CHAPTER 4 MANAGING STRATEGIC CAPACITY 1 Using Decision Trees to Evaluate Capacity Alternatives 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 packages 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. In solving decision tree problems, we work backward from the end of the tree 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 decision point, and the decision problem is thereby solved. We now demonstrate an application to capacity planning for Hackers Computer Store. EXAMPLE 4.4: DECISION TREES The owner of Hackers Computer Store is considering what to do with his business over the next five years. Sales growth over the past couple of years has been good, but sales could grow substantially if a major electronics firm is built in his area as proposed. Hackers owner sees three options. The first is to enlarge his current store, the second is to locate at a new site, and the third is simply to 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 making expansion no longer feasible. The assumptions and conditions are as follows: 1. as a result of the increased population of computer fanatics from the new electronics firm has a 55 percent probability. 2. with a new site would give annual returns of $195 000 per year. with a new site would mean annual returns of $115 000. 3. with an expansion would give annual returns of $190 000 per year. 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 $105 000 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. If 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. SOLUTION We construct a decision tree to advise Hackers owner on the best action. Exhibit 4.8 shows the decision tree for this problem. There are two decision points (square nodes) and three chance occurrences (round nodes).
2 Section 1 STRATEGY EXHIBIT 4.8 Decision Tree for Hackers Computer Store Problem Move 0.55 Revenue-Move_Cost 0.45 Revenue-Move_Cost Hackers Computer Store 0.55 0.45 Revenue-Expansion_Cost Revenue-Expansion_Cost Revenue-Expansion_Cost 0.55 Revenue 0.45 Revenue The values of each alternative outcome shown on the right of the diagram in Exhibit 4.9 are calculated as follows: ALTERNATIVE REVENUE COST VALUE Move to new location, strong growth $195 000 5 yrs $210 000 $765 000 Move to new location, weak growth $1 1 5 000 5 yrs $210 000 $365 000 store, strong growth $190 000 5 yrs $ 87 000 $863 000 store, weak growth $100 000 5 yrs $ 87 000 $413 000 now, strong growth, expand next year $170 000 1 yr $ 87 000 $843 000 $190 000 4 yrs now, strong growth, do not expand next year $170 000 5 yrs $0 $850 000 now, weak growth $105 000 5 yrs $0 $525 000 EXHIBIT 4.9 Decision Tree Analysis Hackers Computer Store Move $585 000 $660 500 ; $703 750 $703 750 Revenue-Move_Cost $765 000 Revenue-Move_Cost $365 000 Revenue-Expansion_Cost $863 000 Revenue-Expansion_Cost $413 000 Revenue-Expansion_Cost $843 000 ; $850 000 Revenue $850 000; P Revenue $525 000; P
CHAPTER 4 MANAGING STRATEGIC CAPACITY 3 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 simply 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)! Due to the five-year time horizon, it may be useful to consider the time value of the revenue and cost streams when solving this problem. If we assume a 16 percent interest rate, the first alternative outcome (move now, strong growth) has a discounted revenue valued at $428 487 (195 000 3.274293654) minus the $210 000 cost to move immediately. Exhibit 4.10 shows the analysis considering the discounted flows. Details of the calculations are given below. The present value table in Appendix C can be used to look up the discount factors. In order to make our calculations agree with those completed by Excel, we have used discount factors that are calculated to 10 digits of precision. The only calculation that is a little tricky is the one for revenue when we do nothing now and expand at the beginning of next year. In this case, we have a revenue stream of $170 000 the first year, followed by four years at $190 000. The first part of the calculation (170 000 0.862068966) discounts the first-year revenue to present. The next part (190 000 2.798180638) discounts the next four years to the start of year two. We then discount this four-year stream to present value. ALTERNATIVE REVENUE COST VALUE Move to new location, strong growth $195 000 3.274293654 $210 000 $428 487 Move to new location, weak growth $115 000 3.274293654 $21 0 000 $166 544 store, strong growth $190 000 3.274293654 $ 87 000 $535 1 1 6 store, weak growth $100 000 3.274203654 $ 87 000 $240 429 now, strong growth, $170 000 0.862068966 $ 87 000 $529 874 expand next year $190 000 2. 798180638 0.862068966 0.862068966 now, strong growth, $170 000 3.274293654 $0 $556 630 do not expand next year now, weak growth $105 000 3.274293654 $0 $343 801 Excel: Capacity Decision Tree Analysis Using Net Present Value Calculations EXHIBIT 4.10 Move $310 613 Revenue-Move_Cost $428 487 Revenue-Move_Cost $166 544 Hackers Computer Store $402 507 Revenue-Expansion_Cost $535 116 Revenue-Expansion_Cost $240 429 NPV Analysis Rate 16% $460 857 Revenue-Expansion_Cost $529 874 ; $556 630 Revenue $556 630; P Revenue $343 801; P
4 Section 1 STRATEGY Excel: Decision Trees Based on this analysis, it appears that the best capacity strategy for Hackers is neither to expand nor to move now. This is due to the fact there is a significant probability (0.45) that growth will be weak. This adversely affects the benefits if the company expands or moves. RELATED PROBLEMS SOLVED PROBLEM E-Education is a new start-up that develops and markets MBA courses offered over the Internet. The company is currently located in Edmonton and employs 150 people. Due to strong growth, the company needs additional office space. The company has the option of leasing additional space at its current location in Edmonton for the next two years, but after that will need to move to a new building. Another option the company is considering is moving the entire operation to the nearby small town of Wetaskiwin immediately. A third option is for the company to immediately lease a new building in Edmonton. If the company chooses the first option and leases new space at its current location, it can, at the end of two years, either lease a new building in Edmonton or move to Wetaskiwin The following are some additional facts about the alternatives and current situation: 1. The company has a 75 percent chance of surviving the next two years. 