Production time in min Part Lathe Drill press 3 1 2 3 234 4695 7 3264
A manufacturing company based in Potchefstroom produces four parts that require the use of a lathe and a drill press.
The two machines are allowed to operate a maximum of 10 hours a day to prevent mechanical failure. The following
table provides the time in minutes required by each part:
It is desired to balance the two machines by limiting the difference between their total operation times to at most 30
minutes. The market demand for each part is at least 10 units. Additionally, the number of units of Part 1 may not
exceed that of Part 2.
(a) Formulate the problem as a goal programming (GP) model
(b) General goal programming can be represented as preemptive and non-preemptive expressions. Considering
these expressions, answer the following questions:
i Suppose that the market demand for each product is of a higher priority than balancing the two
machines, with no overtime allowed. Further, suppose that the manufacturing company specifies
that the number of units produced for Part 1 in excess of Part 2 contains the lowest priority among
all goals. Using preemptive priority factors, formulate the preemptive goal programming model.
ii Suppose that the market demand for each product has a weight of 2 and that the number of units
produced for Part 1 in excess of Part 2 contains a weight of 7. Likewise, suppose that balancing the
two machines comprises a weight of 3, with overtime once again not allowed. Formulate and solve
the non-preemptive goal programming model. Determine if all the goals are satisfied and motivate
your answer.
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