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 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 modelling complications introduced by constraints on the joint process and by inventories.
Published October 1987 , 45 pages