package has yet to go on-line with the process control system, this project demonstrated a very successful application of MILP to solve a difficult problem.