To achieve our stated aims, we first collected data in mass and energy units on all intermediate and primary inputs, and on intermediate and final outputs for the manufacturing sites. Before starting with the onsite data collection we developed a questionnaire, asking for information on throughputs of various inputs and outputs. The questionnaire lists, for example, intermediate outputs such as AMF, cheese whey, casein fines (43 in total). These intermediate outputs are identical with the intermediate inputs. Primary inputs asked for (52 in total) are, for example, ingredients (such as salt), chemical usage (caustic, nitric acid, triplex sodium hypochlorite), energy (electricity usage, thermal energy consumption from black coal, lignite, gas, oil, LPG and biogas, cogenerated steam and waste heat), packaging (for example, kraft liner, cardboard, polypropylene, steel drums, nitrogen and carbon dioxide usage), refrigerant use (R22 and ammonia), and town water usage. Final outputs asked for (29 in total) are milk powders (skim and whole milk powder, butter milk powder, nutritionals, specialty powders, different types of MPC), cheese (dry salt and brine salt cheese, mozz type cheese and cream cheese), fat products (butter, fat blend), casein-based products (casein and caseinate) and whey products (whey powder, whey protein concentrate, whey fractions, lactose, lactalbumin, alamin and ethanol). Final outputs also include milk solids to waste, wastewater discharged to sewer and solid waste.
The data collection was predominantly done by site visits. Relevant data were extracted from onsite meters, data management systems (for example, SAP, Excel) and financial accounts (for example, expenditure data allow backtracking to mass and energy flows). Obtaining high-quality data is challenging as the majority of the mass and energy flows are captured only on a whole-of-plant basis, for example, thermal and electrical energy consumption and town water demand are usually not measured for separate processing steps. However, there are also mass inputs that can be allocated directly (in the qualitative prior) to specific products, for example, salt to cheese, or low density polypropylene for packing cheese. An additional challenge is caused by the intermediate product transfers between sites. There is a large variation of these product transfers among individual sites, while the overall amount of product transfers for all sites is only compared to the total quantity of final products.
Second, we set up a qualitative prior on the basis of extensive interviews with experts from the dairy industry. The qualitative prior reflects the structure of mass flow of all inputs and outputs. In addition to the scaling described above, we also weight the qualitative prior (with weights ranging between 0.001 and 1) in order to suppress some connections and emphasize others (compare with a weighting procedure applied by Müller and Djanibekov ([2009]) for estimating an agricultural model).
Dairy processing is ultimately a milk solids concentration process. Therefore, we start with identifying those intermediate and final outputs that require direct raw milk and whole milk as a primary input. This is straightforward for final outputs such as butter, different types of whey products, powders, cheeses and milk concentrates, but more complex for intermediate outputs, mainly due to the choice of intermediate product names and the variety of how processing sites manufacture their dairy products. For raw milk and whole milk inputs, we have identified 23 intermediate outputs in total, such as cream, homogenized milk, skim milk and whey cream. In these cases 1 is set where an input is required to produce an output, and 0 where this is not the case. A small fraction of milk solids enters the waste stream, that is, wastewater discharged to sewer or municipal household waste.
Some of the primary inputs are ingredients that can be allocated directly to final products: for example, lactose goes into milk powders, salt is used for butter, cheese and MPC, and acetic is used for MPC. In these cases we weight the qualitative prior elements with 0.01 because these ingredients can be expected to contribute less to final products than to intermediate products. Direct allocation is also possible for the majority of cleaning agents (caustic, nitric acid, triplex sodium hypochlorite), for example, triplex being used for cleaning caseinate processing equipment. Packaging material consists of the actual material (kraft liner, cardboard, polypropylene, steel drums) in which the product is contained in and - in the case of powders - nitrogen and carbon dioxide gas that is filled in the packaging material together with the product. Paper, paper cases and LDPE are assumed to be required for all products, while HDPE and some LDPE can be directly attributed to butter and cheese.
Energy inputs (electrical and thermal) are not subject to mass flow constraints as all other inputs. Therefore, we used additional process information for allocating electrical and thermal energy consumption to the final products.
Intermediate inputs are products that are required for producing intermediate and final dairy products. In total there are 43 intermediate inputs, and in our system these are transformed into intermediate outputs in 196 combinations. For example, AMF is potentially used in AMF, beta serum, butter rework, colostrums cream and milk, cream (high-fat and organic), whey AMF serum and whey cream. In addition, intermediate inputs are also used for producing final products that are sold to the market; for example, skim milk concentrate is used for MPC70, cheese dry salt and brine salt, mozz type cheese and cream cheese.
Whilst the above description is nowhere near exhaustive in explaining the entire qualitative prior, it serves as an illustration of the principles followed in constructing such a prior.