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Solving an Assignment Problem

This section presents an example that shows how to solve an assignment problem using both the MIP solver and the CP-SAT solver.

In the example there are five workers (numbered 0-4) and four tasks (numbered 0-3). Note that there is one more worker than in the example in the Overview .

The costs of assigning workers to tasks are shown in the following table.

The problem is to assign each worker to at most one task, with no two workers performing the same task, while minimizing the total cost. Since there are more workers than tasks, one worker will not be assigned a task.

MIP solution

The following sections describe how to solve the problem using the MPSolver wrapper .

Import the libraries

The following code imports the required libraries.

Create the data

The following code creates the data for the problem.

The costs array corresponds to the table of costs for assigning workers to tasks, shown above.

Declare the MIP solver

The following code declares the MIP solver.

Create the variables

The following code creates binary integer variables for the problem.

Create the constraints

Create the objective function.

The following code creates the objective function for the problem.

The value of the objective function is the total cost over all variables that are assigned the value 1 by the solver.

Invoke the solver

The following code invokes the solver.

Print the solution

The following code prints the solution to the problem.

Here is the output of the program.

Complete programs

Here are the complete programs for the MIP solution.

CP SAT solution

The following sections describe how to solve the problem using the CP-SAT solver.

Declare the model

The following code declares the CP-SAT model.

The following code sets up the data for the problem.

The following code creates the constraints for the problem.

Here are the complete programs for the CP-SAT solution.

Except as otherwise noted, the content of this page is licensed under the Creative Commons Attribution 4.0 License , and code samples are licensed under the Apache 2.0 License . For details, see the Google Developers Site Policies . Java is a registered trademark of Oracle and/or its affiliates.

Last updated 2023-01-02 UTC.

A New Method to Solve Assignment Models

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• DOI: 10.1016/j.trb.2021.05.018
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A new transit assignment model based on line and node strategies

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Creating Material Assignments and Component Allocations

After completing this lesson, you will be able to create material assignments .

Material Assignment

You use the material assignment function to determine which material is to be produced with a routing or rate routing. Based on this assignment, the routing can be used for sales and operations planning, material requirements planning, production order creation, and product costing for this material.

A material master record must exist in the system for the material to be produced. It requires a material type that is allowed for assignment to a routing or rate routing.

Material Assignment — Scenarios

Materials can be linked to routings for the following scenarios:

• You can use the same routing to produce several different materials. Each product has its own unique BOM but is manufactured by a common set of activities with the same standard times. For example, both red and green chairs can be produced using the same routing.
• The material and routing can belong to different plants. For example, the planning plant and production plant may not be the same.

Material assignment can be carried out in the following ways:

If you create a routing for a specific material, the system automatically performs the material assignment. No further settings are necessary, and for every order created the system identifies this routing assignment and uses the appropriate routing to create the order.

If you create a non-material-specific routing or a group routing, you can use the material assignment function. When you choose the Material Assignment button in the header of the routing, you can view a list of all the materials that are assigned to use this routing in order to produce them. Using this function allows you to assign more materials to the list. This also applies to using a routing created for one material to produce a different material. The assignment can be for a material in a different plant, which allows you to plan production in one plant and produce in another.

A production version specifies the production technique that can be used to produce a material. It specifies the BOM and routing used for production with date and lot size validities.

Component Allocation

Now let's have a look at the possible component allocation. Be aware of the following: you are able to predefine a routing and at a later stage you do the assignment of a material BOM.

The following data must exist in the system for component allocation:

• The operations in the routing
• The master record for the material to be produced
• The BOM for the material to be produced

Component Allocation and Material Assignment

You can assign and display material components for separate operations in the material component overview. For a clearer overview, you can use different criteria to filter or sort the material component list.

You perform the following actions for allocating components and assigning materials:

• Assign a new component.
• Delete and reassign material assignments.
• Navigate between multiple operations.

The system automatically assigns (default) material components in a BOM (that are not assigned to an operation in the routing) to the first operation when you create a production order.

You can assign each item on the BOM to only one operation. Items that have quantities of more than one and need to be assigned to more than one operation must be adjusted in the BOM to allow this type of allocation. For example, BOM item 10 has two pieces; one is used in operation 20 and the other in operation 40. This will require BOM item 10 to be split into two BOM items, each with a quantity of one, for example, item 10 and item 15. You can then allocate item 10 to operation 20 and item 15 to operation 40.

According to the item category of the assigned components, you can make further decisions about how they are to be processed, for example, backflushing of stock items or cutting the size of variable-size items.

By repeating this process, you can assign material components from several BOMs or alternative BOMs to the same routing. In this case, when you create a production order, you select the BOM and, therefore, the material components that need to be assigned in the production order. The system can do this automatically depending on the system settings.

Variable Size Item

When you maintain the BOM, the final measurements are specified for the items of a variable size.

If you require a large cutting measure for producing this BOM item, you can specify this when you assign the operation. Only those items involved in material staging are assigned these measurements. Inventory management reads the measurements from the BOM.

Create material assignments

Watch the video and understand material routing assignments.

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Generating method and application of basic probability assignment based on interval number distance and model reliability

• Soft computing in decision making and in modeling in economics
• Published: 01 November 2023
• Volume 28 , pages 2353–2365, ( 2024 )

Cite this article

• Junwei Li 1 ,
• Baolin Xie 1   na1 ,
• Yong Jin 1   na1 &
• Lin Zhou   ORCID: orcid.org/0000-0002-2700-834X 1  

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In the Dempster–Shafer (D–S) evidence theory, how to transform the objective data in reality into the basic probability assignment (BPA) is still an open issue. Based on this problem, a new method of generating BPA based on interval number distance model and reliability is proposed. First, construct the interval number model under each attribute. Second, calculate the interval number distance between the test sample and the interval number model and convert it into the initial basic probability assignment (IBPA). Thirdly, the final BPA is obtained by discounting the IBPA by constructing the comprehensive reliability from the static reliability and dynamic reliability of the interval number model. Finally, the Dempster combination rule is used to fuse the final BPA one by one, and the decision is made according to the fusion result. The ten-fold cross-validation results show that the classification accuracy under the three data sets is higher than other methods, and the classification accuracy of the Iris data set is 0.9733. At the same time, it is verified that the proposed method still has good effectiveness and robustness in the incomplete information environment.

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Acknowledgements

The work is partially supported by the National Natural Science Foundation of China (Grant No. 61771006), Programs for Science and Technology Development in Henan Province of China (Grant Nos. 222102210002, 222102210004) Key Research Projects of University in Henan Province of China (Grant Nos. 20B510001, 21A413002), Innovation and Quality Improvement Program Project for Graduate Education of Henan University (Grant No. SYL20060143).

The authors have not disclosed any funding.

Author information

Baolin Xie and Yong Jin have contributed equally to this work.

Authors and Affiliations

School of Artificial Intelligence, Henan University, Zhengzhou, 450046, Henan Province, China

Junwei Li, Baolin Xie, Yong Jin & Lin Zhou

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Correspondence to Lin Zhou .

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Li, J., Xie, B., Jin, Y. et al. Generating method and application of basic probability assignment based on interval number distance and model reliability. Soft Comput 28 , 2353–2365 (2024). https://doi.org/10.1007/s00500-023-09325-z

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Accepted : 18 September 2023

Published : 01 November 2023

Issue Date : February 2024

DOI : https://doi.org/10.1007/s00500-023-09325-z

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