Quant network

Any quant is linked with other quants. The quant gets its supplies from them or delivers to them. Along the link travels a certain quantity of material. Additionally a link describes the dependencies of the two quants, for example minimum or maximum offset time. Quants and links form the quant network. This link type is called a quant link. Quant links may be added or deleted at any time, depending on the process of satisfying the given constraints. 

Generation of quant network the product flow is discretisized... 

The intermediate products (process steps) which are necessary for fulfilling an order can be derived from the existing quant network. 

There is a general operator available to reduce throughput times. This is done by adding artificial limits of perishability. Because of these limits some links in the quant network are not necessary any more (see Figure 4.10). So this operator works in three steps ... 

In principal the generation of the quant network is done by decomposing the overall decision problem into smaller sub-problems by looping around nested recursive functions that are used to divide the search tree into the parts that are useful to... 

In the beginning there is a general loop to decide if more lot sizing procedures should be applied to the existing quant network to meet the constraint of the minimum batch sizes of products. Then the quant network is examined, free usable stocks and free quantities of quants are made available. The material balances of any quant are calculated and decisions are taken whether quants require further explosions of their BOM. Structures for a fast cycle checking, sorting of existing quants and quant links and forecast intervals are built up. A recalculation of the due dates for all quants - also the ones of orders - can be done if specified by the user. 

In example 2 a simpler approach is used to correctly handle backward cycles (co-products). The difference to the forward cycle is that the co-product quant B created by a quant A cannot be used as predecessor of A, because cycles in the quant network are not allowed (violates the cause effect principle). A model can avoid this cycles using aggregation in such a way that cycles are within these quants A and B (see Figure 4.15). 

The user is allowed to define a cost model for controlling the behavior of the optimizers. Rules can be derived from costs, times, resource utilization or lead times. Also parts of the quant network can be deleted again if they are identified as not optimal by applying user defined evaluation procedures. 

The static lot sizing has several positive aspects. Big quant networks are transformed into smaller ones thus making faster calculations possible still fulfilling all constraints. The objective function can be reduced to contain only the changeover costs and the stock costs with the aim to find a trade off between these two costs (see Figure 4.17). 

Berdnik, VY. et al., Characteristics of spherical particles using high-order neural networks and scanning flow cytometry, ]. Quant. Spectrosc. Radiat. Transf., 102,62,2006. 

The product flow connects the products to the product network. Here BOMs (bills of material), work flows and additional information how to control the generation of quants (see Figure 4.1) and how to enumerate all necessary alternative BOMs are represented in this net. Important data are ... 

Comparisons show that the quant-based combinatorial optimization is a leading approach when it comes to big production networks with many constraints which are typical for the chemical or pharmaceutical industry. 

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