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Joint product decisions: The variable proportions case

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  • LLOYD R. AMEY
  • JEAN†LOUIS GOFFIN

Abstract

. This paper is concerned with the decisions (output decisions and associated sell†or†process†further decisions) that arise with joint products when the technology allows some variability in the product proportions. Previous discussions in the literature have failed to convey the full complexity of this variable proportions case. The deficiency is made good by offering a more detailed general formulation of the problem and by analyzing the properties of the solution, including the implicit joint cost assignments. The formulation includes three joint products, each with an associated intermediate product, three ranges of variability in the product proportions, and demand functions for the final products. An activity model is the main vehicle for the analysis; an alternative model specified in terms of deviational variables is also presented. This is followed by five numerical examples covering boundary and extreme point solutions. The paper ends with a consideration of the modeling complications introduced by constraints on the joint process and by inventories. Résumé. Les auteurs s'intéressent aux décisions (les décisions relatives à la production et les décisions connexes relatives au choix de vendre ou de poursuivre le traitement) que suppose la fabrication de produits liés lorsque la technologie permet une certaine variabilité des proportions de produits. L'on constate à la lecture des publications sur le sujet que l'on n'est pas parvenu à cerner dans toute sa complexité la question des proportions variables. Cette lacune est comblée par la formulation générale plus détaillée du problème et par l'analyse des propriétés de la solution, y compris la répartition des coûts communs implicites. La formulation comporte trois produits liés, chacun ayant un produit intermédiaire connexe, trois intervalles de variabilité dans les proportions de produits, et des fonctions de demande relatives aux produits finis. Un modèle d'activité est le véhicule principal de l'analyse; un modèle de rechange exprimé en termes de variables déviationnelles est également présenté. Suivent cinq exemples numériques couvrant les solutions frontières et les points extrêmes. Les auteurs abordent pour terminer les complications relatives à la modélisation amenées par les contraintes relatives au processus commun et par les stocks.

Suggested Citation

  • Lloyd R. Amey & Jean†Louis Goffin, 1988. "Joint product decisions: The variable proportions case," Contemporary Accounting Research, John Wiley & Sons, vol. 5(1), pages 174-198, September.
    • Handle: RePEc:wly:coacre:v:5:y:1988:i:1:p:174-198
    DOI: 10.1111/j.1911-3846.1988.tb00701.x
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