Operation Research

Questions & Answers


4: Suppose that you have been put in charge of managing the clothing supply for a small, newly established space colony. The colony has n colonists each of whom needs at least two pairs of shoes, three jumpsuits, and a hat. You can make each of these products from some combination of cotton, thread, and glue, all of which you need to import. You can also import already made clothing for a fixed cost. For each item that you produce in the factory, you also incur a cost of d per item (a pair of shoes, jumpsuit, and hat each count as an 'item') for the use of electricity in your factory. Write down (but do not solve) a linear program to minimize the cost of acquiring all of the clothing which your colony requires. You may assume that you are allowed to make and import fractional quantities of each of these goods. (20 pts)


1. New estimates made by MAC indicate that the loss rate of air transporters will be much lower than was previously estimated, only 1% rather than the previously estimated 10%. Discuss how the revised estimate changes the strategic mobility deployment plan.

Exercises Ex 1: Find a maximum flow from node s to node t. The number associated with each arc indicates the capacity of the arc. Formulate this maximal flow problem as a linear programming problem and use solver to find the optimal solution.

6-9. In intermodal transportation, loaded truck trailers are shipped between railroad terminals on special flatbed carts. Figure 6.38 shows the location of the main railroad terminals in the United States and the existing railroad tracks. The objective is to decide which tracks should be "revitalized" to handle the intermodal traffic. In particular, the Los Angeles (LA) terminal must be linked directly to Chicago (CH) to accommodate expected heavy traffic. Other than that, all the remaining terminals can be linked, directly or indirectly, such that the total length (in miles) of the selected tracks is minimized. Determine the segments of the railroad tracks that must be included in the revitalization program.

Questions: a) Based on your solution, what was the average travel time (in days) for the 100 containers? b) Based on your solution, what was the average percent damage for the 100 containers? c) Which countries did not ship out all their available containers? Why did these countries, as opposed to those who shipped out all their containers, not ship out more containers? Explain.

6-19. Use Dijkstra's algorithm to find the shortest route between node 1 and every other node in the network of Figure 6.42.

Questions: d) How many total hours of travel time is required to transport all the students to their assigned academy? What is the average travel time per student (in minutes)? e) were all academy's filled to their maximum capacity of 400 students? If not, which academies still have room for additional student? How many more students can these academies accommodate? f) Which district is sending students to more than one academy? Explain.

Questions: a) Which facilities should be constructed? Explain. b) Did the county use their complete budget? Explain. c) There has been a large resurgence in horseback riding and the new estimate for usage is 150 people per day. Would this change your recommendation of facilities to be constructed? How does this impact your budget? Explain.

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