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bottlenecks. However, the calculation of net profit contribution per unit of a bottleneck re-
source and using this to aid in product mix decision situations is not found in common text-
books on business administration.
Fig. 2 Use ofNet Profit Contribution for Product Mix Decisions
It is noteworthy that for a period of more than 20 years, similar principles as discussed
above have been in use in the fishing industry in Iceland. Even in the very small companies,
computers have been used to calculate and print out for the production managers, for every
single product:
cR(j) = c(j)/r(j), net profit contribution per kg raw material ($/kg)
cM(j) = c(j)/m(j), net profit contribution per hour manpower ($/hour)
These numbers can be seen on Fig. 1, where the dual constraints meet the axes. To take
an example of their use, the production manager might select a product with low m(j), a “fast”
product, giving the highest cM(j), on days when manpower is a bottleneck. Vice versa, on
days when there is little raw material available, he would choose the product with highest
cR(j).
The problem is what to do when it is not clear what is the bottleneck. Here we propose
that Fig. 1, the dual model graph, could be used as a decision aid for the production managers.
Graphical Decision Support for Product Mix
By using Fig. 1, the production manager is able to see graphically on the axes the coefficients
cR(j) and cM(j) for the various products, which he is used to read from the computer
printouts. The slope of the objective function for the dual model is determined by the ratio
R/M. He can see which two products are the candidates for the optimal product mix, like