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Capacity Planning

# Capacity Planning - Program DATA TreeAge Software Service l...

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Unformatted text preview: Program DATA TreeAge Software Service l A convenient way to lay out the steps of a capacity problem is through the use of decision trees. The tree format helps not only in understanding the problem but also in ﬁnding a solution. A decision tree is a schematic model of the sequence of steps in a problem and the conditions and consequences of each step. In recent years, a few commercial software pack- ages have been developed to assist in the construction and analysis of decision trees. These packages make the process quick and easy. Decision trees are composed of decision nodes with branches to and from them. Usually squares represent decision points and circles represent chance events. Branches from decision points show the choices available to the decision maker; branches'from chance events show the probabilities for their occurrence. ’ ‘ I In solving decision tree problems, we work from the end of the tree backward to the start of the tree. As we work back, we calculate the expected values at each step. In calculating the expected value, the time value of money is important if the planning horizon is long. Once the calculations are made, we prune the tree by eliminating from each decision point all branches except the one with the highest payoff. This process continues to the ﬁrst deci- sion point, and the decision problem is thereby solved. We now demonstrate an application to capacity planning for Hackers Computer Store. The exhibits used to solve this problem were generated using a program called DATA by TreeAge Software. (A demonstration version of the software, capable of solving the problems given in this chapter, is included on the book DVD.) ‘ EXAMPLE 11.2: Decision Trees The owner ot'Hackers Computer Store is considering what to do with his business over the next ﬁve years. Sales growth overthe past couple of years has been good, but sales could grow substantially if a major elec- tronics firm is built in his area as proposed. Hackers‘ owner sees three options. The first is to enlarge his cur— rent store. the second is to locate at a new site, and the third is to simply wait and do nothing. The decision to expand or move would take little time, and, therefore, the store would not lose revenue. If nothing were done the ﬁrst year and strong growth occurred, then the decision to expand would be reconsidered. Waiting longer than one year would allow competition to move in and wouldmake expansion no longer feasible. The assumptions and conditions are as follows: ' 1. Strong growth as a result of the increased population of computer fanatics from the new elec— tronics ﬁrm has a 55 percent probability. , Strong growth with a new site would give annual returns of\$ 195,000 per year. Weak growth with a new site would mean annual returns of\$1 15,000. Strong growth with an expansion would give annual returns of \$190,000 per year. Weak growth go DJ with an expansion would mean annual returns of \$100,000. 4. At the existing store with no changes, there would be returns of \$170,000 per year if there is strong growth and \$105000 per year if growth is weak. 5. Expansion at the current site would cost \$87,000. 6. The move to‘the new site would cost \$210,000. 7. 1f growth is strong and the existing site is enlarged during the second year, the cost would still be \$87,000. _ 8. Operating costs for all options are equal. We construct a decision tree to advise Hackers' owner on the best action. Exhibit 11.3 shows the decision tree for this problem. There are two decision points (shown with the square nodes) and three chance occurrences (round nodes). Decision Tree for Hackers Computer Store Problem ‘ t ‘I th ,. \$ Tong grow Revenue~Move_Cost I Move .55 . Weak growth .45 Strong growth Revenue-Move_Cost Revenue-Expansion,Cost Hackers Computer Store Revenue-Expansion__Cost Expand Revenue-Expansi0n_Cost Do nothing Revenue #0552527 11%} #3359 0:3,: Analysis Using DATA (TreeAge Soft I ecision Tree Hackers Computer Store Do nothing 0.450 The values of each alternative outcome shown on the right of the diagram in Exhibit 11.4 are calcu— lated as follows: i ALTERNATIVE REVENUE Cosr VALUE Move to new location, strong growth \$195,000 x 5 yrs \$210,000 \$765,000 Move to new location, weak growth \$115,000 x 5 yrs \$210,000 \$365,000 Expand store, strong growth \$190,000 x 5 yrs \$87,000 \$863,000 Expand store, weak growth \$100,000 x 5 yrs \$87,000 \$413,000 Do-nothing now, strong growth, expand next year \$170,000 x 1 yr + \$87,000 \$843,000 \$190,000 x 4 yrs Do nothing now, strong growth, do not expand next year \$170,000 x 5 yrs \$0 Do nothing now, weak growth \$105,000 x 5 yrs \$0 Working from the rightmost alternatives, which are associated with the decision of whether to expand, we see that the alternative of doing nothing has a higher value than the expansion alternative. We therefore eliminate the expansion in the second year alternatives. What this means is that if we do nothing in the ﬁrst year and we experience strong growth, then in the second year it makes no sense to expand. Now we can calculate the expected values associated with our current decision alternatives. We sim- ply multiply the value of the alternative by its probability and sum the values. The expected value for the alternative of moving now is \$585,000. The expansion alternative has an expected value of \$660,500. and doing nothing now has an expected value of \$703,750. Our analysis indicates that our best decision is to do nothing (both now and next year)! ...
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