Explicit Modeling of Multi-Product Customer Orders in a Multi-Period Production Planning Model

Cristian D. Palma (), Francisco P. Vergara and Sebastián Muñoz-Herrera
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Cristian D. Palma: Facultad de Ingeniería, Universidad del Desarrollo, Concepción 4040418, Chile
Francisco P. Vergara: Departamento de Ingeniería en Maderas, Facultad de Ingeniería, Universidad del Bio-Bio, Concepción 4051381, Chile
Sebastián Muñoz-Herrera: Facultad de Ingeniería, Universidad del Desarrollo, Concepción 4040418, Chile

Mathematics, 2024, vol. 12, issue 19, 1-13

Abstract: 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.

Keywords: production planning; customer orders; multi-product orders; mathematical modeling; mixed-integer programming (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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