2. Leasing the new space for two years at the current location in Edmonton would cost $750 000 per year. 3. Moving the entire operation to Wetaskiwin would cost $1 million. Leasing space would run only $500 000 per year. 4. Moving to a new building in Edmonton would cost $200 000, and leasing the new building s space would cost $650 000 per year. 5. The company can cancel the lease at any time. 6. The company will build its own building in five years, if it survives. 7. Assume all other costs and revenues are the same no matter where the company is located. What should E-Education do? SOLUTION S tep 1: Construct a decision tree that considers all of E-Education s alternatives. The following shows the tree that has decision points (with the square nodes) followed by chance occurrences (round nodes). In the case of the first decision point, if the company survives, two additional decision points need consideration. E-Education Stay in Edmonton Lease space for two years Stay in Edmonton Lease new space Move to Wetaskiwin Survive (0.75) $3 112 500 Fail (0.25) Survive (0.75) $2 962 500 Fail (0.25) Survive (0.75) $3 125 000 Fail (0.25) Lease new space in Edmonton $3 650 000 Move to Wetaskiwin $4 000 000 $1 500 000 $3 450 000 $1 500 000 $3 500 000 $2 000 000
CHAPTER 4 MANAGING STRATEGIC CAPACITY 5 Step 2: Calculate the values of each alternative as follows: ALTERNATIVE CALCULATION VALUE Stay in Edmonton, lease space for two years, survive, (750 000) 2 200 000 $3 650 000 lease new building in Edmonton (650 000) 3 Stay in Edmonton, lease space for two years, survive, (750 000) 2 1 000 000 $4 000 000 move to Wetaskiwin (500 000) 3 Stay in Edmonton, lease space for two years, fail (750 000) 2 $1 500 000 Stay in Edmonton, lease new building in Edmonton, survive 200 000 (650 000) 5 $3 450 000 Stay in Edmonton, lease new building in Edmonton, fail 200 000 (650 000) 2 $1 500 000 Move to Wetaskiwin, survive 1 000 000 (500 000) 5 $3 500 000 Move to Wetaskiwin, fail 1 000 000 (500 000) 2 $2 000 000 Working from our rightmost alternatives, the first two alternatives end in decision nodes. Because the first option, staying in Edmonton and leasing space for two years, is the lowest cost, this is what we would do if we decide to stay in Edmonton for the first two years. If we fail after the first two years, represented by the third alternative, the cost is only $1 500 000. The expected value of the first option of staying in Edmonton and leasing space for the first two years is 0.75 3 650 000 0.25 1 500 000 $3 112 500. The second option, staying in Edmonton and leasing a new building now, has an expected value of 0.75 3 450 000 0.25 1 500 000 $2 962 500. Finally, the third option of moving to Wetaskiwin immediately has an expected value of 0.75 3 500 000 0.25 2 000 000 $3 125 000. From this, it looks like the best alternative is to stay in Edmonton and lease a new building immediately. PROBLEMS 14. o, Inc., is considering the possibility of building an additional factory that would produce a new addition to its product line. The company is currently considering two options. The first is a small facility that it could build at a cost of $6 million. If demand for new products is low, the company expects to receive $10 million in discounted revenues (present value of future revenues) with the small facility. On the other hand, if demand is high, it expects $12 million in discounted revenues using the small facility. The second option is to build a large factory at a cost of $9 million. Were demand to be low, the company would expect $10 million in discounted revenues with the large plant. If demand is high, the company estimates that the discounted revenues would be $14 million. In either case, the probability of demand being high is 0.40, and the probability of it being low is 0.60. Not constructing a new factory would result in no additional revenue being generated because the current factories cannot produce these new products. Construct a decision tree to help o make the best decision. 15. A builder has located a piece of property that she would like to buy and eventually build on. The land is currently zoned for four homes per acre, but she is planning to request new zoning. What she builds depends on approval of zoning requests and your analysis of this problem to advise her. With her input and your help, the decision process has been reduced to the following costs, alternatives, and probabilities: Cost of land: $2 million. Probability of rezoning: 0.60. If the land is rezoned, there will be additional costs for new roads, lighting, and so on, of $1 million. If the land is rezoned, the contractor must decide whether to build a shopping centre or 1500 apartments that the tentative plan shows would be possible. If she builds a shopping centre, there
6 Section 1 STRATEGY is a 70 percent chance that she can sell the shopping centre to a large department chain for $4 million over her construction cost, which excludes the land; and there is a 30 percent chance that she can sell it to an insurance company for $5 million over her construction cost (also excluding the land). If, instead of the shopping centre, she decides to build the 1500 apartments, she places probabilities on the profits as follows: There is a 60 percent chance that she can sell the apartments to a real estate investment corporation for $3000 each over her construction cost; there is a 40 percent chance that she can get only $2000 each over her construction cost. (Both exclude the land cost.) If the land is not rezoned, she will comply with the existing zoning restrictions and simply build 600 homes, on which she expects to make $4000 over the construction cost on each one (excluding the cost of land). Draw a decision tree of the problem and determine the best solution and the expected net profit.