Explicit Modeling of Multi-Product Customer Orders in a Multi-Period Production Planning Model
In many industries, companies receive customer orders that include multiple products. To simplify the use of optimization models for planning purposes, these orders are broken down, and the quantities of each product are grouped with the same products from other orders to be completed in the same pe...
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MDPI AG
2024-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/19/3029 |
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| author | Cristian D. Palma Francisco P. Vergara Sebastián Muñoz-Herrera |
| author_facet | Cristian D. Palma Francisco P. Vergara Sebastián Muñoz-Herrera |
| author_sort | Cristian D. Palma |
| collection | DOAJ |
| description | In many industries, companies receive customer orders that include multiple products. To simplify the use of optimization models for planning purposes, these orders are broken down, and the quantities of each product are grouped with the same products from other orders to be completed in the same period. Consequently, traditional production planning models enforce minimum demand constraints by product and period rather than by individual orders. An important drawback of this aggregation procedure is that it requires a fixed order fulfillment period, potentially missing opportunities for more efficient resource use through early completion. This paper introduces a novel mathematical formulation that preserves the integrity of customer orders, allowing for early fulfillment when possible. We compare a traditional linear programming model with a new mixed-integer programming approach using a sawmill case study. Although more complex than the traditional model, the proposed formulation reduces costs by approximately 6% by enabling early order completion and offers greater flexibility and control over the production process. This approach leads to better resource utilization and more precise order management, presenting a valuable alternative to conventional production planning models. |
| format | Article |
| id | doaj-art-ae1d82bba09949229f84656ea0949fda |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-ae1d82bba09949229f84656ea0949fda2025-08-20T02:16:50ZengMDPI AGMathematics2227-73902024-09-011219302910.3390/math12193029Explicit Modeling of Multi-Product Customer Orders in a Multi-Period Production Planning ModelCristian D. Palma0Francisco P. Vergara1Sebastián Muñoz-Herrera2Facultad de Ingeniería, Universidad del Desarrollo, Concepción 4040418, ChileDepartamento de Ingeniería en Maderas, Facultad de Ingeniería, Universidad del Bio-Bio, Concepción 4051381, ChileFacultad de Ingeniería, Universidad del Desarrollo, Concepción 4040418, ChileIn many industries, companies receive customer orders that include multiple products. To simplify the use of optimization models for planning purposes, these orders are broken down, and the quantities of each product are grouped with the same products from other orders to be completed in the same period. Consequently, traditional production planning models enforce minimum demand constraints by product and period rather than by individual orders. An important drawback of this aggregation procedure is that it requires a fixed order fulfillment period, potentially missing opportunities for more efficient resource use through early completion. This paper introduces a novel mathematical formulation that preserves the integrity of customer orders, allowing for early fulfillment when possible. We compare a traditional linear programming model with a new mixed-integer programming approach using a sawmill case study. Although more complex than the traditional model, the proposed formulation reduces costs by approximately 6% by enabling early order completion and offers greater flexibility and control over the production process. This approach leads to better resource utilization and more precise order management, presenting a valuable alternative to conventional production planning models.https://www.mdpi.com/2227-7390/12/19/3029production planningcustomer ordersmulti-product ordersmathematical modelingmixed-integer programming |
| spellingShingle | Cristian D. Palma Francisco P. Vergara Sebastián Muñoz-Herrera Explicit Modeling of Multi-Product Customer Orders in a Multi-Period Production Planning Model Mathematics production planning customer orders multi-product orders mathematical modeling mixed-integer programming |
| title | Explicit Modeling of Multi-Product Customer Orders in a Multi-Period Production Planning Model |
| title_full | Explicit Modeling of Multi-Product Customer Orders in a Multi-Period Production Planning Model |
| title_fullStr | Explicit Modeling of Multi-Product Customer Orders in a Multi-Period Production Planning Model |
| title_full_unstemmed | Explicit Modeling of Multi-Product Customer Orders in a Multi-Period Production Planning Model |
| title_short | Explicit Modeling of Multi-Product Customer Orders in a Multi-Period Production Planning Model |
| title_sort | explicit modeling of multi product customer orders in a multi period production planning model |
| topic | production planning customer orders multi-product orders mathematical modeling mixed-integer programming |
| url | https://www.mdpi.com/2227-7390/12/19/3029 |
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