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Theory of constraints and the combinatorial complexity of the product-mix decision

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  • Linhares, Alexandre

Abstract

The theory of constraints (TOC) proposes that, when production is bounded by a single bottleneck, the best product mix heuristic is to select products based on their ratio of throughput per constraint use. This, however, is not true for cases when production is limited to integer quantities of final products. Four facts that go against current thought in the TOC literature are demonstrated in this paper. For example, there are cases in which the optimum product mix includes products with the lowest product margin and the lowest ratio of throughput per constraint time, simultaneously violating the margin heuristic and the TOC-derived heuristic. Such failures are due to the non-polynomial completeness (NP-completeness) of the product-mix decision problem, also demonstrated here.

Suggested Citation

  • Linhares, Alexandre, 2009. "Theory of constraints and the combinatorial complexity of the product-mix decision," International Journal of Production Economics, Elsevier, vol. 121(1), pages 121-129, September.
    • Handle: RePEc:eee:proeco:v:121:y:2009:i:1:p:121-129
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    References listed on IDEAS

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    1. Lea, Bih-Ru & Fredendall, Lawrence D., 2002. "The impact of management accounting, product structure, product mix algorithm, and planning horizon on manufacturing performance," International Journal of Production Economics, Elsevier, vol. 79(3), pages 279-299, October.
    2. Plenert, Gerhard, 1993. "Optimizing theory of constraints when multiple constrained resources exist," European Journal of Operational Research, Elsevier, vol. 70(1), pages 126-133, October.
    3. Kee, Robert & Schmidt, Charles, 2000. "A comparative analysis of utilizing activity-based costing and the theory of constraints for making product-mix decisions," International Journal of Production Economics, Elsevier, vol. 63(1), pages 1-17, January.
    4. Wahlers, James L. & Cox, James III, 1994. "Competitive factors and performance measurement: Applying the theory of constraints to meet customer needs," International Journal of Production Economics, Elsevier, vol. 37(2-3), pages 229-240, December.
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    Cited by:

    1. Mansouri, S. Afshin & Golmohammadi, Davood & Miller, Jason, 2019. "The moderating role of master production scheduling method on throughput in job shop systems," International Journal of Production Economics, Elsevier, vol. 216(C), pages 67-80.
    2. Davood Golmohammadi & S. Afshin Mansouri, 2015. "Complexity and workload considerations in product mix decisions under the theory of constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(5), pages 357-369, August.
    3. Golmohammadi, Davood, 2015. "A study of scheduling under the theory of constraints," International Journal of Production Economics, Elsevier, vol. 165(C), pages 38-50.
    4. Pacheco, Diego Augusto de Jesus & Antunes Junior, José Antonio Valle & de Matos, Celso Augusto, 2021. "The constraints of theory: What is the impact of the Theory of Constraints on Operations Strategy?," International Journal of Production Economics, Elsevier, vol. 235(C).
    5. Machado, Mariana Paim & Abreu, Jaqueline Lilge & Morandi, Maria Isabel Motta & Piran, Fabio Sartori & Lacerda, Daniel Pacheco, 2023. "Exploratory decision robustness analysis of the theory of constraints focusing process using system dynamics modeling," International Journal of Production Economics, Elsevier, vol. 260(C).

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