Shifting equipment between operations. A coal mining corporation owns threelvaailrge. draglines, with each dragline currently operating at a different site but becoming avail-able in the near future. Draglines are huge shovels that remove coal and overburden from surface (open-pit) coal mines: the bucket of a dragline is lifted vertically and dragged horizontally by a complex pulley system, hence the name dragline. Draglines can be so large that their cabs may hold several personnel and come equipped with a shower.
Several people could easily stand erect in the bucket of a large dragline and not come close to filling it. The point is that shifting a dragline from one mining area to an-other is a very expensive, time-consuming operation. Each dragline may be different. having a different bucket capacity that results in a different rate of coal production and. hence, a different cost per ton of coal removed. The dragline capacity. as well as the thickness of the overburden and coal seam at a particular site, determine the daily cost. as well as the production rate at each mine, with the larger dragline providing a higher daily profit.
The coal company is opening three new mines next month. Each of the mines will require a dragline as the central piece of equipment. The current sites of operation will be phased out in favor of the new mines. topsoil will be replaced at the old sites. and the land will be revegetated.
We need to calculate the total profit of using a particular dragline at a specific site. To do this, we multiply the daily profit when the specific dragline that was at old site i is shifted from that site and used at new mining site j by the number of days to exhaust the coal seam at site j. This gives the total profit. p,,. of assigning the dragline from old mine i to new mine j. but this profit value does not include the significant cog of moving that dragline to site j. The costs of shifting the draglines. numbered 12.3 and indexed by i, between the old mining sites and the new mine sites. numbered 1.2.3. and indexed by j. arc denoted by cη.
Structure-that is. write without summation notation a model to determine which dragline will he shifted to which new mine site in order to achieve the maximum total profit.