Mixed-Integer Linear Programming (MILP) Benchmarks Based on a Multilevel Supply Chain of a Fictive Cellphone Company

Description

The underlying benchmark instances model the supply chain of a fictive company producing and selling cellphones and accessories of different types. The instances are formulated as typical mixed-integer linear optimization problems in the standard MPS format.

Detailed Scenario Description

The planning horizon is subdivided into time periods (also called time buckets) of one week. A network of different locations such as warehouses, factories, distribution centers and customers with a flow of products (components and final products) is the basis. After procurement of components and transport to the factory, the final products are produced consuming the components and additional restricted resources. Via a main distribution center, the products are further transported to local distribution centers where they are stored until they are delivered to satisfy customers' demand. Late delivery or non-delivery is possible. The objective is to minimize the sum of all costs.

Instance Sets

Currently there are three sets of generated instances available. The variable and constraint names in these MPS files are generic, i.e., x0, x1, x2, ..., and c0, c1, c2, ....

public_mps: These instances differ mainly in the size of the network. They are named in the format abc_d.mps. The first number a specifies the number of time periods, whereby the decisions of the first b periods must be discrete. The number of customers is given by c. The last number d is used as factor for lot sizes. For this set of instances exist also decompositions in .dec-format, which can be found in folder public_dec. They are decomposed according to time periods (b), locations (L), and products (P). The number of blocks is either determined by the number of different time periods, locations or products (0), or they are remerged in two (2) or four (4) blocks.

varymatrixrhs_bounds: These instances are similar to the above-mentioned public_mps instances, with specific values of a=6, b=3, c=40, and d=20. Accordingly, all these instances contain the same number of variables (27710, among which 400 are binary, 400 are general integers, and 26910 are continuous), the same number of constraints (16288), and the same ordering of these variables and constraints. Some entries of the constraint matrix, right-hand side vector, and variable upper bound vector vary across these 50 instances.

unbd_semicont: In this set of instances, some of the production and transportation variables are semi-continuous variables with infinite upper bound modeled with indicator constraints. They are named in the format abcd11einff_inf.mps. Numbers a to d are the same parameters as in public_mps. Number e specifies the minimum lot size for production variables and number f specifies the minimum lot size for transportation variables.

Requirements

The benchmark instances are compressed in the .gz format, thus you will need a file archiver software to unpack them. Furthermore, you will need a mathematical programming solver to read and to solve files in the standard MPS format.

Download and Installation

Download and unpack the archive files. Then try to solve the resulting .mps files with a mathematical programming solver.

Known Issues

No known issues.

How to obtain support

Create an issue in this repository if you find a bug or have questions about the content.

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Contributing

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Code of Conduct

Please refer to the code of conduct of the parent repository.

License

Copyright (c) 2023 SAP SE or an SAP affiliate company. All rights reserved. This project is licensed under the Apache Software License, version 2.0 except as noted otherwise in the LICENSE file.