Modelling an agri-waste biofuel supply chain

By Dr. Yasel Costa, ZLC Professor.

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Growing crops purely to convert them into bio-fuel rather than food is not an obvious environmental gain. Converting wastes and residues arising from crops, on the other hand, seems highly desirable.  But optimising a supply chain for these wastes, so that they work in environmental, economic and social terms, is not straightforward as I, working with colleagues Marcela Maria Morales Chavez and Willian Sarache in Colombia, have discovered.

The flows we have been modelling arise from coffee plantations, but the issues we have been analysing are generic to many actual and potential waste conversion flows. In a nutshell (or perhaps millions of them) there are an awful lot of variables, and creating an exact method for optimisation, within a usable timescale, is nigh-on impossible (technically, ‘intractable’).

The agricultural wastes involved are generated, usually, at harvest time (with some crops there may be other generators, for example if the crop has a pruning or thinning cycle). The timing of this is uncertain – it depends on the climate variations through the growing season and, in some cases, whether the ground conditions can support harvesting; for coffee, altitude is a factor. The yield (of crop and of waste) may also vary according to the season’s growing conditions. But for cost-effective production of bio-fuels the convertors, refiners/blenders and their downstream retail distribution requires a balanced and constant flow of raw material during the ‘campaign’. (A refinery may, of course, be processing other wastes from other crops at different times of the year).

So we need to plan a steady flow of material to the refinery to ensure the latter is working at close to most efficient production for as long as possible. But we can’t simply stockpile material – that has its own costs, and the wastes may deteriorate.

We are not just looking at a single flow, either. Typically, one would be looking to gather and pre-process the wastes, for instance by drying and compacting to make transport more efficient. That ideally will be close to the farm or plantation, but ‘close’ is a flexible term and may involve hauling unprocessed waste many miles, perhaps through difficult terrain. The transport modes and vehicles hauling from farm to pre-processor, and from the latter to the refinery, may vary – it may not be possible, for example, to use large trucks in mountainous areas (coffee quality degrades if temperatures are too warm, so the best plantations, at least in South America, are typically at several thousand feet above sea level).

We set ourselves the challenge of creating a model for agricultural waste-based biofuel supply chains. This would have three interlinked objectives – to optimise the locations (and number) of gathering/preprocessing, centres and biorefineries; to ensure the adequate flow of material to meet demand at each stage, and to address route planning for an inevitably heterogenous fleet of vehicles. This Location-Inventory-Routing Problem or LIRP is well recognised and widespread.

There is, it became clear to us, a further complication. All models have to make simplifying assumptions, and most conventional modelling of LIRP assumes that the various processing facilities are fixed, in their physical capacity, their locations, and the timescales over which they are operational. None of those assumptions are necessarily true, or optimal – any given waste stream typically ramps up, peaks, and declines over a period of weeks or months so there is no obvious reason why a particular facility within a network should have to be operating at the beginning of the campaign, or see it out to the end, or not reduce or increase its capacity during the season – a Dynamic Facility Strategy. (Although we didn’t specifically consider this instance, it may be that pre-processing facilities, in particular, could be mobile, moving from farm to farm as the harvest develops at different altitudes or climates. We may visit this aspect in future work).

So, there are a lot of variables, many of which count as ‘stochastic’ – in the mathematical sense that, whilst not being strictly random, they can be validly modelled as if they are. So the classic approach is through Mixed-Integer Non-linear Programming.

But there is a problem – such an approach, to a problem on this scale, takes an awful lot of computational power and, perhaps more importantly, time: there is really no benefit in deriving a mathematically optimal solution to last year’s harvest – we need a close approximation for this year’s situation. So, we have developed a strategy to convert our original model into a Linear Programming formulation, with the capability to be efficient in run-time, and to be highly competitive, in terms of solution quality, with ‘exact method’ approaches.

The model is necessarily complex, but this is a complex business. We believe we have captured the essentials: we have the four stages of production (farms, gathering centres, biorefineries, blending facilities); multiple types of agricultural wastes (from alternative crops, or because wastes may be generated both at harvest, and separately if the crop has a pruning or thinning-out stage); multiple time periods. Suppliers (farms) aren’t tied to one specific gathering station, nor those to a specific refinery, during the campaign. Inventory decisions reflect the refineries’ requirements for raw materials, obviously, but also the perishability or degradation of wastes awaiting processing, and the storage capacity of gathering centres (storage costs). The model also recognises the time-value of money, and the fact that increasing capacity in gathering stations or biorefineries may not produce economies of scale – in fact, fixed and variable costs of processing may increase. That is a major reason why this essentially non-linear problem needs to be ‘linearised’.

For the mathematically inclined, our optimisation model is what is called ‘NP-hard’, and so we used a two-phase heuristic approach. We designed a set of 15 problems or scenarios at small, medium and large scales. In the first phase we define the network structure based on the opening, varying capacity, and closing of gathering/preprocessing facilities and biorefineries. Then we further optimise around the variables related to materials flow, of biomass as an input and biofuel as an output. That includes managing inventory levels at gathering/preprocessing stations, and optimising vehicle routing for waste collection from farms/plantations, between gathering stations and biorefineries, and from those to blending stations (because biofuels are rarely used ‘neat’).

We can then compare our results with ‘exact’ solutions for the particular scenarios to see how close we come to the ‘true’ optimum, bearing in mind that real life, and the harvest season, is too short to calculate exact solutions for every possible combination of variable values, especially since we are trying to optimise across environmental and social, as well as purely economic, factors – carbon emissions, rural employment and so forth.

Our modelling has turned out to be very competitive both in terms of computational time and in approximation to ‘exact’ calculated results, outperforming commercially available software packages for this task.

Perhaps the most important finding is that a Dynamic Facility Strategy, whereby gathering centres and biorefineries are allowed to open, expand or contract, or close as appropriate within the campaign, if it can be properly modelled and managed, really does facilitated greater biofuel production, a more profitable supply chain, more jobs created, and, slightly more distantly, a better use of land so that biofuel production is taking up less of the agricultural land otherwise required for food production.

At the same time we have also begun to get a handle on the impact of uncertainty (around the likely availability of agricultural wastes) on the economic performance of waste-stream biofuel supply chains. This suggests some lines for further research, especially where input parameters, such as biofuel demand, and mass-fuel conversion rations, are data-deficient.

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