Title: Exact approach for the aggregate production plan problem of machine-dependent production systems by considering stochastic parameters

Authors: Juan Camilo Paz; John Willmer Escobar; Rafael Guillermo García-Cáceres

Addresses: Department of Civil and Industrial Engineering, Pontificia Universidad Javeriana, Cali 76001000, Valle del Cauca, Colombia ' Department of Accounting and Finance, Universidad del Valle, Cali 76001000, Valle del Cauca, Colombia ' School of Industrial Engineering, Universidad Pedagógica y Tecnológica de Colombia – UPTC, Avenida Central del Norte 39-115, 150003, Tunja, Boyacá, Colombia

Abstract: This paper considers the variability of specific parameters in the aggregate production plan (APP) problem for machine-dependent production systems. The core issue emerges when assessing the APP's configuration by considering such decisions as the staff size, overtime and subcontracting, and inventory accumulation while reducing the overall production costs. We developed a deterministic mathematical model (MILAPP) and a stochastic mathematical model (SMILAPP) with the minimisation cost as the objective function. The stochastic model's decisions are performed in one stage, considering a penalised objective function for unsatisfied and surplus demand due to demand variation. The stochastic model's solution strategy is referred to as the sample average approximation (SAA). The effectiveness of the proposed approach is tested in the case of a Colombian multinational corporation. The results show that the proposed approach, which considers the predicted contribution of products and the uncertainty of many parameters, is a strong reference for decision support of APP problems.

Keywords: aggregate production planning; APP; production systems; variability of parameters; sample average approximation; SAA; stochastic linear programming.

DOI: 10.1504/IJLSM.2024.139960

International Journal of Logistics Systems and Management, 2024 Vol.48 No.2, pp.195 - 224

Received: 08 Sep 2021
Accepted: 23 Nov 2021
Published online: 15 Jul 2024 *

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