Decomposition 

Use

Using the decomposition methods can reduce optimization runtime and memory requirements in Supply Network Planning (SNP). Decomposition may also represent the only way for the SNP optimizer to find a feasible solution in the event of large discrete problems.

Decomposition is a flexible tool for balancing the tradeoff between optimization quality and required runtime. When runtime is unrestricted, the SNP optimizer usually provides a better (optimal) solution without decomposition; however, when a fixed runtime has been specified, using decomposition could assist the optimizer to find a better or, in fact, feasible solution.

Features

Decomposition Methods

The following decomposition methods are available: Time decomposition, product decomposition, and resource decomposition. You can use time decomposition as well as product decomposition in conjunction with the linear and discrete optimization methods. It is only advisable to use resource decomposition in conjunction with discrete optimization.

·        Time decomposition speeds up the solution process by dividing the source problem into a series of partial problems. The system then solves these partial problems sequentially.

·        Product decomposition speeds up the solution process by forming product groups. The system solves the complete model for one product group at a time according to the window size selected. The rule of thumb is as follows: The smaller the window size, the less time it will take the system to find a solution, but the larger the window size, the better the quality of the solution found.

·        Resource decomposition speeds up the solution process by analyzing the material flow and basic optimizer decisions about production, procurement, and transportation to determine a resource sequence. The optimizer can then create sub-problems for the individual resources, which are solved in sequence. The optimizer makes decisions in every sub-problem that cause the resource to be loaded.

It is particularly advisable to use resource decomposition if the production processes always load the resources in a similar sequence. Resource decomposition does not reduce memory requirements. If you would like to reduce memory requirements, you could use time decomposition alongside this decomposition method. You cannot use resource decomposition in conjunction with strict prioritization If you want to use product and resource decomposition together, the system carries out the resource decomposition first. The product decomposition then tries to improve upon the results of the resource decomposition.

SNP Priority Profile

You can use the SNP priority profile to define priorities for product and resource decomposition, that is, you can change the sequence in which the optimizer groups and plans products and resources in partial problems.

For product decomposition, the sequence of planning is normally based on the costs for non-delivery and the total demand quantity of the product. You can use the priority profile to assign priorities for important products and, thus, control the sequence for planning. The following rules apply:

·        The system groups the products into partial problems according to their priorities and their dependencies defined in the bill of materials. If a partial problem contains products with different priorities, due to product dependencies, the partial problem takes on the priority of the product with the highest priority (that is, the priority with the lowest number).

·        The system plans partial problems with different priorities separately, so no overlapping occurs.

·        If many products have the same or no priority, division into partial problems and the sequence of planning are also based on the costs of non-delivery and the product quantity.

For product decomposition, you can also control division into partial problems using window size, which you can specify for the decomposition methods in the SNP optimizer profile. If you select a small window size, the optimizer plans products with the same priority separately, since the partial problems are very small (0% = separate planning). If you select a larger window size, the optimizer plans products with the same priority together in one partial problem (99% = planning together in one partial problem).

Note that, due to prioritization, the optimizer no longer exclusively considers the defined costs when covering demand. Instead, the system plans the products with the highest priority first. The system only considers costs when solving the individual partial problems.

For resource decomposition, the planning sequence is generally predetermined by the production process models (PPMs) or production data structures (PDSs).  If the sequence is not clear, or if you want another sequence, you can change it by assigning priorities to resources. In this way, you can reverse the standard order that the system uses to plan the assembly and then the end products, or you can plan important resources that must be utilized for cost reasons first.

Activities

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       1.      You specify a decomposition method in the SNP optimizer profile. To do this, select SNP Optimizer Profile in the SNP Customizing or in the current settings, and then select the Solution Methods tab page.

       2.      If necessary, specify a priority profile in the current settings of SNP, under Define SNP Priority Profiles, and assign it to the decomposition methods on the Solution Methods tab page.