Árbók VFÍ/TFÍ - 01.01.1997, Blaðsíða 242

240 Árbók VFÍ/TFÍ 1995/96
model, like [1] page 204 or [2] page 275. It is the experience, however, that this interpretation
is not widely understood or used in industry, at least not in small firms.
Duality is, however, not at all useless in real life. In this paper a graphical decision aid
based on the dual model of Linear Programming, for use in product mix problems, will be
proposed. The objective is that the decision aid is applicable in small companies even though
there is no knowledge of the theory of Linear Programming in the company. As an example
of fields of application the biggest industry of Iceland, fish processing, is chosen. This
industry is characterized by a great number of small firms with practically no knowledge of
optimization models, having to deal with product mix decisions almost daily.
Product mix decisions in fish processing
As other kind of food production, fish processing has to solve the problems connected with
the fact that either the raw materials or the finished products, or in some cases even both, are
perishable and difficult to store because of limited shelf life. Also, the quantity and quality of
raw materials are subject to frequent and often great fluctuations and therefore offer new
problem situations to the production managers, even every day.
In [3] an LP model of daily production planning in fish processing plants was proposed.
The model covers many aspects of day to day decision making. The LP model discussed in
this paper is a special case of the model in [3]. Here, the product mix aspect will be studied
for one fish species and under the following assumptions:
1. The product mix is to be decided for one planning period, say a day or a week, without
any inventory considerations or other coupling between periods.
2. The limiting resources, i.e. potenlial bottlenecks are only two, in our case raw material
and manpower.
These assumptions might seem rather restricting, in particular the latter. However, let us
keep in mind that one is dealing with small firms where it is very likely that the production
bottlenecks that really matter are few. In fish processing the quantity of raw material varies a
lot from day to day so typically the bottleneck is the raw material one day but the manpower
the next day.
The decision variables in our model are x, the quantity to be produced in the planning
period, x(j) for product no. j. Contrary to other manufacturing industries where raw material
is bought as needed, many fish processing plants in Iceland cannot control the supply of fish.
One must process whatever the fishing fleet brings to land. Therefore, raw material quantity
is a constraint rather than a decision variable.
The data for the model is as follows:
c is the net profit contribution of the products, c(j) for product no. j ($/unit)
m is manpower requirements, m(j) for product no. j (hours/unit)
r is raw material requirements, r(j) for product no. j (kg/unit)
M is available manpower (hours)
R is available raw material (kg)