Kirsten Worrall
Department of Industrial and Systems Engineering, University of Pretoria, Hatfield, Lynwood Road, 0001, South Africa.

Kapya Tshinangi
Department of Industrial and Systems Engineering, University of Pretoria, Hatfield, Lynwood Road, 0001, South Africa.

Olufemi Adetunji
Department of Industrial and Systems Engineering, University of Pretoria, Hatfield, Lynwood Road, 0001, South Africa.

V. S. S. Yadavalli
Department of Industrial and Systems Engineering, University of Pretoria, Hatfield, Lynwood Road, 0001, South Africa.

DOI https://doi.org/10.33889/IJMEMS.2026.11.5.077

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Abstract

In production industries such as stainless steel manufacturing, a shared resource (also referred to as a constrained resource) can produce multiple complementary products that are consumed together. The production process yields defective outputs that can be recovered through reannealing and cutting coils into sheets on the constrained resource, while the customers’ demand for each product is impacted by the price of the complementary product. This study develops an Economic Production Quantity (EPQ) model for two mutually complementary products manufactured on a shared resource with imperfect production. Product Type A’s demand can only be satisfied through production from new feedstock, while Product Type B’s demand can be satisfied through remanufacturing of non-conforming products and production from new feedstock. The model incorporates complementary price-dependent demands and remanufacturing to optimise lot sizes by minimising total cost. The total cost function is fundamentally driven by baseline elements (setup and holding costs) along with recovery operational metrics (remanufacturing and disposal costs). The objectives are to formulate a joint lot-sizing problem and provide insight for cost efficiency and sustainability. To achieve this, the study analyses two distinct operational scenarios based on remanufacturing capacity requirement: firstly, where remanufacturing rate exceeds demand rate, and secondly, where demand rate exceeds remanufacturing rate. Optimality condition was proven, and sensitivity analysis was done to identify which parameters have the greatest impacts on system performance. The model uniquely integrates in a single model: (i) complementary cross-price effect, (ii) imperfect production with remanufacturing on a shared resource, and (iii) joint lot-sizing of initial and remanufactured products. The model performance was compared to two other base models, and the possible extent of recoverable cost of imperfect quality was shown. Guidance for managerial decision was provided from the model’s insights.

Keywords- Economic production quantity, Remanufacturing, Shared resource, Complementary demand.

Citation

Worrall, K., Tshinangi, K., Adetunji, O., & Yadavalli, V. S. S. (2026). An Economic Production Quantity (EPQ) Model for Multi-Product Manufacturing with Consideration Towards Complementary Price-Dependent Demand and the Possibility of Product Recovery. International Journal of Mathematical, Engineering and Management Sciences, 11(5), 1929-1954. https://doi.org/10.33889/IJMEMS.2026.11.5.077.