PAPUA NEW GUINEA MINING COMPANY

The Papua New Guinea Mining Company (PNGM Co.) mines gold, silver, and copper from four sites on the island of New Guinea. The mining activities takes place in the highlands, which provide no major sources of water. Water is an essential ingredient in the bacterial leaching, done at three sites at lower elevations. Currently only pilot operations are being conducted while the ore sites are surveyed, and final planning is done.

The overall scheme is to extract the ore and transport it to one of the leaching sites.

There, the metals will be separated from the nonmetallic compounds, using several strains of Thiobacillus. The concentrated metallic “soup” will then be transported to the port facility in Port Moresby, loaded onto tankers, and shipped to Australia to be refined and smelted.

Papua New Guinea is an extremely undeveloped place with few roads. Except for the port facility, the PNGM Co. sites are in remote jungle or mountain locations unconnected by roads or navigable waterways. Three major transportation projects are being considered. One is to construct a railway connecting the various sites. The railway may just connect the mines to the leaching sites, or it may also connect the latter to the port. If the shorter rail option is adopted, the enriched slurry will be routed to port through pipelines. A series of aqueducts must also be constructed to connect the leaching sites to water sources.

The final railroad bed and pipeline choices will be based on the distances separating the various sites. These are shown in Table 1, in which the distances (in kilometers) between neighboring sites are listed as candidate routes.

The water sources include two lakes – Lake Amau (LA) and Lake Karena (LK) – two rivers – the Mor (RM) and the Vanapa (RV) – and one well (W). The maximum possible flows (millions of cubic liters per hour) are shown in Table 2, along with the maximum required or available.

Chief engineer Roy Youngblatt has selected a special gondola car for hauling ore to the leaching sites. When empty, these cars can accommodate a large removable rubber bladder which will contain the metal-enriched liquid drawn from the leaching sites, so the same cars can be used to move the liquid to port. Rail cars with empty bladders can then be returned to the leaching sites, where the bladders are removed before the empty cars are returned to the mines.

In terms of number of filled gondola cars, the daily ore volume limitations listed in Table 3 apply to the shipments from the mines.

For most of the routes from mines to leaching sites, there is no lower bound on the number of gondola carloads. Generally, at most 40 carloads can be shipped. There are several exceptions. The maximum number of carloads is 30 over route A-D; 20 over route C-D, and 10 over route E -G. The minimum number of carloads is 20 each over routes A-G and C-G.

When each ore car is emptied at the leaching site, it is reconfigured as a gondola-bladder car. Thus, every car entering a leaching site full of ore leaves it loaded with a full bladder of metallic soup pumped from the holding ponds. The carload limitations listed in Table 4 apply to shipments from leaching sites to the port.

Questions

1. Each site will be connected to at least one other site by the railroad. The rail links will traverse some subset of the linkages in Table 1.

a. Determine the minimum track length and the corresponding routes and spurs that will be needed if the port and leaching sites are included.

b. Repeat part (a), leaving out the linkages to the port.

2. Determine the minimum pipeline length for connecting the port to the leaching sites, leaving out the linkages to mine sites A, C, and F. Prune any legs ending at a mine site. 

3. Find the aqueduct volumes that will maximize the flow from the water sources to the leaching sites.

4. Suppose that the metallic liquid pipelines are not built, and the leaching sites are connected to the port by rail. Due to land ownership disputes, the track routing found in Question 1(a) cannot be used. The six usable links are as follows:

A-D B-D C-D C-F D-E E-G G-H

It is possible to route shipments from one site to another, going through a third site without loading or unloading there.

a. Prepare a new railroad mileage table showing how far cars will have to travel between mines and leaching sites and between leaching sties and the port, allowing for all possibilities, no matter how unattractive.

b. In solving the shipment problem as a minimum-cost maximum-flow problem, can you meet all necessary constraints? Explain.

c. Sketch a network that portrays all arcs and nodes needed to solve the problem. Then indicate for each arc the lower bound and the upper bound. Assuming that each car-mile costs PNGM Co. $1, use the distances you found in part (a) to determine the unit cost for each arc.

5. Find the transportation schedule that minimizes daily shipping cost.

6. Consider the problem of getting gondola cars back to the mines and the bladders back to the leaching sites. Suggest how you would solve this problem.