# 8.3.3 Consideration of a Nonlinear Usage Quantity and of a Product Structure with Loops

### Intended learning outcomes: Present the quantity of a manufactured product P as a nonlinear function of the usage quantity of a resource R. Identify possible solutions of issues entailed by a nonlinear usage quantity.

In the process industry, the quantity per, or usage quantity, corresponds to the selective use of starting materials to produce intermediate, end, or by-products.

The operation/process yield is the relationship of usable output from a process, process stage, or operation to the input quantity (compare [APIC16]).

Operation/process yield can often be expressed by a ratio, usually as a percentage. However, chemical and biological processes are subject to conditions that cannot always be predicted accurately (for example, external influences like the weather). In addition, the technologies and production processes used, as well as variations in the quality of the raw materials, have an effect on the consumption of resources that is not quantifiable in every respect. For example, excessive use may be made of certain materials in the startup phase of a process or in the course of the process — namely, as the produced quantity increases. In such cases, the usage quantity ceases to be a linear function of the quantity produced.

A nonlinear usage quantity is an operation/process yield that cannot be expressed by a linear function of the quantity produced.

Just as with the usage quantity, the duration of the process is no longer proportional to the quantity produced. Thus, the effective consumption could change, as shown in Figure 8.3.3.1. See also [Hofm95], p. 74 ff.

Fig. 8.3.3.1        Quantity of a manufactured product P as a nonlinear function of the usage quantity of a resource R.

In some cases, the nonlinear function for calculating the nonlinear usage quantities may be known in advance. The problem is then solved using a parameterized formula, rather than as a constant value for the usage quantity or quantity per attribute. In the event of a transition from the production structure to an order structure, the formula is evaluated using the parameter values associated with the order (e.g., the batch size), and the appropriate demand for the resource is thus determined. This procedure is exactly the same as described in Section 7.3 for one-of-a-kind production of products with many variants. There, formulas are linked with various attributes, and not just with the usage quantity and the operation load.

Most products with a product structure with loops are those that can be returned to the production process. These may be by-products (such as broken chocolate or energy in the form of steam or heat) or processing aids (catalysts, for example) that can be used for further production. It thus follows that the by-products or waste products are not subject to external demand, and their use can therefore be optimized internally. There are, however, certain quantity or time-related marginal conditions concerning usability (spoilage, deterioration) or storability and shelf life. Most of the soft­ware packages based on the conventional MRP technique, as described in Section 12.3, do not allow loops. This is because the technique deals with the individual items in the order of their low-level code. In a production structure with loops, the low-level code would be regarded as “infinite.”

One possible solution to this problem is to identify such items (by-products or waste products) and then to omit them from the structure-level code calculation or to allocate to them a maximum structure-level code. The MRP technique should then be used to schedule such by-products or waste products only at the end. At this time, all the demand is already known, as are also all the planned receipts in response to planned orders. Any net requirements for such by-products or waste products would then have to be produced or procured. Consequently, an additional production structure without further by-products should be allocated to each of these products. This is then converted into an order structure.

For the manufacture of chemical products, the features and qualities are determined by a multitude of parameters. Among others, there are the mixture proportions of the final product, temperature, holding time in the apparatus, etc. This often makes it difficult to plan the need for resources precisely and results in losses in production and energy during the commissioning phase.

Exercise: Process Train
In the following exercise, try to commission a very simplified continuous process, a process train of two manufacturing steps, and convert it to a steady operating state. As is often the case in practice, the criterion for product quality is the color of the products. Variation parameters are: the demand ratio to the raw materials and the holding time in the processors, which can be influenced by the demand quantity and the level. The goal of this task is to keep the amount of waste as small as possible.

## Course section 8.3: Subsections and their intended learning outcomes

• ##### 8.3 Processor-Oriented Resource Management

Intended learning outcomes: Explain campaign planning. Differentiate between processor-dominated Scheduling and material-dominated scheduling. Describe a nonlinear usage quantity and a product structure with loops.

• ##### 8.3.1 Campaign Planning

Intended learning outcomes: Explain campaign planning using an example of a process chain in chemical production. Identify campaign cycles for the example and a minimum campaign of one day’s production.

• ##### 8.3.1b Synchronizing Process Stages

Intended learning outcomes: Describe how the process stages could be synchronized.

• ##### 8.3.2 Processor-Dominated Scheduling versus Material-Dominated Scheduling

Intended learning outcomes: Differentiate between processor-dominated scheduling and material-dominated scheduling. Produce an overview on the use of the MRP II / ERP concept or of the lean / just-in-time concept compared to the processor-oriented concept.

• ##### 8.3.3 Consideration of a Nonlinear Usage Quantity and of a Product Structure with Loops

Intended learning outcomes: Present the quantity of a manufactured product P as a nonlinear function of the usage quantity of a resource R. Identify possible solutions of issues entailed by a nonlinear usage quantity.