Question

Refer to the MOLP example:

The following example illustrates the issues involved in an MOLP problem. Although this example involves only three objectives, the concepts and techniques presented apply to problems involving any number of objectives.

Lee Blackstone is the owner of the Blackstone Mining Company, which operates two different coal mines in Wythe and Giles counties in southwest Virginia. Due to increased commercial and residential development in the primary areas served by these mines, Lee is anticipating an increase in demand for coal in the coming year. Specifically, her projections indicate a 48-ton increase in the demand for high-grade coal, a 28-ton increase in the demand for medium-grade coal, and a 100-ton increase in the demand for low-grade coal. To handle this increase in demand, Lee must schedule extra shifts of workers at the mines. It costs $40,000 per month to run an extra shift of workers at the Wythe county mine and $32,000 per month at the Giles mine. Only one additional shift can be scheduled each month at each mine. The amount of coal that can be produced in a month's time at each mine by a shift of workers is summarized in the following table.

Type of Coal	Wythe Mine	Giles Mine
High grade	12 tons	4 tons
Medium grade	4 tons	4 tons
Low grade	10 tons	20 tons

Unfortunately, the methods used to extract coal from these mines produce toxic water that enters the local groundwater aquifers. At the Wythe mine, running an extra shift will generate approximately 800 gallons of toxic water per month, whereas the mine in Giles county will generate about 1,250 gallons of toxic water. Although these amounts are within EPA guidelines, Lee is concerned about the environment and doesn't want to create any more pollution than is absolutely necessary. Additionally, although the company follows all OSHA safety guidelines, company records indicate that approximately 0.20 life-threatening accidents occur per shift each month at the Wythe mine whereas 0.45 accidents occur per shift each month at the Giles mine. Lee knows that mining is a hazardous occupation, but she cares about the health and welfare of her workers and wants to keep the number of life-threatening accidents to a minimum.

a) What weights could be used to generate the solution at x1= 2.5, x2= 4.5 ?

b) What weights could be used to generate the solution at x1= 4.0, x2= 3.0 ?

c) What weights could be used to generate the solution at x1= 10.0, x2=0.0?

d) What weights could be used to generate solutions along the edge of the feasible region that runs from the point x1= 0, x2= 12.0 to the point x1=2.5, x2= 4.5?

Define decision variables

Answer 1