Árbók VFÍ/TFÍ - 01.01.1997, Blaðsíða 243

Hagnýt notkun gagnvirkni 241
In [4] it is pointed out how important it is to calculate the net profit contribution coeffici-
ents c(j) correctly. The standard definition of unit contribution is unit sales price minus all
variable unit costs, including in particular labor and raw materials, resulting in contribution
to cover fixed costs and profit. However, one should be careful not to subtract sunk cost but
only cost that will be affected by the decision making for which the calculation of contribu-
tion was intended.
As we have observed in the fish processing industry, il is a common error to subtract labor
and raw material costs as these are usually considered variable costs. In our case however,
when planning production for say a day in fish processing, this is wrong as people will be
paid for the whole day regardless of the product mix decisions made, and the raw material is
already bought and the price paid is therefore sunk cost. So c(j) is mainly the sales price
($/unit) minus some small amount of variable cost like packing material and possibly an esti-
mated inventory cost depending on how long time we anticipate until the product will be sold
and paid for.
The LP model and its dual are:
Primal:
Manpower:
Raw material:
Dual:
Product no. j:
max z = S c(j) x(j)
I m(j) x(j) < M
S rO) x(j) < R
x > 0
min w = M yM + R yR
m(j) yM + r(j) Yr ^ c(í)
yM. yR ^ o
(maximizing total contribution)
(shadow price of M is yM $/hour)
(shadow price of R is yR $/kg)
Notice that because the primal has only two constraints the model will never propose more
than two products in the production plan. This is actually a fortunate property in our case as
many reasons outside the scope of our model suggest that few products should be in the
product mix at the same lime.
Lab RawMat 600 65 Table 1 0 Buy R 0 Overt 100 2500 0 Sell R 0 Sell W 35 200
1/0 Prod Yield kg/kg Prod. kg/h Price $/kg RM $/kg Labor $/kg Emb $/kg Contr $/kg $/hour $/Rkg
1 kl 41% 14,2 299 159 42 10,2 88 4246 123
1 k2 41% 15,0 294 159 40 8,1 87 4410 121
0 k3 41% 14,3 400 159 42 9,4 190 5720 164
1 k4 41% 18,7 255 159 32 5,3 59 4769 105
1 k5 41% 20,3 248 159 30 5,0 55 5034 102
1 k6 45% 28,4 227 144 21 7,9 54 6447 102
1 k7 43% 22,8 240 151 26 7,9 55 5472 103
1 k8 43% 21,2 236 151 28 8,5 48 5003 101
1 k9 41% 15,0 312 159 40 7,2 106 4680 128