order to create the model for this situation, I first need to identify the
goal, decision variables, and production restraints. The goal is to
identify the optimal capacity utilization for the various product groups, in
order to maximize our profit. Our decision variables, which we
adjust in order to achieve our goal, are the number of each product that we
produce. As for restraints, we have 2 categories, Capacity restraints &
Our capacity Restraints relate to our ability to perform a maximum
number of repetitions of the various steps in the process. In this example,
there are 4 steps, and we are able to perform each step a maximum number of
time in any month, as follows:
A maximum of 1,600 hours of printing is possible each month.
A maximum of 2,600 hours of mounting is possible each month.
A maximum of 1,700 hours of assembly is possible each month.
A maximum of 1,500 hours of inspection is possible each month.
Our demand restraints relate to customer demand for the products. If we
are producing more products than there is demand for, we will be losing money
on each product we make beyond demand. Thus we want to restrict our production
numbers to below the following demand restraints provided.
A maximum of 210 each month.
A maximum of 370 each month.
A maximum of 450 each month.
A maximum of 180 each month.
approach is not very effective without further analysis, because it does not
take into account the resources required to produce these high margin products.
Though it is true that our margins are higher per product on FL & HL, if we
are only able to produce a small number of these products due to heavy production
requirements, our overall profit may be smaller than if we produce a very large
number of products that have a smaller profit margin.
algebraic model formulation is as follows:
Printing Capacity: 1ML + 1.5SL + 1.5FL + 0.5HL =