Industrial Engineering Mathematics

Blank and Tarquin

Problems 8-13, 8-28, 9-6, 9-12, and 9-26

Trans-West Railway has budgeted $1.8 million to be invested in safety improvements. They are considering 13 different possible projects. The benefits have already been converted into dollar terms, and expressed in present value. The costs and benefits of each project are listed below, in order of decreasing benefit/cost ratio:

Project Cost Benefit Net Ben. Benefit/Cost Ratio

1 $96K $280K $184K 2.92

2 $31K $85K $54K 2.74

3 $100K $255K $155K 2.55

4 $212K $410K $198K 1.93

5 $282K $510K $228K 1.81

6 $373K $620K $247K 1.66

7 $262K $390K $128K 1.49

8 $464K $690K $226K 1.49

9 $423K $580K $157K 1.37

10 $549K $720K $171K 1.31

11 $615K $730K $115K 1.19

12 $705K $800K $95K 1.13

13 $876K $860K -$16K 0.98

1. Which safety improvement(s) should Trans-West invest in? (You can assume that it is acceptable to invest in multiple different projects, since none are mutually exclusive.) What will be the total cost of these improvements? What will be the total benefit? What is the overall benefit/cost ratio achieved by these expenditures?

2. Did you choose projects strictly in order of decreasing benefit/cost ratio? Why or why not? How much of the total budget of $1.8 million was left unspent by the set of projects you chose?

3. Do you know a general mathematical technique for solving problems of this type?

4. How much additional benefit could be achieved if the budget were increased by $20,000 (a little more than 1%)? How much would the total level of expenditure have to increase in order to achieve that benefit? What would be the incremental benefit/cost ratio achieved