The basic problem in the process of verification the production capacity level, in
the described example, is an appropriate ascribing of manufactured series of halffinished
products and finished products to machines in the whole planning procedure.
The number of products and the variety of technological routs are the reason
for the fact that people who planned the process needed even 2 weeks to carry it
out. That’s why in the first stage of the work a operational research model has been
suggested. This model allows to ascribe the production series to the machines in a
way that the production capacity is only slightly exceeded. The model, presented in
the next part of this study, is used to analyze one planning period. Its application to
the whole planning horizon is possible, but the model should be used separately for
every planning period. This form of model is not a classical formulation which enhance
planning. In models like this, the planning process is carried out for the whole
planning horizon, and one of the basic variables included in the model are stocks
on hand in the warehouse. Evaluating the production capacity was the main goal of
putting into operation the model in the analyzed example. The size of production
72 P. Hanczar, M. Jakubiak
and appropriate levels of stock on hand are chosen by employees of the company.
In the model written by the formulas (1) to (5) two groups of decision-making variables
xijk and zmax were used. The first group are binary variables which task is to
ascribe operation j manufacturing a series of half-finished and finished products i
on the machine k. The variable has the value 1 if an according operation is carried
out on the machine, or 0 otherwise. The list of series i is generated, on the basis of
production plans and the size of series of given half-finished products, before the
operational research process starts. Another group is a variable zmax which can have
any real values. For the positive values it is interpreted as the highest exceeding of
machine’s capacity, whereas negative values correspond to the lowest reserve of the
machine’s capacity.